Damping and Frequency Shift in Microscale Modified Couple Stress Thermoelastic Plate Resonators
Subject Areas : Engineering
1 - Department of Mathematics and Statistics, Himachal Pradesh University, Shimla, India
2 - Department of Mathematics, Kurukshetra University, India
Keywords:
Abstract :
Lord H.W., Shulman Y., 1967, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids 15: 299-309.
[2] Mindlin R. D., 1963, Influence of couple-stresses on stress-concentrations, Experimental Mechanics 3: 1-7.
[3] Mindlin R. D., Tiersten H. F., 1962, Effects of couple-stresses in linear elasticity, Archive for Rational Mechanics and Analysis 11: 415-448.
[4] Toupin R. A., 1962, Elastic materials with couple-stresses, Archive for Rational Mechanics and Analysis 11(1): 385-414.
[5] Yang F., Chong A. C. M., Lam D. C. C., Tong P., 2002, Couple stress based strain gradient theory for elasticity, International Journal of Solids and Structures 39: 2731-2743.
[6] Eringen A. C., 1966, Linear theory of micropolar elasticity, Journal of Mathematics and Mechanics 15: 909-923.
[7] Tsiatas G. C., 2009, A new Kirchhoff plate model based on a modified couple stress theory, International Journal of Solids and Structures 46: 2757-2764.
[8] Sun Y., Tohmyoh H., 2009, Thermoelasic damping of the axisymmetric vibration of circular plate resonators, Journal of Sound and Vibration 319: 392-405.
[9] Sun Y., Saka M., 2010, Thermoelasic damping in micro-scale circular plate resonators, Journal of Sound and Vibration 329: 338-337.
[10] Sharma J. N., Sharma R., 2011, Damping in micro-scale generalized thermoelastic circular plate resonators, Ultrasonics 51: 352-358.
[11] Ezzat M.A., El-Karamany A.S., Samaan A.A., 2001, State-space formulation to generalized thermoviscoelasticity with thermal relaxation, Journal of Thermal Stresses 24(9): 823-846.
[12] El-Karamany A.S., Ezzat M.A., 2002, On the boundary integral formulation of thermo-viscoelasticity theory, International Journal Engineering Sciences 40(17): 1943-1956
[13] Ezzat M.A., El-Karamany A. S., 2003, On uniqueness and reciprocity theorems for generalized thermoviscoelasticity with thermal relaxation, Canadian Journal of Physics 81(6): 823-833.
[14] Ezzat M.A., El-Karamany A.S., El-Bary A.A., 2017, Two-temperature theory in Green–Naghdi thermoelasticity with fractional phase-lag heat transfer, Microsystem Technologies 24(2): 951-961.
[15] Fang Y., Li P., Wang Z., 2013, Thermoelasic damping in the axisymmetric vibration of circular microplate resonators with two dimensional heat conduction, Journal of Thermal Stresses 36: 830-850.
[16] Shaat M., Mahmoud F. F., Gao X. L., 2014, Faheem A. F., 2014, Size-dependent bending analysis of Kirchhoff nano-plates based on a modified couple-stress theory including surface effects, International Journal of Mechanical Sciences 79: 31-37.
[17] Simsek M., Aydm M., Yurtcu H. H., Reddy J. N., 2015, Size-dependent vibration of a microplate under the action of a moving load based on the modified couple stress theory, Acta Mechanica 226: 3807-3822.
[18] Darijani H., Shahdadi A. H., 2015, A new shear deformation model with modified couple stress theory for microplates, Acta Mechanica 226(8): 2773-2788.
[19] Gao X. L., Zhan G. Y., 2016, A non-classical Kirchhoff plate model incorporating microstructure, surface energy and foundation effects, Continuum Mechanics and Thermodynamics 28: 195-213.
[20] Reddy J. N., Romanoff J., Loya J. A., 2016, Nonlinear finite element analysis of functionally graded circular plates with modified couple stress theory, European Journal of Mechanics- A/Solids 56: 92-104.
[21] Chen W., Wang Y., 2016, A model of composite laminated Reddy plate of the global-local theory based on new modified couple-stress theory, Mechanics of Advanced Materials and Structures 23(6): 636-651.
[22] Marin M., 1998, A temporally evolutionary equation in elasticity of micropolar bodies with voids, Scientific Bulletin Series A Applied Mathematics and Physics 60: 3-12.
[23] Marin M., 2010, Harmonic vibrations in thermoelasticity of microstretch materials, Journal of Vibration and Acoustics 132(4): 044501-044506.
[24] Sharma K., Marin M., 2013, Effect of distinct conductive and thermodynamic temperatures on the reflection of plane waves in micropolar elastic half-space, Scientific Bulletin Series A Applied Mathematics and Physics 75(2): 121-132.
[25] Marin M., Agarwal R. P., Codarcea L., 2017, A mathematical model for three-phase-lag dipolar thermoelastic bodies, Journal of Inequalities and Applications 109: 1-16.
[26] Rao S. S., 2007, Vibration of Continuous Systems, John Wiley & Sons, Inc. Hoboken, New Jersey.
[27] Sharma J. N., Kaur R., 2014, Transverse vibrations in thermoelastic-diffusive thin micro-beam resonators, Journal of Thermal Stresses 37: 1265-1285.
[28] Sharma J. N., 2011, Thermoelastic damping and frequency shift in Micro/Nanoscale anisotropic beams, Journal of Thermal Stresses 34(7): 650-666.
[29] Daliwal R.S., Singh A., 1980, Dynamical Coupled Thermoelasticity, Hindustan Publishers, Delhi.