, A M E R I C A N N A T I O N A L S T A N D A R D Symbols for Mechanical and Acoustical Elements as Used 0 In Schematic Diagrams ANSI Y32 18 1972 FOR CURRENT COMMITTEE PERSONNEL PLEASE SEE ASME MANUAL[.]
, A M E R I C ANNA T I O N ASLT A N D A R D Symbols for Mechanical and Acoustical Elements as Used In Schematic Diagrams ANSI Y32.18 - 1972 REAFFIRMED 2013 FOR CURRENT COMMITTEE PERSONNEL PLEASE E-MAIL CS@asme.org FOR CURRENT COMMITTEE PERSONNEL PLEASE SEE ASME MANUAL AS-I SECRETARIAT INSTITUTE OF ELECTRICAL AND ELECTRONICS ENGINEERS THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS PUBLISHED BY T H EA M E R I C A NS O C I E T Y United Engineering Center OF M E C H A N I C A LE N G I N E E R S East 47th Street N e w York, N Y 10017 No part of this document may be reproduced in any form, in an electronic retrieval system or otherwise, without the prior written permission of the publisher Copyright 8, 1972, by THE AMERICAN SOCIETY OF MECHANICAL ENGINEERS Printod in U.S.A FOREWORD Ever increasing use has been made during recent decades of schematic diagrams in representing mechani- cal and acoustical systems This development is a natural outgrowth of the same technique as was developed earlier for electric networks Such diagrams are important because of their usefulness in two connections First, a mechanical or an acoustical system can be analyzed much more rapidly with a schematic diagram than without Indeed, systematic methods have been developed in recent years which can generate correct descriptive equations for the system given i t s schematic diagram and specifications of the properties of each element in the system Furthermore, the use of such methods tends to minimize blunders in analyses, such as wrong signs for terms, which even the mostexperiencedanalyst is apt to make from time to time Second, as an analyst gains experience with schematic diagrams he develops an insight into the characteristic performance of collections of interconnected elements Thus he develops an ability to anticipate the performance of a system, a t least in a qualitative way, based solely on a study of i t s schematic diagram This is an attribute of schematic diagrams that is most useful, as was discovered earlier by electrical and electrical and electronics engineers It is to be noted that each of the foregoing points concerns a determination of the performance of a system; i.e., an analysis of the system It is not surprising, therefore, that schematic symbolsare constructed primarily to make analyses easier and more straightforward In recent years, however, there has developed a considerable interest in schematic diagrams in connection with the synthesis problem From this point of view one starts with a specification of the overall performance desiredin a system If some specifications are then assigned to theschematicdiagram,such as thenumber of juri-ctions andbranches in the diagram, i t is conceivable that the constitutive equations for the elements can be determined Although techniques of this sort have not been worked out in detail as yet, they are receiving a lot of attention a t the time of this writing and hold great promises for the future Because this standard concerns a relatively new field, the Writing Group was forced to make some decisions The most important one concerned the question whetherit is desirable to try toevolve some standard symbols now rather than to wait a number of yearsin the hope that some fairly uniform practices m.?y evolve It is recognized that standardsare much easier to establish i f a unanimity of opinion exists l e Writing Group believed, however, that a significant contribution could be made t o an evolving practice i f some sort of a standard practice could be adopted now No doubt, any user of this standard will find some things that he likes andsome that he would like to see changed.Suggestions for improvement based on experience gained in the use of this standard will always be welcome and should be mailed to the Secretary, American National Standards Committee Y32, in care of the ASME This standard was prepared by a committee working under the auspices of the American National Standards Committee on Acoustics, S1, and the American National Standards Committee onMechanicalShock and Vibration, S2 It was approved by the above American National Standards Committees and by American National Standards Committee Y32 on Graphic Symbols and Designations on November 23, 1971 when it wassent to AmericanNationalStandard Institute for approval as an American National Standard.The A N S I approval was received on April 20, 1972 and it was designated ANSI Y32.18-1972 Ill AMERICAN NATIONAL STANDARDS COMMITTEE Y32 GRAPHIC SYMBOLS AND DESIGNATIONS OFFICERS C A Fricke,Choirman J L Fisher,ViceChoirmon W L Hewetson, Vice Choirman L A Meadows, Vice Choirman C - Mechanical - Chemical and Process - Government - Electricol R Muller, Vice Choirman Lioison I Sherr,Secretory COMMITTEE MEMBERS ACOUSTI CAL SOCI ETY OF AMERICA L a u r e n c e B a t c h e l d e r , 983 M e m o r i a l D r i v e, C am b r i d g e, Massach u set t s H F Olson, R.C.A L a b o r a t o r i e s , P r i n c e t o n , N e w J e r s e y AMERICAN CHEMICAL