Vibration Response of a Sandwich Higher-Order Micro Beam based on Shear and Normal Deformation Theory on Kerr Elastic Foundation with Thickness Stretching Effect

Abstract

The novelty of this study is to consider the vibration analysis of a sandwich structure using shear and normal deformation beam theory (SNDBT) with a porous core and various reinforcement materials, including carbon nanorods (CNRs), graphene platelets (GPLs), and carbon nanotubes (CNTs), by considering the size effect based on modified couple stress theory (MCST) or nonlocal strain gradient theory (NSGT) on various elastic foundation such as Winkler, Pasternak, and Kerr, simultaneously. Also, each layer in the microbeam has different mechanical properties as a function of temperature. The governing equations of motion are derived using Hamilton's principle and the energy approach by considering the variational method, and then these equations are solved using Navier's method. The results are compared with those recently published by other scientists. The purpose of this study is to present a comprehensive and efficient innovative analytical framework for understanding the vibration behavior of a sandwich microbeams with different cores and reinforcements, and types of elastic foundations. In the higher-order shear and normal deformation theory by applying the stretching functions, the proposed model offers advantages that can increase the computational efficiency. In addition, a comprehensive parametric study is carried out to evaluate the effect of various properties, including porosity distributions, small-scale parameters, different elastic foundations, thickness, axial wave number, small-scale theories, volume fraction, and different reinforcements such as GPLs, CNTs, and CNRs. It is concluded that GPLs have the highest frequency, and CNRs have the lowest frequency. Also, by increasing the volume fraction of the reinforcements, the natural frequency of the sandwich microbeam increases for GPLs by 10%, the CNTs by 7%, and the CNRs by 4%. The current study shows that the considering of an elastic foundation for a beam has been demonstrated to result in an increase in the frequencies. Furthermore, the results with and without the thickness stretching effect show that the shear and normal beam theory improves the results. The natural frequency increases by 67.4%, when FG-XX is compared to FG-UU face sheets. It decreases by 24.8% when FG-OO is compared to FG-UU. The sandwich beams are compared to those without reinforcement.