Plane waves in nonlocal thermoelastic solid with voids
Abstract: This work is concerned with the propagation of time harmonic plane waves in an infinite nonlocal thermoelastic solid having void pores. Three sets of coupled dilatational waves and an independent transverse wave may travel with distinct speeds in the medium. All these waves are found to be dispersive in nature, but the coupled dilatational waves are attenuating, while transverse wave is nonattenuating. Coupled dilatational waves are found to be influenced by the presence of voids, thermal field and elastic nonlocal parameter. While the transverse wave is found to be influenced by the nonlocal parameter, but independent of void and thermal parameters. For a particular model, the effects of frequency, void parameters, thermal parameter and nonlocality have been studied numerically on the phase speeds, attenuation coefficients and specific losses of all the propagating waves. All the computed results obtained have been depicted graphically and explained.
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Citations
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Cites background or methods or result from "Plane waves in nonlocal thermoelast..."
...reduces to the classical transverse wave speed, a result recently obtained by Sarkar and Tomar [14] in the relevant medium when r 61⁄4 1....
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...Within the framework of Eringen’s theory of nonlocal elasticity [1], the constitutive relations for thermoelastic solid with voids are given by [12,14] 1 e2r2 ð Þsij 1⁄4 sij 1⁄4 2leij þ kekk þ b/ ch ð Þdij; (1) 1 e2r2 ð Þhi 1⁄4 hij 1⁄4 a/;i; (2) 1 e2r2 ð Þg 1⁄4 g 1⁄4 s _ / n/ bekk þmh; (3) 1 e2r2 ð Þqg 1⁄4 qg ð Þ 1⁄4 cekk þ ahþm/; (4)...
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...(28) gives the coupled longitudinal wave velocities for Lord-Shulman thermoelastic model [19] which are recently obtained by Sarkar and Tomar [14]....
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...For this purpose, we have borrowed the values of relevant material parameters from Sarkar and Tomar [14] and Sing et al....
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...This shows that x 1⁄4 xc acts as a cutoff frequency for the existing transverse wave, a conclusion in accordance with that earlier mentioned by Sarkar and Tomar [14]....
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19 citations
Cites background from "Plane waves in nonlocal thermoelast..."
...Khurana and Tomar [12] extended the theory of nonlocal elasticity to nonlocal theory of microstretch elasticity and then they investigated wave propagation in nonlocal microstretch solid....
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...Recently, Sarkar and Tomar [20] studied plane waves in nonlocal thermoelastic solid with voids and thermal relaxation time and Mondal et al....
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...Recently, Sarkar and Tomar [20] studied plane waves in nonlocal thermoelastic solid with voids and thermal relaxation time and Mondal et al. [21] reported waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity....
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19 citations
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References
4,124 citations
"Plane waves in nonlocal thermoelast..." refers background in this paper
...(23)–(26) propagating in the positive direction of a unit vector n with speed c, we take the form of various potentials as [45,53,54] /; h; q;W f g 1⁄4 A/;Ah;Aq;B exp ik n r ct ð Þ ; (27) where A/; Ah and Aq are constant amplitudes, which may be complex, i 1⁄4 ffiffiffiffiffiffi 1 p is imaginary number, B is a vector constant, r ð1⁄4 x̂i þ ŷj þ zk̂Þ is the position vector and k is the wavenumber....
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2,848 citations
"Plane waves in nonlocal thermoelast..." refers methods in this paper
...These relations and equations are the same as those obtained in the Lord–Shulman theory [51,52] of thermoelasticity with one relaxation time....
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1,930 citations
"Plane waves in nonlocal thermoelast..." refers background in this paper
...(23)–(26) propagating in the positive direction of a unit vector n with speed c, we take the form of various potentials as [45,53,54] /; h; q;W f g 1⁄4 A/;Ah;Aq;B exp ik n r ct ð Þ ; (27) where A/; Ah and Aq are constant amplitudes, which may be complex, i 1⁄4 ffiffiffiffiffiffi 1 p is imaginary number, B is a vector constant, r ð1⁄4 x̂i þ ŷj þ zk̂Þ is the position vector and k is the wavenumber....
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1,929 citations
"Plane waves in nonlocal thermoelast..." refers background in this paper
...The theory of classical coupled thermoelasticity (CCT) [1] is found to be penurious for many physically acceptable situations....
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...Introduction The theory of classical coupled thermoelasticity (CCT) [1] is found to be penurious for many physically acceptable situations....
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1,821 citations