SOCIETY R F Sc h u e r e r , Li n d e n , Ne w J e r s e y AMERICAN GEAR MANUFACTURERS ASSOCIATION G e n e L Sc o t t , Am e r i c a n Ge a r M a n u f act u r er s A sso ci at i o n , Wash i n g t o n , D.C AM ERI CAN I NSTI TUTE OF CHEM I CAL E N G I N E E R S J R Couper, IJniversity of A r k a n s a s , F a y e t t e v i l l e , A r k a n s a s W L Hewetson, A m e r i c a n I n s t i t u t e of I n d u st r i al E n g i n eer s, N ew Y o r k , N ew Y o r k R Go l d s t e i n , Ne wa r k Co l l e g e of Engineering, Newark, New Jersey AMERICAN INSTITUTE O F MINING, ME T A L L U R G I C A L A N D P E T R O L E U M E N G I N E E R S J W Worren, The Anaconda Company, Butte, Montana AMERICAN SOCIETY OF AGRI CULTU R A L E N G I N E E R S J A Ba s s e l m a n , Am e r i c a n So c i e t y of A g r i cu l t u r al E n g i n eer s, S t Jo sep h , Mi ch i g an P L Bellingel; Al t e r n a t e , Am e r i c a n S o ci et y o f A g r i cu l t u r al E n g i n eer s, St Joseph, Michigan AMERICAN SOCIELTY OF C I V I L E N G I N E E R S K R J a c o b s , G e o r g i a I n s t i t u t e of T ech n o l o g y , A t l an t a, G eo r g i a AMERICAN SOCIECTY FOR ENGI NEER I N G E D U C A T I O N L H i l l , I l l i n o i s I n s t i t u t e o f T e c h n o l o g y , C h i c a g o , I l l i n o i s J G McGuire, Texas A & M C o l l e g e , C o l l e g e S t a t i o n , T e x a s R T Northrup, Wayne State University, Detroit, Michigan AMERICAN SOCIETY OF HEATING, REFRIGERATING AND AIR-CONDITIONING ENGINEERS *C F Koyon, Columbia University, New York, New York G W MocPhee, Alternote, ASHRAE, New York, N.Y N LaCourte, Alternate, ASHRAE, New York, N.Y AMERICAN SOCIETY OF MECHANICAL ENGINEERS, THE R W Co c k r e l l , Fl u o r Corp Lt d Lo s A n g el es, C al i f o r n i a A R Machell, Jr., Xerox Corporation, Rochester, New York J Moho, Parker-Hannifin Corporation, Cleveland, Ohio H E W a l c h i , W e s t i n g h o u s e E l e c t r i c C o r p o r a t i o n , P i t t s b u r g h , P e n n s y l v a n i a AMERICAN S0CIE:TY OF SANITARY ENGINEERING J c Church, Mannaroneck, New York AMERICAN WATER WORKS ASSOCIATION R R Ko u n t z , Am e r i c a n W a t e r W o r k s A sso ci at i o n , U n i v er si t y P ar k , P en n sy l v an i a iv AMERICAN WELDING SOCIETY W E M c K e n r i e , U.S Naval Weapons Laboratory, Dahlgren, Virginia ASSOCIATION OF AMERICAN RAILROADS M F M c C o r c l e , S t L o u i s - S a n F r a n c i s c o R a i l w a y , S p r i n g f i e l d , M i s s o u r i Martin, Alternate, Baltimore & Ohio Railroad, Baltimore, Maryland J L McNabb, Association.of American Railroads, Chicago, Illinois c w CANADIAN STANDARDS ASSOCIATION (LIAISON) E F V R o b i n s o n , N a t i o n a l R e s e a r c h C o u n c i l , O t t a w a , O n t a r i o , C a n a d a ELECTROCHEMICAL SOCIETY Abner Brenner, National Bureau of Standards, Washington, D.C ILLUMINATING ENGINEERING SOCIETY L E Barbrow, National Bureau of Standards, Washington, D.C J E K a u f r n a n , A l t e r n a t e , I l l u m i n a t i n g E n g i n e e r i n g S o c i e t y , N e w Y o r k N.Y INSTRUMENT SOCIETY OF AMERICA George Platt, Bechtel Corporation, Los Angeles, California I N S T I T U T E OF E L E C T R I C A L & E L E C T R O N I C S E N G I N E E R S , T H E R V R i c e , B e l l T e l e p h o n e L a b o r a t o r i e s , W h i p p a n y , N e w J e r s e y R F S h e a ,A l t e r n o t e ,S c h e n e c t a d y ,N e wY o r k MANUFACTURERS STANDARDIZATION SOCIETY OF T H E V A L V E & FITTINGS INDUSTRY R V Warrick, Manufacturers Standardization Society, Arlington, Virginia MECHANICAL CONTRACTORS ASSOCIATION J R Mance, Mance Corporation, New York, O F AMERICA, THE N.Y NATIONAL ASSOCIATION O F P L U M B I N G , H E A T I N G , C O O L I N G C O N T R X Z T O R S R E White, South Bend, Indiana NATIONAL DISTRICT HEATING ASSOCIATION J A S h e p p a r d , J r , , C o n s o l i d a t e d E d i s o n C o m p a n y of New York, Inc., New York, N.Y NATIONAL ELECTRICAL CONTRACTORS ASSOCIATION W H P a u l e s , N a t i o n a l Electrical C o n t r a c t o r s A s s o c i a t i o n , Inv., W a s h m g t o n , D.C KennethPriestley,TheEasternElectricConstructionCo.,Bridgeport,Connecticut NATIONAL ELECTRICAL MANUFACTURERS ASSOCIATION W F Huette, Allen-Bradley Company, Milwaukee, Wisconsin F V K u p c h a k , W e s t i n g h o u s e E l e c t r i c C o r p o r a t i o n , P i t t s b u r g h , P e n n s y l v a n i a E N e a r y , A l t e r n a t e , G e n e r a l E l e c t r l c C o m p a n y , S c h e n e c t a d y , N e w Y o r k W A S o m s o n o f f , A l t e r n a t e , N a t i o n a l E l e c t r i c a l M a n u f a c t u r e r s A s s o c i a t i o n , N e w Y a r k , Roland Russo, Alternate, Clark Controller Company, Cleveland, Ohio N.Y NATIONAL FLUID POWER ASSOCIATION J L Fisher,Jr.,Bellows-Valvair,Akron,Ohio S O C I E T Y OF AUTOMOTIVE ENGINEERS H L Dubocq, Grumman Aircraft Engineering Corporatio?, Ldng Island, New York T E C H N I C A L DRAWING ASSOCIATES V F D u g a r , R e l i a n c e E l e c t r i c & E n g i n e e r i n g Co., C l e v e l a n d , O h i o R N A u s t i n , A l t e r n a t e , I n t e r n a t i o n a l B u s i n e s s M a c h i n e s Corp., E n d i c o t t , N e w