Closed form solutions – Analysis and optimal design of supersonic composite laminated flat plates considering mechanical and thermal effects

Abstract

Bolotin (1961) published the book presenting the analytical solution of the flutter problem for isotropic plates having finite dimensions (i.e. a width and a length). His results are much more broader than those discussed by Hedgepeth (1956) and Houbolt (1958) for plates having one infinite dimension (i.e. in fact reduced to the analysis of beams). The present paper is an extension of Bolotin’s analytical method to the analysis of multilayered laminated plates and includes the analysis of anisotropic plates with different wavenumbers m, n at the x and y directions, respectively. It is shown how easily that method can be used in the optimal analysis of laminated plates searching for the maximal aerodynamic pressure. In our opinion the obtained results can be easily adopted as the benchmark for numerical (finite element) investigations of flutter problems for plates. The effects of in-plane mechanical and thermal loads, boundary conditions, stacking sequences and orthotropic modulus ratio on flutter characteristics are examined in an analytical way. The analysis is conducted for the normal oncoming flow.