Free in-plane vibration of plates with arbitrary curvilinear geometry: Spectral-Chebyshev model and experimental study

Abstract

The spectral-Chebyshev method is firstly applied to the free in-plane vibration of arbitrarily shaped plates with curvilinear geometry under different boundary conditions. With the aim of facilitating the calculation of energy, an arbitrarily shaped plate is mapped into a square plate by the one-to-one coordinate transformation. The displacement functions of the plate after transformation are then generally expressed as the two-dimensional Chebyshev polynomials. The experimental study of in-plane natural frequencies of six aluminum plates with different shapes is carried out for the first time, including free boundary conditions and cantilever support boundary conditions. The proposed spectral-Chebyshev method is applied to simulate the in-plane vibration of six aluminum plates to evaluate the precision and demonstrate the applicability of the current solution. The present calculated natural frequencies converge with the increase of Chebyshev polynomials and are in good agreement with the experimental results and the FEM solution. Thus, our conclusion is that the current spectral-Chebyshev model can accurately and quickly calculate the in-plane vibration of plates with arbitrary curvilinear geometry. Moreover, the in-plane experimental results of plates with six different curvilinear geometries can provide a reference for future theoretical research.