Wave propagation in transversely isotropic plates in generalized thermoelasticity

Verma, K. L.; Hasebe, Norio

doi:10.1007/s00419-002-0215-z

Cited by 17 publications

(3 citation statements)

References 20 publications

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“…Wu and Zhu [19] endeavored to investigate the Lamb‐type wave motion in an elastic plate which is plunged into the non‐viscous fluid and derived the secular equations. Verma and Hasebe [20] focused to solve the boundary value problem related to the wave propagation in the transversely isotropic plate of finite thickness in the context of generalized thermoelasticity. Al‐Qahtani and Datta [21] attempted to analyze the propagation of generalized thermoelastic waves in an infinitely extended homogeneous, thermally conducting, anisotropic plate using three different methods.…”

Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

Pathania

Dhiman

2022

Z Angew Math Mech

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In this contribution, the thermoelastic Lamb waves in the homogeneous, transversely isotropic, plate with voids have been investigated in the context of classical and non‐classical theories of thermoelasticity. To investigate the problem, the fundamental governing equations have been developed in a unified way. On the solutions of these governing equations, the thermal and mechanical stress‐free boundary conditions, as well as constraints due to voids, have been imposed. The solutions of governing equations indicate that there exists a coupled system of wave motion called thermal waves (T‐mode), void wave motion (V‐mode), and elastic waves (E‐mode). However, the shear horizontal component of elastic wave decouples from the system is unaffected by elasto‐poro‐thermal coupling. For the symmetric and anti‐symmetric families of vibrations, the secular equation for the wave motion along with its special cases has been derived. To discover the wave characteristics, the secular equation has been solved using the numerical‐functional iteration method in MATLAB software, and the findings have been manifested by plotting the graphs. It has been concluded that the presence of voids affects the magnitudes of phase velocity, attenuation coefficient, and specific loss. This work may be helpful for geophysicists and engineers in the field of earthquake engineering. The developers of modern facilitating things such as acoustic touch screens, liquid viscosity sensors, etc. which are based on Lamb‐type wave propagation may also get benefitted.

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Section: Introductionmentioning

confidence: 99%

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

Pathania

Dhiman

2022

Z Angew Math Mech

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“…Dynamic distribution of displacements and thermal stresses in multilayered media, in generalized thermoelasticity, has been studied by Verma et al [23]. Verma [24] and Verma and Hasebe [25] investigated wave propagation problems in transversely isotropic plates in generalized thermoelasticity. Verma and Hasebe [26] studied the wave propagation in plates of general anisotropic solids in generalized theory of thermoelasticity.…”

Section: Introductionmentioning

confidence: 99%

Ultrasonic waves in an orthorhombic porous piezo-thermoelastic laminated structure immersed in a fluid

Vashishth¹,

Sukhija²,

Gupta³

2016

Smart Mater. Struct.

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Reflection and transmission of plane elastic waves in porous piezo-thermoelastic laminated plate immersed in a fluid has been studied. A theoretical model is derived which is based on transfer matrix method. The layered structure is considered to be consisting of ‘n’ number of layers of porous piezo-thermoelastic materials immersed in a fluid. All the layers are considered to be 2 mm PPTE materials. The formal solution for the mechanical displacements, electric potential, mechanical stresses, electric displacements, temperature changes and temperature gradient are derived. The transfer matrix technique is used to study the layered materials. The closed form expressions of the elements of transfer matrix are derived. The analytical expressions for the reflection coefficient and transmission coefficient are derived. The effects of frequency, angle of incidence, number of layers, layer’s thickness and porosity on the reflection coefficient and transmission coefficient, reflection loss and transmission loss are investigated numerically for different configurations. Particular cases of the present study have also been obtained for the verification of the results.

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“…Nevertheless, the problem is not formally intractable and has been extended and solved by various Dhaliwal and Sherief (1980) and Banerjee and Pao (1974). Many problems in generalized thermoelasticity are considered and solved by Verma (1997);Verma (2001Verma ( , 2002Verma ( , 2012; Bajeet(2012); Verma and Hasebe (2002); Verma and Hasebe (2004). Chiriţă (2013) studied the Rayleigh surface waves on an anisotropic homogeneous thermoelastic half space.…”

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confidence: 99%

Thermoelastic slowness surfaces in anisotropic media with thermal relaxation

Verma¹

2014

Lat. Am. j. solids struct.

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Analysis for general closed form solution of the thermoelastic waves in anisotropic heat conducting materials is obtained by using the solution technique for the biquadratic equation in the framework of the generalized theory of thermoelasticity. Obtained results are general in nature and can be applied to the materials of higher symmetry classes such as transvesely isotropic, cubic, and isotropic materials. Uncoupled and coupled thermoelasticity are the particular cases of the obtained results. Numerical computations are carried out on a fiber reinforced heat conducting composite plate modeled as a transversely isotropic media. The two dimensional slowness curves corresponding to different thermal relaxations are presented graphically and characteristics displayed are analyzed with thermal relaxations. Keywords Slowness Surfaces; thermoelasticity; anisotropic; coupled and thermal relaxation times.Thermoelastic slowness surfaces in anisotropic media with thermal relaxation INTRODUCTIONMost materials experience volumetric variations when are subjected to temperature variations and the consequent thermal stresses developed due to temperature gradient in the surface vicinity results in micro-crack and others imperfection development at the surface of anisotropic materials. Thus owing to anisotropic material's applications in aeronautics, astronautics, plasma physics, nuclear reactors and high-energy particle and in various others engineering sciences, theory of thermoelasticity has aroused intense attention in our challenge to understand the nature of the interaction between temperature and strain fields. Main characteristics of the waves when they propagate within an anisotropic media are: phase and group velocities depend on direction -anisotropy, there is a difference between the phase velocity (propagation of the wave) and the group velocity (propagation of energy), occur shear wave splitting. Since the last century generation of waves in thermoelasticity is already known by chopping the sunlight coming onto a heat conduct-

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Wave propagation in transversely isotropic plates in generalized thermoelasticity

Cited by 17 publications

References 20 publications

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

Generalized thermoelastic waves in a homogeneous anisotropic plate with voids

Ultrasonic waves in an orthorhombic porous piezo-thermoelastic laminated structure immersed in a fluid

Thermoelastic slowness surfaces in anisotropic media with thermal relaxation

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