Free vibration of sandwich micro-beam with porous foam core,GPL layers and piezo-magneto-electric facesheets via NSGT

The aim of this research is to investigate free vibration of a novel five layer Timoshenko microbeam which consists of a transversely flexible porous core made of Al-foam, two graphen platelets (GPL) nanocomposite reinforced layers to enhance the mechanical behavior of the structure as well as two piezo-magneto-electric face sheets layers. This microbeam is subjected to a thermal load and resting on Pasternak\'s foundation. To accomplish the analysis, constitutive equations of each layer are derived by means of nonlocal strain gradient theory (NSGT) to capture size dependent effects. Then, the Hamilton\'s principle is employed to obtain the equations of motion for five layer Timoshenko microbeam. They are subsequently solved analytically by applying Navier\'s method so that discretized governing equations are determined in form of dynamic matrix giving the possibility to gain the natural frequencies of the Timoshenko microbeam. Eventually, after a validation study, the numerical results are presented to study and discuss the influences of various parameters such as nonlocal parameter, strain gradient parameter, aspect ratio, porosity, various volume fraction and distributions of graphene platelets, temperature change and elastic foundation coefficients on natural frequencies of the sandwich microbeam.