Y o r k TELEPHONE GROUP G, A E i s n e r , W e s t e r n E l e c t r i c C o m p a n y , C h i c a g o , I l l i n o i s R V R i c e , B e l l T e l e p h o n e L a b o r a t o r i e s , W h i p p a n y , N e w J e r s e y R E T h i e m e r , A l t e r n a t e , B e l l T e l e p h o n e L a b o r a t o r i e s , N e w Y o r k , N.Y U.S D E P A R T M E N T O F C O M M E R C E P A T E N T O F F I C E D M M i l l s , T h e C o m m i s s i o n e r of P a t e n t s , N a t i o n a l B u r e a u of Standards, Washington, D.C C H P a g e , N a t i o n a l B u r e a u of Standards, Washington, D.C U.S D E P A R T M E N T O F I N T E R I O R R T Montgomery, Department of Interlor Washington D.C V U.S DEPARTMEN'T O F T H E ARMY, ORDNANCE c A Nozion, F r a n k f o r d A r s e n a l , P h i l a d e l p h i a , P e n n s y l v a n i a U.S D E P A R T M E N T O F T H E NAVY BUREAU OF SHIPS L A Meadows, Navel Ship Engineering Center, Hyattsville, Maryland WESTERN UNION 'TELEGRAPH COMPANY H E Wenzel, The Western Union Telegraph Co., New York, N.Y INDIVIDUAL MEMBER C A Fricke, Philco-Ford Corporation, Willow Grove, Pennsylvania - WRITING GROUP S1-2-W-39 SYMBOLSFOR MECHANICAL AND ACOUSTICAL ELEMENTS (RESPONSIBLE FOR THE PREPARATION OF Y32.18) M D Burkhard, Choirman, Industrial Research Products, Inc., 321 North Bond Street, Elk Grove Village, Illinois 60007 B B Bouer, CBS 1,aboratories High Ridge Road, Stamford, Connecticut 06900 *H.M Trent, U.S Naval Research Laboratory, Washington, D.C Vincent Sa/mon, Department of P h y s i c s , S t a n f o r d R e s e a r c h I n s t i t u t e , Menlo Park, California 94025 W C Sperry, 1106 Brentfield Drive, McLean, Virginia 22101 E L Hixon, Department of Electrical Engineering, University of T e x a s , A u s t i n , T e x a s *Deceased vi AMERICAN NATIONAL STANDARDS COMMITTEE ON ACOUSTICS OFFICERS W W Long, Chairman Mrs Avril Brenig, Secretory PERSONNEL OF COMMITTEE S ACOUSTICAL AND INSULATING MATERIALS ASSOCIATION H J Sobine, 102 Miller Avenue, Granville, Ohio 43023 ACOUSTICAL SOCIETY OF AMERICA w W L o n g , IBM Acoustlcs Laboratory, poughkeepsie, New York 12602 Wolter Koidon, Alternote, Section 213.01 (Sound), National Bureau of Standards, Washington, D C 20234 AIR-CONDITIONING AND REFRIGERATION INSTITUTE R W K e l t o , A i r t e m p D i v i s i o n , C h r y s l e r C o r p o r a t i o n , P O B , D a y t o n , O h i o 4 R J Evans, Sr., Alternate, Air-conditioning and Refrigeration Institute, 1815 North Ft Myer Drive, Arlington, Virginia 22209 AIRMOVING AND CONDITIONING ASSOCIATION, INCORPORATED R E P o r k e r , C h i c a g o B l o w e r C o r p o r a t i o n , G l e n E l l y n R o a d , G l e n d a l e H e i g h t s , I l l i n o i s AMERICAN SOCIETY O F H E A T I N G , R E F R I G E R A T I N G AND AIR CONDITIONING ENGINEERS P K Boode, Carrier Corporation, Carrier Parkway, Syracuse, New York 13202 AMERICAN SOCIETY O F MECHANICAL ENGINEERS, THE C J Hemond, J r , Department of M e c h a n i c a l E n g i n e e r i n g , U n i v e r s i t y Connecticut 06101 A M E R I C A N S O C I E T Y F O R T E S T I N G AND MATERIALS Rolph Huntley, Cedar Knolls Acoustical Laboratories, of Hartford, POB 1948, Hartford, Saddle Road, Cedar Knolls, New Jersey 07927 ICANADIAN STANDARDS ASSOCIATION (Liaison) T D Northwood, Division of B u i l d i n g R e s e a r c h , N a t i o n a l R e s e a r c h C o u n c i l , O t t a w a ELECTRIC LIGHT POWER C Murroy, C o n s o l i d a t e d E d i s o n C o m p a n y of New York, Inc., ELECTRONICS INDUSTRIES ASSOCIATION P B Williams, Jensen Manufacturing Company, 6601 2, O n t a r i o , C a n a d a Irving Place, New York, New York S L a r a m e e A v e n u e , C h i c a g o , I l l i n o i s I N S T I T U T E OF E L E C T R I C A L & E L E C T R O N I C S E N G I N E E R S c G V e i n o t t , C l a r k w o o d P a r k w a y , Apt , C l e v e l a n d , O h i o 4 NATIONAL BUREAU O F STANDARDS Mortin Greenspon, National Bureau of Standards, Washington, D C 20025 NATIONAL ELECTRICAL MANUFACTURERS ASSOCIATION R Muso, W e s t i n g h o u s e E l e c t r i c C o r p o r a t i o n , B e u l a h R o a d , P i t t s b u r g h , P e n n s y l v a n i a 5 tWithout v o t e vii 60638 10003 SOCIETY OF AUTOMOTIVE ENGINEERS J A Groening, General Motors Proving Ground, Noise and Vibration Laboratory, Milford, Michigan 48042 SOCIETY O F MOTION P I C T U R E AND TELEVISION ENGINEERS f e t r o V / a h o s , 14ssociation of Motlon Picture and TV producers Incorporated, 8480 Beverly Boulevard, Hollywood, California 90048 TELEPHONE GROUP R N Thurston, Bell Telephone Laboratories, Murray Hill, New Jersey 07971 ULTRASONIC MANUFACTURERS ASSOCIATION Edword Cook, Crest Ultrasonics Corporation, Mercer County Airport, Trenton, New Jersey UNITED STATES DEPARTMENT OF THE ( T o be oppointed) ARMY, E C & L (Uiaison) U N I T E D S T A T E S D E P A R T M E N T O F T H E AIR F O R C E Henning E vonl Gierke, 6570 ARML (MRBA), U S Department of the Air Force, Wright P a t t e r s o n A F B , Ohio 45433 U N I T E D S T A T E S D E P A R T M E N T O F HOUSING AND URBAN DEVELOPMENT G E Winzer, Office of the Assistant Secretary for Research and Technology, Department Urban Development, Washington, D C 20410 of Housing