Applied Structural and Mechanical Vibrations 2009 Part 6 docx

... eq (6. 168 ) in the generalized eigenproblem gives and since we arrive at (6. 169 ) where we have defined the matrix Now, premultiply eq (6. 169 ) by N –1 , insert the identity matrix between K and ... LLC Equations (6. 119) and (6. 121) can be put together to express the family of orthogonality conditions (6. 122) 6. 6 Unrestrained systems: rigid-body modes Suppose that, for a giv...

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... to its midband value, and it decreases at a 20 dB/decade (or 6 dB/octave) rate for The phase shift is π /2 at low frequency becomes π /4 at ω 1 , and tends to zero for If both 1 and 2 are ... follower) and a low-output impedance. R T and C T include the impedance of the transducer, of the amplifier input and of the ranging capacitor if present. The product R T C T give...

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... LLC Applied Structural and Mechanical Vibrations Theory, methods and measuring instrumentation Paolo L.Gatti and Vittorio Ferrari Copyright © 2003 Taylor & Francis Group LLC Applied Structural ... 1959– Applied structural and mechanical vibrations: theory, methods, and measuring instrumentation/Paolo L.Gatti and Vittorio Ferrari. p. cm. Includes bibliographi...

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... (5 .60 a) or, alternatively (5 .60 b) or, in complex notation (5 .60 c) where establish the relation between eqs (5 .60 a) and (5 .60 b), and give the relation between eq (5 .60 a) and the ... (eq (2.6b) or (2.10)) (5 .61 ) for the expression of eq (5 .60 a) and (5 .62 ) for the complex representation of eq (5 .60 c). The mean (over one period) and mean-square...

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... Section 6. 3.1, eq (6 42a)) and get (6. 67b) It is then easy to verify the orthogonality relationships, i.e. or and if we decide to use the eigenvectors of eqs (6. 67a)—to obtain the modal masses and ... eq (6. 42) is (6. 44) so that the concise form of eqs (6. 42b) and (6. 44) now reads (6. 45) where P is the modal matrix formed with the vectors p i (sometimes called the weighted...

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... H( ω ) and hence (7.47) where, for brevity, we write H Re and H Im for the real and imaginary part of H, respectively. In addition, we can express h(t) as (7.48) divide the real and imaginary parts ... to eq (7 .67 ) and leads, in the end, to (7.82) 6. The matrix of right eigenvectors S can be partitioned into two n×2n matrices as (7.83a) and, by the same token, it is also con...

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... the differential operators K and M parallels the symmetry of the matrices K and M, the othogononality conditions (6. 44) and (6. 42b) are the counterpart of eqs (8.128) and the expansion theorem is ... boundary conditions in eq (8.58) leads to and to the frequency equation (8 .60 ) which implies and hence (8 .61 ) The eigenfunctions are then given by (8 .62 ) and have the sam...

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... Plates, NASA SP- 160 , 1 969 . 16. Gerardin, M. and Rixen, D., Mechanical Vibrations: Theory and Applications to Structural Dynamics, John Wiley, New York, 1994. 17. Timoshenko, S. and Woinowsky-Krieger, ... inconvenience, because we have shown in Chapter 6 (Section 6. 8, eqs (6. 165 ) and (6. 166 )) that the generalized eigenvalue problem can be transformed into a standard e...

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... assumption, the excitation and the response are usually broadband signals (for example, random or impact) and the tests are often performed by using a two channel analyser and a single-input single-output ... referring, for example, to DOFs 1 and 2 for the measurements at point 1 and 2, respectively, along the x direction and to DOFs 3 and 4 for the measurements at points 1 and...

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... (12 .69 a) we have Then, the variance of the derived process is obtained by combining the results of eq (12 .62 ) and the first of eqs (12. 46) to get where H( ω ) is given by eq (12 .67 a) and ... cross-relationships (12 .65 ) from which we can obtain another expression for H( ω ). In fact, putting together eq (12 .61 b) and the second of eqs (12 .65 ) we have from which i...

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