Three-dimensional vibration analysis of cantilevered skew plates

Abstract

Three-dimensional (3-D) free vibration of cantilevered thick skew plates is analyzed, based on the exact, linear and small-strain elasticity theory. The skew domain of the plate is mapped onto a cubic domain. A set of triplicate Chebyshev polynomials multiplied by a boundary function is developed as the trial functions of each displacement components. Using the Ritz method, the eigenvalue equation is derived from the strain energy and kinetic energy of the plate. The vibration modes are divided into the antisymmetric and symmetric ones in the thickness direction, therefore, can be studied individually. The convergence study shows that the first eight frequency parameters for each mode categories can be obtained with an accuracy of at least four significant figures. The effect of geometric parameters, such as skew angle, aspect ratio and span-thickness ratio, on frequency parameters is studied. The results are compared with those obtained by using the algebraic polynomials as trial functions and the 3-D finite element solutions, respectively. It is shown that the Chebyshev polynomials can provide better numerical stability than the algebraic polynomials, especially for the plates with large skew angle. The present results can serve as the benchmark data for the accuracy evaluation of other computational techniques.