and UNITED STATES NAVY DEPARTMENT Naval Ship Systems Command, Technical Society Liaison, NAVSHIPS Code 053, Washington, UNITED STATES DEPARTMENT OF THE NAVY F E Hein, Code 041210, Naval Facilities Engineering Command, Washington, D C 20360 D C 20390 INDIVIDUAL MEMBERS Lourence BotcheIder, 983 Memorial Drive, Cambridge, Massachusetts 02138 R W Benson, Robert W Benson & A s s o c i a t e s , 633 Thompson Lane, Nashville, Tennessee 37204 L L Beronek, Bolt, Beranek and Newman, Incorporated, 50 Moulton Street, Cambridge, Massachusetts 02138 R J Bobber, 1VRL Underwater Sound Reference Division, POB 8337, Orlando, Florida 32806 R K Cook, Box A 311, Building 226, National Bureau of Standards, Washington, D C 20234 Hollowel/ D o v i s , Central Institute for the Deaf, 818 S Euclid, St Louis, Missouri 63110 R w Hosse, J r , USN Underwater Sound Laboratories, Fort Trumbull, New London, Connecticut 06320 J Hirsh,WashingtonUniversity,Box1094, St Louis, Missouri 63130 C W Horton, 3213 Cherry Lane, Austin, Texas 78703 F V Hunt, 2621 Calle d e l Oro, La Jolla, California 92037 Douglos Muster, University of Houston, Houston, Texas 77004 A P G Petcr:ron, General Radio Company, 22 Baker Avenue, West Concord, Massachusetts 01781 Lane, A u s t i n , T e x a s Wayne Rudmose, Tracor, Incorporated, 6500 Tracor R W Young, Naval Undersea R & D Center, San Diego, California 92132 viii AMERICAN NATIONAL STANDARDS COMMITTEE ON MECHANICAL VIBRATION ANDSHOCK OFFICERS D C Kennord, Jr., M r s Avril Brenig, Chairman Secretary PERSONNEL OF COWITTEE S2 ACOUSTICAL SOCIETY OF AMERICA Golt Booth, 44 Briston St., Short Beach, Connecticut H a r r y H i m e l b l o u , 14206 Mulholland Drive, Los Angeles, California AMERICAN SOCIETY FOR TESTING AND MATERIALS J W Goff, Michigan State University, East Lansing, Michigan 90026 48823 AMERICAN SOCIETY O F MECHANICAL ENGINEERS, T H E Douglas M u s t e r , University of Houston, Houston, Texas 77004 D C Kennord, Jr., Northwestern Michigan College, Traverse City, Michigan 49684 CANADIAN STANDARDS ASSOCIATION (Liaison) T D Northwood, Division of Building Research, National Research Council, Ottawa 2, Ontario, Canada ELECTRONIC INDUSTRIES ASSOCIATION C R M u l l e r , Krollwood Drive, North Caldwell, New Jersey I N S T I T U T E O F E L E C T R I C A L AND ELECTRONICS ENGINEERS C A A r e n t s , West Virginia University, Morgantown, West Virginia 26506 INSTITUTE OF ENVIRONMENTAL SCIENCES R G Shaulberg, 6009 Musker Road, Fort Washington, Pennsylvania 19034 INSTRUMENT SOCIETY O F AMERICA J E Manning, 105 Arena Terrace, Concord, Massachusetts NATIONAL BUREAU O F STANDARDS J D R a m b o z , National Bureau of Standards, MB5, Sound Building, Washington, NATIONAL ELECTRICAL MANUFACTURERS ASSOCIATION S o m u e l L e v y , General Electric Company, One River Road, Schenectady, New D c York NAVALSHIPREARCH ANDDEVELOPMENTCENTER H a r r y R i c h , (Code 701) Department of Structural Mechanics, Washington, D C 20007 SOCIETY OF AUTOMOTIVE ENGINEERS M L Stoner, A l t e r n a t e , SAE, Pennsylvania Plaza, New York, N Y 10001 SOCIETY O F E X P E R I M E N T A L S T R E S S ANALYSIS E G F i s c h e r , Westinghouse Research Laboratories, Pittsburgh, Pennsylvania TELEPHONEGROUP J P W h i t e , Bell Telephone Laboratories, Whippany, New Jersey 07981 UNITED STATES DEPARTMENT O F T H E AIR F O R C E ( L i a i s o n ) Carl G o l e u k e , (FDDS), Air Force Flight Dynamics, Wright-Patterson AFB, Ohio UNITED STATES ARMY ORDNANCE CORPS (Liaison) S t e f a n Bogolea, U.S Army Materiel Command, AMCMA-WW, Washington, D.C UNITED STATES DEPARTMENT OF DEFENSE W W M u t c h , (Code 6020) Naval Research Laboratory, Washington, ix 45433 20315 D C 20390 20234 UNITED STATES NAVY DEPARTMENT Naval Ship Systems Command, Technical Society Liaison, NAVSHIPS Code 053, Washington, D C 20360 UNITED STATES NAVY ORDNANCE SYSTEMS ( T o be appointed) INDIVIDUAL MEMBERS Laurence Botchelder, 983 Memorial Drive, Cambridge, Massachusetts 02138 L L Beranek, Bolt, Beranek & Newman, Inc., 50 Moulton Street, Cambridge Massachusetts 02138 R K Cook, Box A311, Bldg 226, National Bureau of Standards, Washington, D.C 20234 J Hirsh, Washington University, B o x 1094, St Louis, Missouri 63130 Walter Koidan, Alternate, Section 213.01 (Sound) National Bureau of Standards, Washington, D C 20234 F V Hunt, 2621 Calle del Oro, La Jolla, California 92037 W W Long, IBM Bldg 704, Acoustics Laboratory, Pou&keepsie New York 12602 Wayne Rudinose, Tracor Incorporated, 6500 Tracor Lane, Austin, Texas 78721 H E von Gierke, 6570 AMRL(MRBA) Wright-Patterson AFB, Ohio 45433 R w Young, Naval Undersea R & D Center, San Diego California 92132 X AMERICAN NATIONAL STANDARD GRAPHIC 'sYMBOLS AND DESIGNATIONS opencirclejoinedtothecodingby S u b s e c t i o n 4.4) ANSI Y32.18-1972 4.1 a line.