Plane waves in nonlocal generalized thermoelasticity
The Lord–Shulman (LS) model of generalized thermoelasticity and the Eringen's model of nonlocal elasticity are used to formulate the new constitutive relations and the field equations. The propagation of plane thermoelastic waves are then probed in a homogeneous isotropic nonlocal thermoelastic solid by employing this new model. We found two sets of the coupled longitudinal waves and one independent shear-type wave. All these waves are found to be dispersive and attenuating in nature in the presence of nonlocality in the medium. We found that the shear-type wave faces a critical frequency, while the coupled longitudinal waves may face critical frequency conditionally. A reflection of thermoelastic waves at a stress-free thermally insulated and isothermal boundary of a thermoelastic half-space are also considered in case of incident coupled longitudinal thermoelastic wave. The amplitude ratios of the reflected waves to that incident wave are determined analytically. For a particular model, various graphs are plotted to analyze the behavior of the phase speeds, attenuation coefficients and reflection coefficients. To investigate the effect of elastic nonlocal parameter on the variations of phase speeds, attenuation coefficients and amplitude ratios of the reflected waves are presented graphically. Some interesting results are noticed: All the waves are detected to be influenced by the nonlocality of the medium. The longitudinal waves are influenced by the thermal parameters but the shear-type wave is independent of the thermal effect. Moreover the presence of elastic nonlocality reduces the classical shear-type wave speed.
|Journal||Data powered by TypesetZAMM Journal of applied mathematics and mechanics: Zeitschrift für angewandte Mathematik und Mechanik|
|Publisher||Data powered by TypesetWiley Online Library|