Analysis of waves in micropolar generalized thermoelastic plate with memory dependent derivatives

Abstract

AbstractA new model has been framed for mathematical investigation of a micropolar thermoelastic plate with memory dependent derivatives (MDDs). The governing equations are expressed for the two‐dimensional (2‐D) case and simplified by using dimensionless quantities. The resulting equations are decomposed by considering the Helmholtz decomposition approach and the normal mode analysis technique is applied for further investigation. The normal mode analysis is a powerful technique that provides appropriate solutions with no assumptive restriction on the temperature, displacement and stress distributions. The dispersion equations for symmetric and anti‐symmetric modes are obtained for stress‐free isothermal and insulated thermal restrictions on the boundary surface of the plate. The characteristics of waves for symmetric and anti‐symmetric modes are examined under the impact of MDD and different classical and generalized theories of thermoelasticity. Numerical solutions of the dispersion equations for both symmetric and anti‐symmetric modes are presented graphically employing MATLAB programming software. Various particular cases are explored. The obtained results are also compared with some earlier studies.