(See RectilinearMotion 4.1.1 lnertance 3.4 AcrossVariables Across v a r i a b l e sd e s c r i b e q u a n , t i t i e s w h i c h a r e o b s e r v a b l e or a c t o n a n e l e m e n t r e l a t i v e t o a reference M +k-$ 3.5 ThroughVariables Through variables des c r i b eq u a n t i t i e sw h i c r eo b s e r v a b l eo r e transmitted continuously through an element 3.6 Directivity D i r e c t i v i t yi s a property ass o c i a t e d w i t h a path connecting two terminals of the same element It specifies either the reference terminal of t h e a s s o c i a t e d a c r o s s v a r i a b l e o r t h e direction of propagation of t h ec o r r e s p o n d i n g throughvariable.Intheformer case a - s i g n i s a + sign by placed by the reference terminal and theotherterminal;inthesecond case an arrowto t h el i n et e r m i n a t i n go nt h e h e a di sa d d e d reference node with the arrowhead pointing toward the reference node (See Subsection 4.4) of i n d i c a t i n g d i r e c tivity are not independent for one implies the! o t h e r T h u si ti sn o tn e c e s s a r yo r d e s i r a b l et ou s eb o t hd e s i g n a t i o n si n the symbol for any element S e e 4.7.2 4.1.2 Compliance NOTE: T h e s e t w o m e t h o d s 4.1.3 Dissipation RhA 3.7 Labels L a b e l s a r e n u m b e r s or letter symb o l s p l a c e d b e s i d e o r o n t h e c o d i n g of a n e l e m e n t T h e y a r e u s e d a s needed to provide information to a u s e r of the diagram of a s y s t e m ( S e e S u b s e c tion 4.4) 3.8 Notations T h e r e w i l l b e c e r t a i n i t e m s of informationwhichwillbeneededinadditionto the above symbol information in order to completely d e s c r i b et h es y s t e mw h i c hc o r r e s p o n d st ot h e d i a g r a m T h e s e e x t r a i t e m s of information may be added by a margin of t h e d i a g r a m a n d a r e c a l l e d notations Typical items that are contained in the notations are: a S t a t e m e n t sd e s c r i b i n gt h ec o o r d i n a t es y s tems assigned to the system; b.Definitions of l a b e l s ; S e e N o t e C 4.1.4 Generator(acrossvariable) c Constraints imposed by perfect couplers General Symbols NOTE A: L e t t e r n o t a t i o n l a b e l s i d e n t i f y m o d e s 4.1.5 Generator (through variable) o f motion NOTE 6: S e n s e of motion indicated by +,- or+ NOTE C: T h e e x a c t m e a n i n g of thelabelmust be given in notations for any non-linear dissipative lement ANSI Y32.18-1972 AMERICAN NATIONAL STANDARD GRAPHIC SYMBOLS AND DESIGNATIONS 4.2 4.3 RotaryMotion Acoustical(Eulerian) 4.3.1 4.2.1 lnertance lnertancc MA 4.3.2 Compliance See 4.7.2 CA 4.2.2 Compliance CR See 4.7.2 4.3.3 Dissipation 4.2.3 Dissipation RR See Note C 4.3.4 Generator(acrossvariable) See Note C -+ 4.2.4 Generator(acrossvariable) 4.3.5 Generator (through variable) 4.2.5 Generator (through variable) ANSI Y32.18-1972 AMERICAN NATIONAL STANDARD GRAPHIC SYMBOLlS AND DESIGNATIONS 4.4 TypicalApplication; 4.5.2 InverseCoupler Schematic Diagram [ fi = n: spj sui + 4.5 PerfectCoupler uj = o* *Relationisredundantinthatitcan be inferred from t h e f i r s t r e l a t i o n a n d t h e f a c t t h a t t h e e l e ment is a perfect coupler It is helpful however to include it in the notations 4.5.1 DirectCoupler NOTE 1: A l t h o u gohntlw ys oe c t i o na rse shown in the above symbols, by extens i otnheel e m e nmt aiyn c l u daen y finite number of s e c t i o n s N V E It is frequently the case t h a t t h e r e a r e interconnections between the sections of a coupler 4.6 Multi-terminalElement E x a m p l e s of notations: [ UI = 1: 1uj Ifi + f j = o* H d e f i n e d i n t e r m s of t h e a c r o s s v a r i a b l e the corresponding through variables a , and ANSI Y32.18-1972 AMERICAN NATIONAL STANDARD GRAPHIC SYMBOLS AND DESIGNATIONS onepart of a systemtoanother.Therearetwo types of couplers, the distinction being based on the nature of the constraints they impose Symbols for perfect couplers are shown in Section 4.5.1 and 4.5.2 4.7 Supplementary Symbols 4.7.1 Uncoded L i n e e 5.6.2 Direct Couplers A directcoupler transformsthroughandacrossvariables in one system to through and across variables, respectively,inanothersystem It is necessary to assign directivities to all sections of a perfect coupler 4.7.2ReferenceTerminal 5.6.3 Inverse couplers An inverse coupler transformsacrossandthroughvariablesinone system to throughandacrossvariablesinthe othersystem,orviceversa.The sense of the direction of all s e c t i o n s of the coupler must be indicated Description of Symbols 5.1 General The standard symbols are listed in Section General Symbols 5.2 Symbols for PureInertances Symbols for a pure inertance are suggestive of rigid pieces of matter or a portion of fluidwithin a stationary a solidcircle at i t s pipe.Thecodingcontains centroid,suggestingthattheelementcan be specified precisely by considering only the motion of its center of mass and as if all forces were concentrated at this point 5.3 Symbols -forPureCompliance T h e Symbols for pure compliance are suggestiveof springs i n t h e c a s e of rectilinear and rotary motions and of a cavity i n acoustical systems 5.4 Symbols for PureDissipations T h e Symbolsforpuredissipationsaresuggestive of a pistonmovingin a viscous oil, a disk spinning in a viscous oil, or a fluid being forced through a porous screen 5.5 Symbols for Pure Sources ofExcitations (Generators) The symbols given in Section are simple and obvious modifications of the symbols used for electrical sources so as to allow ready distinctionbetweenthetwotypes of energy sources It should be noted that