Abstract
A theoretical as well as a numerical investigation of the propagation of thermoelastic waves and vibration of transversely isotropic cylinders of finite length is discussed. Lord-Shulman theory is adopted here to model the thermoelastic deformation of cylinders. A semi analytical finite element (SAFE) method is employed to study dispersion of thermoelastic waves and natural frequencies of vibration of finite cylinders with traction free curved surfaces having both ends insulated and constrained by frictionless rigid walls. Numerical results obtained by the SAFE method for the frequencies of vibration of a sapphire rod are found to be in excellent agreement with published results. Natural frequencies of vibration for first three axisymmetric and asymmetric modes are presented graphically for a silicon nitride thermoelastic cylinder. Also, numerical results showing dispersion of both propagating and evanescent circumferential waves in infinite and finite cylinders are presented also.
Highlights
Isothermal vibration of finite–length cylinders has been studied by many investigators
In their study [6], they considered the axisymmetric vibrations of finite – length transversely isotropic cylinders and presented experimental results for sapphire rods. [8] estimated natural frequencies of axisymmetric modes of finite length transversely isotropic cylinders by applying the Ritz method. [9] and [10] studied axisymmetric and asymmetric vibrations of a finite transversely isotropic cylinder using potential functions and compared their results with the experimental observations of [6]. [11] studied free vibrations of finite orthotropic thin cylindrical shells by employing shell theory
The natural frequencies of vibration of finite length cylinders have been studied in the context of the L-S generalized theory of thermoelasticity
Summary
Isothermal vibration of finite–length cylinders has been studied by many investigators. In their study [6], they considered the axisymmetric vibrations of finite – length transversely isotropic cylinders and presented experimental results for sapphire rods. [8] estimated natural frequencies of axisymmetric modes of finite length transversely isotropic cylinders by applying the Ritz method. Thermoelastic circumferential wave propagation in a finite – length transversely isotropic cylinder has been investigated. To our knowledge, propagating and evanescent modes of circumferential waves in a finite-length transversely isotropic cylinder have not been studied in the past. Solutions obtained by the SAFE formulation are validated by comparing the numerical results for finite length transversely isotropic elastic cylinders (isothermal case) with those published by [9], [10]. Numerical results are presented here for both propagating and evanescent modes in a transversely isotropic silicon nitride cylinder
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