Vibration Characteristics of Simply Supported Thick Skew Plates in Three-Dimensional Setting

Abstract

A procedure is presented for determining the three-dimensional elasticity solutions for free vibration analysis of simply supported thick skew plates. The exact expressions of strain and kinetic energies are derived from linear, small-strain, three-dimensional elasticity theory. To allow the treatment of soft and hard simple support conditions, sets of three-dimensional spatial displacement functions are expressed in terms of unit normals to the edges. By virtue of the three-dimensional elasticity theory, the present method does not require a special treatment for stress singularity at the obtuse corners. This method is also demonstrated to be free from shear locking phenomena. The significant difference in the vibration response of skew plates with soft and hard simple support conditions is highlighted. The influence of skew angle on the eigenvalues of thick skew plate is discussed in the context of the three-dimensional elasticity solutions.