only two types of generators have had widespread use in mechanical of and acoustical systems In one type the value an across variable is a specified function of the time; in the other a through variable is a specified function of the time In either case the device has an inherent directivity so that their symbols must include this information 5.6 Symbols for PerfectCouplers 5.6.1 General Aperfectcoupler is a conceptual element which does not generate, store or dissipateenergy,yetcantransferenergy from 5.7 Symbols for General Elements ,Many mechanical and acoustical systems may, be represented by lumped or pure elements given in Section 5.2 through 5.6 and often this.is the most informativething to do.Yet cases d oa r i s ei n whichit is advantageous to consideraninterconnected set of pure elements as a single entity withperhapsmultipleterminals For example, generators are not easily' included in an analysis if single 2-terminal elements are created conceptually by combining each puregeneratorwith a conceptual compurely passive element Such bination is still called an element The element its constitutiverelations mustbelabeledand specified-inthenotations.Furthermore, if t h e element has more than two terminals the assignment of an independent set of across variables, s a y a , mustbespecifiedbetweenappropriate a general pairs of terminals.Thesymbolfor multi-terminal element is shown in Section 4.6 5.8 Supplementary Symbols The following supplementary symbols may be used 5.8.1 Uncoded Line An uncoded line is used to interconnect any two (or more) terminals is for which the appropriate across variable always zero in the system being analyzed 5.8.2 ReferenceTerminal Thereference terminal isusedtoidentify a stable point of reference, normally external to the system being represented by the schematic diagram The reference terminal need not represent an identifiable or fixedphysicalstate A minimum of one reference terminal should appear in any schematic diagram APPENDIX General Information on the Construction of Schematic Diagram A1 Purpose and Scope of Appendix taken implies that the performance of the system is notknowninadvance.However,theanalyst can mentally divide the system into a sequence of smaller parts and this division can be carried to a point where the performance of each part is wellknown.Theendpoint of thedivision is arbitrary, obviously, for arriving at a s e t of parts whoserespectiveperformancesareknown is a function of the training, experience and above all the taste of theanalyst.Thegreatmajority of workers, however, prefer to carry a decomposition to thepointwheretheresultingpartsrepresent pure elements Typical pure elements are inertias withoutanycompressibility or viscouseffects, springs without inertia, levers w\ithout inertia or springiness, generators without passive reactions, etc 'It is t o be noted that this standard concerns mainly symbols for pure elements although some allowance has been made for other elements Thisappendix,althoughnot a part of t h e of readers so standard, is prolvidedfortheuse that they may halve at hand a brief description of thoseconceptswhichprovidethetheoretical basis on which the construction of such diagrams restsand a summary of thosetechniquesthat have been found to have general applicability in this s u b j e c t areal A2 Basic Concepts A2.1 T h e primaryfunction of a schematic diagram is to provide a useful conceptual tool for analysis ofphysical systems It is not surprising, therefore, that the concepts associated- with the construction of schematicdiagrams are derived from those constructs created in the mind of a n analyst and those operations which he pursues in creating accurate descriptions of the performance of thesystems An analyst is concernednot of the performance only with an accurate description of a systembutwiththefinding of accurate numericalpredictions of its action.Thedescriptivephase of h i s work is partlyconceptual andpartlymathematical,whilethepredictive p h a s e is purelynnathematical and i n fact concerns the formal solution of a set of equations usually integro-different:ial in form It is important to realize that schematic diagrams are designed to be aids only in the descriptive phase of an analy s i s - not in the solution of mathematical relations If a n a n a l y s t seems to u s e a schematic diagraminpredictingtheperformance of a system, it is probably because he has developed an intuition for the way solutions will come outby virtue of his having previously solved other systems havingsimilarschematicdiagrams.Hence this discussion will be limited hereafter to the descriptive phase of an analysis A2.3 A decompositionassumesthateach of the resulting elements has a knownperformance be specified acandthatthisperformancecan curately.Thestatementimpliesthattheperformance of an individual element can be represented by a set of mathematical relations Clearlysuch a set of relationsinvolves a s e t of variablesand some parameterscharacteristic of theelement.Relations of thissort are called Constitutive Equations and are a basic ingredient ineveryanalysis.One of theprimefunctions performedby a schematicdiagram is to suggest for eachelementthenature