Vibration analysis of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory

Abstract

Abstract This paper studies the free vibration characteristics of arbitrary straight-sided quadrilateral plates using a simple first-order shear deformation theory (SFSDT), which contains only four unknown displacement components. The arbitrary straight-sided quadrilateral plate is mapped into a unit square plate uniformly, and accordingly, the problem can be solved directly by the existing vibration modeling method of rectangular plate. The admissible functions of displacements are generally expressed as superposition of the periodic functions based on the improved Fourier series method. All the series expansion coefficients can be determined by the Rayleigh-Ritz procedure. Combined with the artificial virtual spring technology, the present method could be used to analyze the vibration characteristics of quadrilateral plates under arbitrary boundary conditions. Convergence and accuracy of the present method are checked out through some numerical examples of plate with rectangular, skew, trapezoidal and general quadrilateral shapes, and various boundary conditions. In addition, some new results and new conclusions have been given as the benchmark for future research.