Exact Finite Strip Method for Free Vibration of Axially Moving Sandwich Plate with FGM Face Sheets

In this article, an exact finite strip method is developed for free vibration of axially moving thin sandwich plate made of functionally graded material (FGM). For this purpose, the plate is divided to several finite strips. Displacement function of the strip along direction perpendicular to moving direction is assumed sinusoidal. The function along another direction has an exponential form as satisfies the differential equation governing the vibration of such sandwich plates and the boundary conditions of the problem. By defining nodal displacement and nodal forces at any line of a finite strip, the exact stiffness matrix of the strip is extracted. This matrix is a transcendental function of natural frequencies, axial speed, membrane forces, volume fraction exponent, and other parameters of geometry and material characteristics of the problem. Using global stiffness matrix of the plate, the natural frequencies of the plate which is under in-plane forces and moves on several rollers are calculated. Comparison studies are performed to verify the validity of the present results. The exact vibration solutions obtained for such plates are indeed valuable as they serve as important benchmark solutions for checking the convergence and accuracy of numerical methods for the analysis of such plates.