of itsconstitutive equations; in fact it is just the representation of this sort of informationwhichingeneralmakes of onesymboldiffer from another.Theprocess adding this information is called Coding the Diagram Beforeconstitutiveequationscanbewritten down, the analyst must select the variables which are usedintheequations.Thatthischoice is generally arbitrary is readily seen byexamining a few situations Take a pure spring as one such example Its constitutive equation can be written in the form f = - K s where f is the force transmitted by the spring, K is its stiffness, and s i s the extension of one end of the spring relative to A2.2 As an analyst begins his consideration of a systemhe is facedwithfoursorts of arbitrary choices The f i r s t of these concerns a decomposition o f the given system into a set of simpler parts called elements The notions behindsuch a decompositioncan be viewed as follows The fact that an analysis is being under- conditionsholdsabsolutely,and (2) considering the air in a short section of an acoustical pipe system to b e a pure inertia whereas it is certainly compressible.Approximations of t h i s sort a r e made regularly in practice and if done judiciously andwithinsight,very little error is introduced into an analysis Again the point is that such approximationsmust be decided in advance of the construction of a schematicdiagram,forsuch decisions affect the number of pure elements that must be represented in the diagram the other However, it could be written equally a s well in terms of variables which were time derivatives of f and/or s toanyorder.Other examplesareeasilyfound.Henceananalyst must specify the variables he expects to use in writingconstitutiveequations.Consistencyrequires that if a choice is made for one element, the same choicemustbemadefor all other elements;thus a choice of variables is characteristic of thesystem as a whole This second arbitrarydecisiononthepart of theanalyst is not alwaysindicatedin a schematicdiagram There are instances in which a letter symbol or notationin a schematicdiagrammight seem to imply a unique selection of variables Two examples are the letter symbol placed beside the g r a p h i c s y m b o l for a generator and the notation associated with the graphic symbol for a perfect coupler Such symbols and notations are intended to be only suggestive and not mandatory in use A2.6 There are certain basic mechanical concepts which must be kept in mind if one is to construct schematic diagrams with facility To illustrate these notions, consider an element-of a mechanicalsystem.It is wellknownthatthis element can be treated as if it were subjected to (1) a set of forces (or tractions) which act at the surface of element, (2) a set of surface moments (or couples), (3) a set of body forces, and (4) a set of body moments Forces of types (1) and (2) are usually elastic in their origins but not example with surface necessarily so, as for forces arising as a result of the reactions of surface chargeswithanelectricalfield.Furtheritem (2) ,have more, some of themomentsunder their origins in the surface forces of item (l), but a moment c a n exist as a mechanicalentitynot uniquelydecomposableinto a set of forces and lever arms An example of the latter is the moment a concrete wall on a protruding created by cantileverbeam.Bycontrast,bodyforcesand moments are associated with volume elements of the device Well knownexamples of body forces farces, aregravitationalattractionsandinertial the latter being the morefrequentlyencountered for they always appear wherever an inertance is accelerated As for the fourth item, a magnetized bar placed in a uniform magnetic field experiences a body moment and no body force, and is thus 'an example of the fourth type of external excitation A2.4 The third arbitrary choice which an analyst must make concerns whichof those energy mechanismspresentin a givensystem he s h a l l a loudspeaker,for analyzeindetail.Consider example A certain amount of heat is produced by of airaboutthevoice coil andcone theflow or not t o Now theanalystmustdecidewhether describethisthermalmechanismindetail Most generally it is not so described and its presence is indicatedbyassigning a viscositytothe relative motion of the voice coil and cone Since in this case thermal effects are not analyzed in is detail,themechanismwhichproducesheat s a i d to be dissipative, i.e., itconvertsenergy from a form which is beinganalyzedin detail into a form which is not being so analyzed The converse of thissituation,namelyanelement which converts energy from a form not described is in detail into one which is analyzed in detail, called an energy source or generator to Any element which does not convert energy a form notbeinganalyzed is of coursecalled is that an conservative The important point here analyst must make decisions of this sort prior to the drawing of a schematic diagram or the prosecution of a formal analysis A2.7 Ineach of thefour cases giveninthe previous section the forces or moments c a n b e associated with a particular surface or point T h i s statement is obvious in the case of surface forces andmoments.Bodyforcesandmomentscanbe associated with an appropriate