RESEARCH PAPER
Forced vibrations of a thermoelastic double porous microbeam subjected to a moving load

More details
Hide details
 1 Kurukshetra University, Department of Mathematics, Kurukshetra, Haryana, India 2 H.P. University, Department of Mathematics and Statistics, Shimla, HP, India
Publish date: 2019-01-20
Submission date: 2017-05-09
Acceptance date: 2018-08-23

Journal of Theoretical and Applied Mechanics 2019;57(1):155–166
KEYWORDS:
ABSTRACT:
The present paper deals with forced vibrations of a homogeneous, isotropic thermoelastic double porous microbeam subjected to moving load, in context of Lord-Shulman theory of thermoelasticity with one relaxation time. The Laplace transform has been applied to obtain expressions for the axial displacement, lateral deflection, volume fraction field and temperature distribution. A numerical inversion technique has been used to recover the resulting quantities in the physical domain. Effects of velocity and time parameters are shown graphically by plotting axial displacement, lateral deflection, volume fraction field and temperature distribution against distance. Some particular cases are also deduced.

REFERENCES (23):
 1 Barenblatt G.I., Zheltov I.P., Kochina I.N., 1960, Basic concept in the theory of seepage of homogeneous liquids in fissured rocks (strata), Journal of Applied Mathematics and Mechanics, 24, 1286-1303. 2 Biot M.A., 1941, General theory of three-dimensional consolidation, Journal of Applied Physics, 12, 155-164. 3 Chang T.P., Liu Y.N., 1996, Dynamic finite element analysis of a nonlinear beam subjected to a moving load, International Journal of Solids and Structures, 33, 12, 1673-1688. 4 Cowin S.C., Nunziato J.W., 1983, Linear elastic materials with voids, Journal of Elasticity, 13, 125-147. 5 Esen I., 2015, A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory, Latin American Journal of Solids and Structures, 12, 808-830. 6 Honig G., Hirdes U., 1984, A method for the numerical inversion of the Laplace transforms, Journal of Computational and Applied Mathematics, 10, 113-132. 7 Iesan D., Quintanilla R., 2014, On a theory of thermoelastic materials with a double porosity structure, Journal of Thermal Stresses, 37, 1017-1036. 8 Kaghazian A., Hajnayeb A., Foruzande H., 2017, Free vibration analysis of a piezoelectric nanobeam using nonlocal elasticity theory, Structural Engineering and Mechanics, 61, 5, 617-624. 9 Kargarnovin M.H., Ahmadian M.T., Talookolaei R.A.J., 2012, Dynamics of a delaminated Timoshenko beam subjected to a moving oscillatory mass, Mechanics Based Design of Structures and Machines, 40, 2, 218-240. 10 Khalili N., 2003, Coupling effects in double porosity media with deformable matrix, Geophysical Research Letters, 30, 22, 2153, DOI: 10.1029/2003GL018544. 11 Kumar R., 2016, Response of thermoelastic beam due to thermal source in modified couple stress theory, Computational Methods in Science and Technology, 22, 2, 95-101. 12 Kumar R., Vohra R., Gorla M.G., 2015, State space approach to boundary value problem for thermoelastic material with double porosity, Applied Mathematics and Computation, 271, 1038-1052. 13 Lord H., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of Mechanics and Physics of Solids, 15, 299-309. 14 Mehri B., Davar A., Rahmani O., 2009, Dynamic Green function solution of beams under a moving load with different boundary conditions, Scientia Iranica, 16, 3, 273-279. 15 Michaltsos G., Sopianopoulo D., Kounadis A.N., 1996, The effect of moving mass and other parameters on the dynamic response of a simply supported beam, Journal of Sound and Vibration, 191, 357-362. 16 Nunziato J.W., Cowin S.C., 1979, A nonlinear theory of elastic materials with voids, Archive of Rational Mechanics and Analysis, 72, 175-201. 17 Olsson M., 1991, On the fundamental moving load problem, Journal of Sound and Vibration, 145, 2, 299-307. 18 Rao G.W., 2000, Linear dynamics of an elastic beam under moving loads, Journal of Vibration and Acoustics, 122, 3, 281-289. 19 Sharma J.N., Grover D., 2011, Thermoelastic Vibrations in micro-/nano-scale beam resonators with voids, Journal of Sound and Vibration, 330, 2964-2977. 20 Sherief H., Saleh H., 2005, A half space problem in the theory of generalized thermoelastic diffusion, International Journal of Solids and Structures, 42, 4484-4493. 21 Sun Y., Fang D, Saka M , Soh A.K., 2008, Laser-induced vibrations of micro-beams under different boundary conditions, International Journal of Solids and Structures, 45, 1993-2013. 22 Tzou D., 1996, Macro-to-Micro Heat transfer, Taylor & Francis, Washington DC. 23 Zenkour A.M., 2017, Thermoelastic response of a microbeam embedded in visco-Pasternak’s medium based on GN-III model, Journal of Thermal Stresses, 40, 2, 198-210.
 eISSN: 2543-6309 ISSN: 1429-2955