Laser generated thermoelastic waves in finite and infinite transversely isotropic cylinders
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Date
2010, 2011, 2011
Authors
Chitikireddy, Ravi
Journal Title
Journal ISSN
Volume Title
Publisher
Taylor & Francis Group, LLC
Mathematical Sciences Publishers
Elsevier Ltd.
Mathematical Sciences Publishers
Elsevier Ltd.
Abstract
This thesis presents a theoretical study of thermoelastic guided waves in cylinders in the context of Lord-Shulman generalized theory of thermoelasticity. Two different methods were formulated to study dispersion relations in infinite cylinders. One of them is a Semi Analytical Finite Element (SAFE) method and the other is an analytical method. In the SAFE method, the dispersion equation has been formulated as a generalized eigenvalue problem by treating radial displacement and temperature with a one dimensional finite element model through the thickness of the cylinder. In the analytical method, displacement potentials are introduced to obtain the dispersion relations of guided wave modes. This method is applicable to isotropic cylinders and has been developed primarily to cross check the SAFE formulation. Frequency spectra obtained by both methods for an isotropic cylinder have shown excellent agreement with each other. Since the SAFE method can be used for an anisotropic composite cylinder, guided wave modes for anisotropic and composite cylinders are presented.
Transient analysis of ultrasonic guided waves generated by concentrated heating of the outer surface of an infinite anisotropic cylinder has also been studied. The SAFE method is employed to model the response of a cylinder due to a pulsed laser focused on its surface. Green’s functions were constructed numerically by superposition of guided wave modes in frequency and wave number domains. Time histories of the propagating modes are then calculated by applying an inverse Fourier transformation in the time domain. Transient radial displacements of longitudinal and flexural modes of a silicon nitride cylinder are presented.
Propagation of thermoelastic waves in finite length circular cylinders have also been investigated. The SAFE method is used to simulate the guided wave modes in the cylinder. Frequency spectra obtained by the SAFE formulation, for a finite length transversely isotropic cylinder, are validated by comparing the numerical results with relevant publications. Frequency spectra for axisymmetric and asymmetric modes in a silicon nitride finite cylinder with both ends insulated and restrained by frictionless rigid walls are presented. The plain strain problem of circumferential guided waves is also studied and the results are validated for an isothermal case.
Description
Keywords
Thermoelastic waves, Ultrasonic guided waves, Semi-analytical finite element, Frequency spectra, Modal superposition, Transient response
Citation
Journal of thermal stresses
Journal of Mechanics of Materials and Structures
International Journal of Solids and Structures
Journal of Mechanics of Materials and Structures
International Journal of Solids and Structures