A unified solution for free in-plane vibration of orthotropic circular, annular and sector plates with general boundary conditions

摘要

To study the free in-plane vibration for the orthotropic circular, annular and sector plates with general boundary conditions, a modified Fourier-Ritz approach is developed. In this approach, several auxiliary closed-form functions are added to the standard Fourier cosine series to obtain a robust function. The introduction of these auxiliary functions can eliminate all the potential discontinuities of the original displacement function and its derivatives in whole domain and then effectively improve the convergence of the results. All the displacements are expressed with the modified Fourier series expansion and the arbitrary boundary conditions and the appropriate continuity conditions along the radial edges are realized by introducing the artificial boundary spring technique and artificial coupling spring technique. In addition, the Ritz procedure based on the energy functions of the plates is adopted to obtain the accurate solution since the constructed displacement field is adequately smooth in the whole solution domain. By numerical examples involving the plates of various shapes and with different boundary conditions, the reliability, accuracy and versatility of the current method get fully demonstrated. On this basis, some new results for the free in-plane vibration problem of orthotropic circular, annular and sector plates with various boundary conditions and the parameter study are also presented, which may be served as benchmark solutions for future researches.