j n reddy introduction to continuum mechanics

... spectral analysis of light, universal gravitation and differential and integral calculus are only too well known There are so many scientific terms named after Newton (Newton's rings and Newton's law ... their combinations The units of such fundamental quantities are called base Units and dimensions units, combinations of them being called derived units The system in which length, mass and time ... Dimension All physical quantities are expressed in combinations of base units The index number of the combination of base units expressing a certain physical quantity is called the dimension,

Ngày tải lên: 22/10/2012, 10:59

... etymological origin Also, ‘aqualung’ is diving gear meaning water lung The Japanese word aka appeared in Japanese classics in the tenth, eleventh and thirteenth centuries Furthermore, aka also means bilge ... If J is the moment of inertia around the longitudinal axis passing through the centre of gravity, tJ the inclination angle and m the mass, the movement equation for crosswise vibration is (whenever ... as an inclined manometer When the angle of inclination is a and the movement of the liquid surface level is L, the differential pressure H i s as shown in the following equation: H = Lsina (3.23)

Ngày tải lên: 22/10/2012, 10:59

... through a narrow channel flow, while undergoing deformation and rotation, are shown in Fig 4.8 Fig 4.8 Deformation and rotation of fluid particles running through a narrowing channel 48 Fundamentals ... Professor of Engineering He was one of the most original and independent of men and never did anything or expressed himself like anybody else The result was that we had to trust mainly to Rankine's text ... thermodynamics, electricity, navigation, rolling friction and steam engine performance He was the first to clarify the phenomenon of cavitation and the accompanying noise He discovered the difference

Ngày tải lên: 22/10/2012, 10:59

... can be expressed as kgm2/(s2kg ) Since kgm2/s2= J (for energy), then v2/2,p / p and gz in eqn 60 Onedimensional flow Daniel Bernoulli (1700-82) Mathematician born in Groningen in the Netherlands ... of energy are exchangeable and, again ignoring frictional losses, the total energy is constant This is an expression of the law of conservation of energy applied to a fluid Consewation of energy ... distance ds away The gravitational force acting on this element is its weight, pg dA ds Applying Newton’s second + 58 Onedimensionalflow Fig 5.4 Force acting on fluid on streamline law of motion to

Ngày tải lên: 22/10/2012, 10:59

... reduction extends to a further outside layer and thus the boundary layer increases its thickness in succession, beginning from the front end of the plate as shown in Fig 6.21 In this manner, an orderly ... upper plane is stationary and of length inclined to the x axis by a, and that the lower plane is an infinitely long plane moving at constant velocity U in the x direction By the movement of the ... university observed and photographed this train of vortices Therefore, Benarl insisted on his priority in observing this phenomenon at a meeting on International Applied Dynamics Karman responded

Ngày tải lên: 22/10/2012, 10:59

... roughness only, and is not related to Reynolds number value To simulate regular roughness, Nikuradse performed an experiment in 1933 by iacquer-pasting screened sand grains of uniform diameter onto the ... is as shown in Fig 7.12, and is expressed by the following equations:6 if the entrance is Weisbach, J. , Ingenieur- und Machienen-Mechanik, I (1896), 1003 Hibi, et al., Joumalof the Japan HydrauIics ... is the total loss factor, and [ is the loss factor due to the bend effect The values of are shown in Table 7.1 ' In a bend, secondary flow is produced as shown in the figure owing to the introduction

Ngày tải lên: 22/10/2012, 10:59

... necessary inclination using the Manning equation with n = 0.01 For a concrete-coated water channel with the cross-section shown in Fig 8.13, compare the discharge when the channel inclination ... an open channel of constant section and inclination angle of the bottom face Now examine the balance of forces on water between the two sections a distance apart Since the water depth is uniform, ... important for analysing the flow in an open channel Fig 8.6 Open channel 142 Flow in a water channel There are three variables, E, h, Q Keeping one of them constant gives the relation between the

