Dynamic Analysis of Sigmoid Bidirectional FG Microbeams under Moving Load and Thermal Load: Analytical Laplace Solution

This paper presents for the first time a closed-form solution of dynamic response sigmoid bidirectional functionally graded (SBDFG) microbeams under moving harmonic load and thermal environmental conditions. The formulation is established in context modified couple stress theory to integrate effects microstructure. On basis elasticity theory, nonclassical governing equations are derived by using Hamilton’s principle combination with parabolic higher-order shear deformation considering physical neutral plane concept. Sigmoid distribution functions used describe temperature-dependent thermomechanical material bulk continuums beam both axial thickness directions, gradation length scale parameter also considered. Linear nonlinear temperature profiles considered present loads. Laplace transform exploited evaluate proposed model simply supported (SS) boundary condition. verified comparing predicted fundamental frequency previously published results. A parametric study conducted explore impacts gradient indices parameters, loads, speed acted on microbeams. results can serve as evaluating multi-functional optimal design upon load.