Experimental and theoretical studies of free vibration of a sandwich functionally graded nanocomposite beam under thermal condition

Abstract

The free vibration analysis of a sandwich three-layer functionally graded beam is studied experimentally and theoretically based on Timoshenko beam theory. The beam consists of a pure epoxy in the mid-plane and two inhomogeneous multi walled carbon nanotube (MWCNT)/epoxy nanocomposite on the upper and lower layers. The effect of weight fraction of MWCNT on the first natural frequency are obtained theoretically and experimentally and then compared with each other in this study. The effect of distribution of MWCNT is studied through a semi-analytical approach. A detailed parametric study is conducted on functionally graded MWCNT/epoxy beams. The effects of geometrical parameters, boundary conditions, slenderness ratio and temperature change are also studied. The differential quadrature method is employed as a numerical method to solve the equations of motion. The main contribution of this work is to present comparable experimental and theoretical results for sandwich functionally graded beams. Comparison of the results revealed that the obtained non-dimensional frequencies from theoretical approach are in good agreement with experimental results, especially for lower weight fractions of carbon nanotubes.