Vibration characteristics of sandwich microshells with porous functionally graded face sheets

This work, for the first time, studies the vibrations of sandwich microshells with porous functionally graded face sheets by not neglecting in-surface curvilinear motions. The governing motion equations are formulated via Hamilton principle where a curvilinear framework for the modified couple stress (MCS) scheme is employed for the length-scale parameter participation. For the curvilinear and normal displacements, the vibration modes are assumed via trigonometric functions and the pertinent natural frequencies of the oscillatory motion are determined numerically. Effects of different layer arrangements, different layer material compositions and porosity-type imperfection on the vibration behaviour of the microsystem are studied. For verification purposes, the effect of size-dependence on the normal and curvilinear motions are cancelled as well as the porosity imperfections and also the nature of being functionally graded, and then the results of this simplified model are compared to an ANSYS based finite element model. Also, other simplified versions of the thin-walled microsystem are compared to the literature. All the verifications showed very good agreement.