Abstract
Mechanical systems in general consist of structural components which have distributed mass and elasticity. Examples of these structural components are rods, beams, plates, and shells. Our study of vibration thus far has been limited to discrete systems which have a finite number of degrees of freedom. As has been shown in the preceding chapters, the vibration of mechanical systems with lumped masses and discrete elastic elements is governed by a set of second-order ordinary differential equations. Rods, shafts, beams, and other structural components on the other hand are considered as continuous systems which have an infinite number of degrees of freedom. The vibration of such systems is governed by partial differential equations which involve variables that depend on time as well as the spatial coordinates.
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Dym, C. L., & Shames, I. H. (1973). Solid mechanics: A variational approach. New York: McGraw-Hill.
Timoshenko, S., Young, D. H., & Weaver, W. (1974). Vibration problems in engineering. New York: Wiley.
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Shabana, A. (2019). Vibration of Continuous Systems. In: Vibration of Discrete and Continuous Systems. Mechanical Engineering Series. Springer, Cham. https://doi.org/10.1007/978-3-030-04348-3_4
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DOI: https://doi.org/10.1007/978-3-030-04348-3_4
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Online ISBN: 978-3-030-04348-3
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