By Clarence W. de Silva

ISBN-10: 0849315808

ISBN-13: 9780849315800

Vibration and surprise are ubiquitous phenomena, and a latest, useful reference for the sphere is late. This striking new Vibration and surprise Handbook presents a completely updated, handy, and authoritative reference at the strategies, instruments, and information proper to the modeling, research, layout, instrumentation, and regulate of vibration, surprise, noise, and acoustics. In forty five chapters contributed by way of execs in present perform, the e-book covers either the theoretical and the sensible points, together with using MATLAB<sup>®</sup> toolboxes and LabVIEW<sup>®</sup> instruments. It offers a wealth of examples and case experiences and provides all the fabric in a structure that's perfect for simple reference and recollection.

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101 will be unity. 100) the initial conditions will become yð0þ Þ ¼ 0 and y_ ð0þ Þ ¼ v2n ð1:102Þ þ Also, beyond t ¼ 0 the excitation uðtÞ ¼ 0; according to the definition of an impulse. 102. The three cases of damping ratio (z , 1; z . 1; and z ¼ 1) should be considered separately. We obtain the following results: vn ð1:103aÞ yimpulse ðtÞ ¼ hðtÞ ¼ pffiffiffiffiffiffiffiffi expð zvn tÞsin vd t for z , 1 1 z2 vn yimpulse ðtÞ ¼ hðtÞ ¼ pffiffiffiffiffiffiffiffi ð1:103bÞ ½exp l1 t exp l2 t for z . 1 2 z2 1 yimpulse ðtÞ ¼ hðtÞ ¼ v2n t expð vn tÞ for z ¼ 1 ð1:103cÞ An explanation concerning the dimensions of hðtÞ is appropriate here.

D. R. 1979. Industrial Noise and Vibration Control, Prentice Hall, Englewood Cliffs, NJ. Meirovitch, L. 1986. , McGraw Hill, New York. S. 1995. , Addison Wesley, Reading, MA. L. T. 1990. Dynamic Modeling and Control of Engineering Systems, MacMillan, New York. H. 1971. Introduction to System Dynamics, Addison Wesley, Reading, MA. F. 1979. , Wiley, New York. T. D. 1998. , Prentice Hall, Upper Saddle River, NJ. Volterra, E. C. 1965. Dynamics of Vibrations, Charles E. Merrill Books, Columbus, OH. 2 Clarence W.

2 1 19 Logarithmic Decrement Method The damping ratio z may be experimentally determined from the free response by the logarithmic decrement method. 67, the logarithmic decrement, zvn nT ¼ ln xðtÞ xðt þ nTÞ However, vn T ¼ vn vn 2p 2p 2p ¼ pffiffiffiffiffiffiffiffi ¼ pffiffiffiffiffiffiffiffi 2 vd 1 z vn 1 z2 Hence, with xðtÞ=xðt þ nTÞ ¼ r we have the logarithmic decrement. 2pnz pffiffiffiffiffiffiffiffi ¼ ln r 1 z2 Note that ð1=nÞln r is the “per cycle” logarithmic decrement and ð1=2pnÞln r is the “per radian” logarithmic decrement. The latter is z 1 pffiffiffiffiffiffiffiffi ¼ ln r ¼ a 2 p n 2 1 z Then, we have sffiffiffiffiffiffiffiffiffiffi a2 z¼ 1 þ a2 ð1:68Þ ð1:69Þ This is the basis of the logarithmic decrement method of measuring damping.

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Vibration and Shock Handbook (Mechanical Engineering) by Clarence W. de Silva

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