On wave propagation in a random micropolar thermoelastic medium, second moments, and associated Green’s tensor
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Cites background or methods from "On wave propagation in a random mic..."
...The components of Green’s tensor corresponding to L0 < V0 >¼ dð~x, ~x 0Þdij were computed earlier by Mitra and Bhattacharyya [13] in the form: Glj ¼ G0 G1 0 G2 G3 0 0 0 G4 0 @ 1 A (14) where G4 rð Þ ¼ 14pr e ibrI3, b ¼ b1 þ ib2, sayð Þ, and b1 ¼ xg0 2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ t20x2 q þ t0x 1 2 , b2 ¼ xg0 2 0 ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 1þ t20x2 q t0x 1 2 : (15) Now, L0 < V ~xð Þ > ¼ q0- 2~A k0 þ l0ð Þ ~k:~A ~k ðl0 þ j0Þk2~A þ ij0ð~k ~BÞ ij0 ~k ~A a0 þ b0ð Þ~k ~k:~B c0k2~B 2j0~B þ q0jx2~B ixg0 1 ixt0ð ÞC 0k2C 0 BB@ 1 CCA ei~k:~x : (16) Now by virtue of (10) and (11), we get < L1 >< V ~xð Þ > ¼ i m2 ixm3ð ÞC~k 0 xh0m2ð1 ixt0dlkÞð~k:~AÞ 0 B@ 1 CAei~k:~x : (17) < L2 >< V ~xð Þ > ¼ 0: (18) < L1 > L 1 0 < L1 >< V ~xð Þ > ¼ ei~k:~x ð xh0m2 1 ixt0dlkð Þ m2 ixm3ð Þ ~k:~A r!...
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...It has been shown that the mean field quantity, < V >, a seven-vector, representing the displacement vector, the micro-rotation vector, and temperature, satisfies an integro-differential equation involving the associated Green’s tensor which was computed by Mitra and Bhattacharyya [13]....
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...Mitra and Bhattacharyya [13] perhaps for the first time endeavored to study wave propagation phenomenon in the micropolar thermoelastic medium, second moments and associated Green’s tensor in the random domain....
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...were computed earlier by Mitra and Bhattacharyya [13] in the form:...
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4 citations
Cites background or methods from "On wave propagation in a random mic..."
...[16] R. K. Bhattacharyya, “On wave propagation in a random magneto-thermo-viscoelastic medium,” Ind. J. Pure Appl....
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...The present paper perhaps is the second attempt in micropolar literature at computing effects of random variation of parameters in a well-defined interacting medium, the first one being the paper by Mitra and Bhattacharyya [14]....
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...Earlier, Bhattacharyya in two © Taylor & Francis Group, LLC successive papers ([15], [16]) examined problems of wave propagation in a random magneto-thermo-viscoelastic medium and wave propagation in a random magnetothermo-viscoelastic medium respectively....
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...Kumar and coworkers studied various problems of wave propagation, reflection CONTACT R.K. Bhattacharyya rabindrakb@yahoo.com Biswakosh Lane, Kolkata , India. and refraction in micropolar elastic, micropolar thermoelastic and micro-stretch media ([6], [7])....
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...Bhattacharyya ([16], [42]) and Bera [17] pursued the method in the study of wave propagation phenomena in coupled media....
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References
929 citations
"On wave propagation in a random mic..." refers background or methods in this paper
...[25] Eringen AC....
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...[2] Eringen AC....
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...References [1] Eringen AC....
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...The equations of motion, constitutive equations, and boundary conditions for the micropolar elastic field have been derived by Eringen [1,2]....
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...[4] Eringen AC....
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584 citations
376 citations
"On wave propagation in a random mic..." refers background in this paper
...The classical thermoelasticity instead of generalized thermoelasticity [9] has been chosen as the first simplest model in the random micropolar thermal domain of research....
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