centroid; for example inertial forces are accurately associated withthecenter of mass of theelement.The points or surfacesatwhichforces or moments c a n be considered to act are called the Terminals of the element The identification of terminals on A2.5 Thefinaltype of arbitrary decision whichananalystmustmakehastodowiththe possibleintroductiontoapproximationsintothe analysis Typical examples of the idea being deare (1) treating a lever as being scribedhere rigid and massless whereas neither of t h e s e eachelement is a necessarystepintheconstruction of any, schematic diagrams whichsatisfythecontinuityprinciples For example, a necessary ingredient in the analysis of electric networks Kirchhoff’s is current law which is thus one of the field equations for the discipline.Itcanbeconcludedthereforethat a continuity principle must hold for every possible analysis,andthatthisnotionwhenapplied in any particular situation defines a field equation This notion of continuity of through variables is so basic that it has been conventional from the verybeginning of schematicdiagramstoimply of a thisprinciplebyrepresentingallelements system by codedcontinuouslines.Suchatechnique gives rise to junction points in the diagram to a statementclearly andthisinturnhasled motivated by the diagrammatical representation of a system to the effect that at all junction points the sum of the through variables entering a junctionpointmustbeequaltothe s u m of those A2.7.1 It is necessary to comment in passing that a terminal may or may not coincide with a physical junction in the original mechanical system A physicaljunctionimpliesaconnection made by a process such as bolting, riveting, welding, soldering, etc: Suchjunctionscharacteristically specify some of the terminals of elements butnot all of them For example,thepointterminal associated with an inertial force is never created by any of the shop processes mentioned above It is best,, therefore, to think of terminals as being mental constructs and i f one or more of the terminals so identified turns out to coincide with a physically created junction then this should be treated a s j u s t a happy circumstance A2.8 Forcesandmomentsactingonthe elements of a syst’emwereidentifiedinsectionsleaving A2.6 and A2.7with the terminals of that element of theseforcesor It is wellknownthateach moments is a Directed Quantity where by “directed” we not mean the notion of a directedvector :in 3-spacebutratherthemore elementary notion that the forces or moments act or out of theelement Now it is a eitherinto generallaw of mechanicsthatthesum of the is forces (or moments)actingintoanelement always exactly equal to the sum of those leaving the element where clearly both surface and body excitations must be inqluded in order to achieve a balance This balance is true of each and every mechanicalelementnomatterwhatit may be; hence it is a universal law applicable to all mechanical system:; A universalrelationsuch as t h i s is called a Field Equation - A2.10.1 Thereisasecondtype of field equationwhich i s pertinent to an analysis of a mechanical system and hence of importance in the construction of schematic diagrams To introduce thissubjectletusreturntotheconstitutive equations for a linear spring end let us write this in the form dt - Kv where u is the relative velocity between the ends of thespring.Onevariable is thetransmitted force, f, which is a throughvariable.Therelation, however, r e q u i r e s the u s e of another variable, u , which is not a through variable The important physical characteristic of this variable is that it its involvestwoterminals of theelementfor specification.On a more experimentallevel, it may be noted that the quantity can be measured by attaching a relativevelocitymetertothe twoterminals of thespring so thatthemeter spans the spring Variables which have this twopointpropertycanbemeasuredconceptuallyby attachinganappropriatemeterattwoterminals of an element, which property led Firestone [l]to call them Across Variables since meters for their measurement span the element Across variablesareinfactthedifference of twolike scalarquantities as theyexist at thetwoterminals associated with the variables These variables are also directedquantitiesbecause as a reference oneterminalmustbeselected position and the scalar quantity at the other term i n a l then compared to the value existing at the A2.9 Thefieldequationdescribedin A2.8 forces (or c a n be interpreted as implyingthat moments) are propagated continuously through an element; i.e as much force (or moment) comes if it is out of the element as goes into it Thus assumed that foxes and moments are transmitted continuouslythroughanelementthenprediction of the action of t h e element whensubjectedto those excitations will be exactly those which occur in fact This notion is called the Principle o f the Continuity o f Force Thus forces(or moments) act as if they were transmitted continuously through an element and it is for this reason that [I] such variables have been called by Firestone Through Variables One can go so far as t o a s s e r t be analyzed if and that any physicall system can onlyif it is p o s s i b l e to findthroughvariables ,