Flutter of clamped orthotropic rectangular plate

A new approach for dynamic stability analysis of rectangular orthotropic plates is presented. In particular, in the approximation of the theory of planar sections the problem of the flutter of a panel in a supersonic gas flow is reduced to a boundary value problem for nonsymmetric differential operator. To improve standard technique of the Bubnov-Galerkin method, it is proposed to use new analytical representations of the eigenmodes of vibrations of a rectangular orthotropic plate in a vacuum as the basis functions of this method. According to this approach, the boundary value problem is essentially reduced to a homogeneous infinite system of linear algebraic equations. By using the asymptotic analysis and theory of regular infinite systems of linear algebraic equations, the effective and accurate algorithm for constructing the mode shapes in vacuum is developed. So, both the algorithm for constructing basis functions and the algorithm for determining the critical value of the velocity parameter are presented in this paper. The convergence of the Bubnov-Galerkin method is studied numerically for different problem parameters. The results of numerical modeling show that good convergence of the method can be achieved with first 16 basis functions when the values of in-plane forces and elastic constants vary. An analogous convergence of the method is also observed for an elongated plate. The computational efficiency of the method is illustrated by examples.