Vibratory characteristics of pretwisted cantilever trapezoids of unsymmetric laminates

Treated in this paper is a theoretical investigation on the vibratory characteristics of twisted unsymmetric laminates. An approach based on the global energy principle is developed to examine the effects of initial twist upon the vibration response of cantilevered unsymmetric laminates of a trapezoidal planform. It employs the Ritz extremum energy principle with a set of admissible pb-2 shape functions. These kinematically orientated pb-2 shape functions are composed of the product of 1) mathematically complete two-dimensional orthogonally generated polynomials and 2) a basic function to ensure satisfaction of the geometric boundary conditions. Numerical convergence of the eigenvalues is established by increasing the degree of polynomial of the shape functions. Results covering wide ranges of angles of twist and fiber orientation for 2-ply, 4-ply and 8-ply unsymmetric graphite/epoxy laminates are presented. Several findings with respect to these results are highlighted and conclusions are drawn. Finally, a set of vibration mode shapes illustrating the effects of aspect ratio, chord ratio, angles of twist, and fiber orientation is also included.