As was said in the Introduction, Poisson’s reduction of the 3-D equations of elasticity to 1-D equations of low-frequency vibrations of rods has been the subject of many revisions and extensions to higher frequencies. In this chapter we highlight the application of the variationalasymptotic method in deriving a one-dimensional theory of elastic rods that describes their vibrations in a wide range of frequencies.
KeywordsDispersion Curve Strain Energy Density Longitudinal Vibration Flexural Vibration Edge Mode
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