Free vibration analysis of orthotropic doubly-curved shallow shells based on the gradient elasticity

The comprehensive free vibration analysis of doubly-curved shallow shells which are made of an orthotropic material is presented. The size effect is taken into consideration using the gradient elasticity theory. Novozhilov's linear shallow shell theory is used and it is assumed that the shell is simply supported. The governing equations of the doubly-curved shallow shells with consideration of the length scales are developed. Analytical solutions to the equations are proposed to obtain the frequencies of the shells. Numerical results are presented for various shell curvatures including spherical, cylindrical and hyperbolic paraboloidal shells and compared with those available in the literature. (c) 2012 Elsevier Ltd. All rights reserved.