Vibration Analysis of Doubly Curved Shallow Shells With Elastic Edge Restraints

An analytical method is derived for the vibration analysis of doubly curved shallow shells with arbitrary elastic supports alone its edges, a class of problems which are rarely attempted in the literature. Under this framework, all the classical homogeneous boundary conditions for both in-plane and out-of-plane displacements can be universally treated as the special cases when the stiffness for each of restraining springs is equal to either zero or infinity. Regardless of the boundary conditions, the displacement functions are invariably expanded as an improved trigonometric series which converges uniformly and polynomially over the entire solution domain. All the unknown expansion coefficients are treated as the generalized coordinates and solved using the Rayleigh–Ritz technique. Unlike most of the existing solution techniques, the current method offers a unified solution to a wide spectrum of shell problems involving, such as different boundary conditions, varying material and geometric properties with no need of modifying or adapting the solution schemes and implementing procedures. A numerical example is presented to demonstrate the accuracy and reliability of the current method.