Free vibration of orthotropic skew plates

The main purpose of this paper is to develop a fast converging semianalytic al method for assessing the vibration effect on thin orthotropic skew (or p arallelogram/oblique) plates. Since the geometry of the skew plate is not h elpful in the mathematical treatments, the analysis is often performed by m ore complicated and laborious methods. A successive conjunction of the Kant orovich method and the transition matrix is exploited herein to develop a n ew modification of the finite strip method to reduce the complexity of the problem. The displacement function is expressed as the product of a basic t rigonometric series function in the longitudinal direction and an unknown f unction that has to be determined in the other direction. Using the new tra nsition matrix, after necessary simplification and the satisfaction of the boundary conditions, yields a set of simultaneous equations that leads to t he characteristic matrix of vibration. The influence of the skew angle, the aspect ration, the properties of orthotropy, and the prescribed boundary c onditions are investigated. Convergence of the solution is investigated and the accuracy of the results is compared with that available from other num erical methods. The numerical results show that the convergence is rapidly deduced and the comparisons agree very well with known results. [S0739-3717 (00)00202-6].