Nonlinear analyses of magneto-electro-elastic laminated beams in thermal environments

Abstract

This paper is concerned with the nonlinear vibration and bending problems of magneto-electro-elastic laminated beams in thermal environments. A higher order shear beam theory in conjunction with von Kármán type of kinematic nonlinearity is considered in the beam model. As a prior, the temperature field in the beam is determined by solving the heat conducting equation, and the magneto-electric field is obtained based on magneto-electric equilibrium relationships. Then, the nonlinear governing equations are obtained considering the magneto-electro-thermo-elastic coupling. A two-step perturbation technique applied to the dimensionless governing equations results in the solutions of various nonlinear problems. Finally, the numerical calculations are performed to investigate the nonlinear vibration, nonlinear bending, and magneto-electric potential distributions through the thickness of the beam in different thermal environmental conditions. The results reveal that the material lay-up and temperature have a significant influence on the nonlinear mechanical behaviors as well as the magneto-electric potential responses of the magneto-electro-elastic laminated beams. Moreover, it is found in the studies that the magneto-electric potential distributions vary significantly with the degree of bending deformation.