Numerical Study of Characteristic Equations of Thermoelastic Waves Propagating in a Uniaxial Prestressed Isotropic Plate

Shih-Ming Hsu ； Ching-Chung Yin

《ISRN Applied Mathematics》 2011 (2011/12) Pp. 532-547

並列摘要

Thermoplastic waves propagating in an isotropic thin plate exerted by a uniaxial tensile stress are represented in this work. Characteristic equation of guided thermoelastic waves is formulated based on the theory of acoustoelasticity and classical thermoelasticity. Curve-tracing method for complex root finding is used to determine the attenuation, which is the imaginary part of the complex-value wavenumber. It is found that each plate mode of thermoplastic wave propagating in an isotropic plate with or without pre-stress has a minimum attenuation at a specific frequency except the A(subscript 0) mode. These modes are called the Lamé modes, which are the volume resonances in the thickness direction and propagate along the plate with the least energy dissipation. Frequency spectra of the phase velocity dispersion and attenuation of thermoplastic waves propagating along various orientations in the uniaxial pre-stressed thin plate have further been discussed.