Ngày tải lên: 22/10/2012, 10:59

... shown in Fig 9.2 In general, the force R acting on a body is resolved into a component D in the flow direction U and the component L in a direction normal to U The former is called drag and the ... the surrounding fluid When a flat plate is placed in the flow direction, it is only subject to a force in the downstream direction A wing, however, is subject to the force R inclined to the flow ... into a flow running round the trailing edge B Since the trailing edge is sharp, however, the flow is unable to run round the wing surface but separates from it producing a vortex as shown in

Ngày tải lên: 22/10/2012, 10:59

... conducted 172 Dimensional analysis and law of similarity In order to perform the dimensional analysis, it is convenient to use the n theorem Consider a physical phenomenon having n physical variables ... u,, and k basic dimensions' (L, M, T or L, F, T or such) used to describe them The phenomenon can be expressed by the relationship among n - k = rn non-dimensional groups nl, n2 ,n, , , x, In other ... of dynamical conditions between the two is also necessary When the above dimensional analysis is employed, if the appropriate non-dimensional quantities such as Reynolds number and Froude number

Ngày tải lên: 22/10/2012, 10:59

... As shown in Fig 11.13, when a conducting fluid flows in a non-conducting section of a measuring tube to which a magnetic field of flux density B is applied normal to the flow direction, an electromotive ... beam type (3single- lntederence fringe type As shown in Fig 11.6(b), the flow velocity is obtained by using a photomultiplier to detect the alternating light intensity scattered when a particle ... interference fringes The velocity is again calculated using eqn (1 1.2) Single-beam tvpe As shown in Fig 11.6(c), by using the interference of the scattered light in two directions from a single

Ngày tải lên: 22/10/2012, 10:59

... constant on the z plane as shown in Fig 12.13 That mesh transforms to another mesh composed of = constant and q = constant on the plane In other words, the pattern on the z plane is different ... cylinder on the z plane is conformally mapped onto the flat board on the i plane The mapping function in eqn (12.50) is renowned, and is called Joukowski's transformation If conformal mapping ... onto the [ plane by utilising Joukowski’s conversion by eliminating z from eqns (12.50) and (12.52) to obtain the complex potential on the [ plane The resulting flow pattern around a wing can

Ngày tải lên: 22/10/2012, 10:59

... proofreading of the first edition and to many other readers for supplying both corrections and support, in particular V Dannon, H Johnston, J Larsen, M Olufsen, and T Ratiu and G Rublein These corrections, ... ξ ∂y ψ = J( ξ, ψ), the Jacobian of ξ and ψ Thus, the flow is stationary (time independent) if and only if ξ and ψ are functionally dependent (If functional dependence holds at one instant it will ... definite functional form to σ For more information, see J Jeans [1867] An Introduction to the Kinetic Theory of Gases, Cambridge Univ Press 32 The Equations of Motion As before, Newton’s second...

Ngày tải lên: 24/04/2014, 16:46

... Introduction to Continuum Mechanics This page intentionally left blank Introduction to Continuum Mechanics Third Edition W MICHAEL LAI Professor of Mechanical Engineering and Orthopaedic ... indicating a summation with the index running through the integers 1,2, , n This convention is known as Einstein's summation convention Using the convention, Eq (2A1.1) shortens to We also note that It ... tensors, then Tp.-1-Sp are components of a third order tensor To prove this rule, we note that since Tljk=QmiQnjQrkTmnr and S;jk=QmiQnjQrkSmnr we have, *ijk+Sijk = QmiQnjQrk*mnr+QmiQnjQrkTmnr...

Ngày tải lên: 27/06/2014, 17:20

... Introduction to Continuum Mechanics This page intentionally left blank Introduction to Continuum Mechanics Third Edition W MICHAEL LAI Professor of Mechanical Engineering and Orthopaedic ... indicating a summation with the index running through the integers 1,2, , n This convention is known as Einstein's summation convention Using the convention, Eq (2A1.1) shortens to We also note that It ... Cartesian Components of a Tensor Defining Tensors by Transformation Laws Symmetric and Antisymmetric Tensors The Dual Vector of an Antisymmetric Tensor Eigenvalues and Eigenvectors of a Tensor Principal...

