Free Vibration Response of FG Porous Sandwich Micro-Beam with Flexoelectric Face-Sheets Resting on Modified Silica Aerogel Foundation

Abstract

The free vibration analysis of sandwich micro-beam (SMB) which is subjected to electrical field is investigated by adopting the Euler–Bernoulli beam theory (EBBT) and modified strain gradient theory (MSGT). SMB is made of three layers, including a functionally graded (FG) porous core and two flexoelectric face-sheets. The porosities are assumed to be distributed over the beam thickness based on the two distribution functions. Also, due to the electric properties of flexoelectric materials, face-sheets of SMB are subjected to the external electric field. The modified Silica Aerogel foundation model is employed to consider the effects of elastic foundation on SMB. The size-dependent governing equations of motion are derived using Hamilton’s principle and solved by Navier’s solution method for a case of simply supported SMB. The effects of various parameters, such as length to thickness ratio, porosity index, flexoelectric loadings (the load applied to the flexoelectric face-sheets caused by external electric field), small scale parameter and foundation parameters on dimensionless frequency of SMB, are assessed. The results of this work can be used for optimum design and control of micro-electro-mechanical devices.