Size-dependent thermomechanical vibration of FGP microbeams using a higher-order shear deformable beam element

Abstract The thermoelastic vibration of porous microbeams is explored via a higher-order shear deformable element. The porosities are smoothly graded in the beam thickness, while the elastic moduli are temperature-dependent. The theory of third-order shear deformation is employed to formulate a size-dependent beam element, in which the theory of couple stress theory is used to model the microstructural size effect. The frequencies are predicted for microbeams with different and conditions. The performance of the formulated element is shown through a comparison study. The impacts of the size scale parameter, coefficient of porosities as well as the boundary conditions on the frequencies are highlighted. The impacts of temperature change on the vibration of the porous microbeams are also studied and discussed.