Ngày tải lên: 13/08/2014, 16:21

... eigenvalue A Then, by definition, Tnj = An^ and Tn2 = An2 so that for any a, and ft, T(an1+/ 3n2 )=aTn1+/TTn2=A(ani+/ ?n2 ) That is ctn1-» -j8 n2 is also an eigenvector with the same eigenvalue A In ... equation has roots A! and A2=A3=A (Aj distinct from A) Let nj^ be the eigenvector corresponding to Aj, then nj is perpendicular to any eigenvector of A Now, corresponding to A, the equations 44 Tensors ... then Tp.-1-Sp are components of a third order tensor To prove this rule, we note that since Tljk=QmiQnjQrkTmnr and S;jk=QmiQnjQrkSmnr we have, *ijk+Sijk = QmiQnjQrk*mnr+QmiQnjQrkTmnr ~ QmiQn}Qrk(^mnr+^nmr)...

Ngày tải lên: 13/08/2014, 16:21

... was in the direction n, is given by n • En In particular, if the element was in the ej direction in the reference state, then n = ej, and EH = ej • Eej so that EH is the unit elongation for an element ... (2D3.24c) 3 Kinematics of a Continuum The branch of mechanics in which materials are treated as continuous is known as continuum mechanics Thus, in this theory, one speaks of an infinitesimal volume ... T, R, and S are related by T - RS Tensors R and S have the same eigenvector n and corresponding eigenvalues rx and jj_ Find an eigenvalue and the corresponding eigenvector of T 2B32 If n is a...

Ngày tải lên: 13/08/2014, 16:21

... material element in the direction of n, its rate of extension (i.e., rate of change of length per unit length ) is given by Dnn(no sum on n) The rate of extension is also known as stretching In particular ... Conditions for Infinitesimal Strain Components When any three displacement functions MI, u^, and u$ are given, one can always determine dUj the six strain components in any region where the partial ... displacementstrain equations We now state the following theorem: If EifiX\JtiJQ are continuous functions having continuous second partial derivatives in a simply connected region, then the necessary and sufficient...

Ngày tải lên: 13/08/2014, 16:21

... unit elongation in the direction 2ej + 2e2 + 63? (b) What is the change of angle between two perpendicular lines (in the undeformed state) emanating from the point and in the directions of 2ej ... that convention, for example, TI\ and T2^ are tangential components of the stress vector on the plane whose normal is 62 etc These differences in meaning regarding the nondiagonal elements of T ... tne stationary value of 7j VI If I *-ftlf/ \Sttr * But the dni,dn2 and dn$ can not vary independently Indeed, taking the total derivative of Eq (4.6.6), i.e., nj+nl+wi = we obtain If we let and...

Ngày tải lên: 13/08/2014, 16:21

... on planes defined by the unit vectors m and n and pass through the point P Show that if k is a unit vector that determines a plane that contains !„, and tn, then t,,, is perpendicular to m and ... tensor, E is the infinitesimal strain tensor, with T (0) = If in addition, the function is to be linear, then we have, in component form The above nine equations can be written compactly as Since ... equation can be written and in Cartesian component form Equations of Motion - Principle of Linear Momentum 189 These are the equations that must be satisfied for any continuum in motion, whether...

Ngày tải lên: 13/08/2014, 16:21

... principal directions of stress and strain coincide (b) Find a relation between the principal values of stress and strain Solution, (a) Let nj be an eigenvector of the strain tensor E (i.e., Enj ... polarized normal to the plane of incidence, no longitudinal component occurs Also, when an incident longitudinal wave is reflected, in addition to the regularly reflected longitudinal wave, there ... is often not known, only the resultant force is known The question naturally arises under what conditions can an elasticity solution such as the one we just obtained for simple extension be applicable...

Ngày tải lên: 13/08/2014, 16:21