A simple and efficient analytical model for the natural frequencies of sandwich plates made of flexible core and composite face sheets with embedded pre‐strained shape memory alloy wires

Abstract Two main goals are followed in the present work. The first objective is the development of a simple analytical model based on piecewise low‐order shear deformation theory (PLSDT) for the natural frequencies of sandwich plates made of flexible core with temperature‐dependent mechanical properties and laminated composite face sheets with embedded pre‐strained shape memory alloy (SMA) wires. Brinson's model is applied in this research to estimate the recovery stress produced by SMAs. A comparative study is performed to show the ability of the proposed model to offer high solution accuracy at low computational costs. Specifically, the results of the present research exhibit less than a 2% difference from those obtained from the mixed LW/ESL models in the framework of Carrera's unified formulation (CUF). As the second goal, the influences of some parameters such as the pre‐strain of SMAs, the volume fraction of SMAs, and core thickness on the fundamental frequencies of SMA‐reinforced sandwich plates are examined. The results reveal that depending on the geometric parameters and operating temperature, SMAs may have constructive or destructive effects on the free vibration of sandwich plates.