Analytical solutions to the fundamental frequency of arbitrary laminated plates under various boundary conditions

Abstract

In recent years, as the composite laminated plates are widely used in engineering practice such as aerospace, marine and building engineering, the vibration problem of the composite laminated plates is becoming more and more important. Frequency, especially the fundamental frequency, has been considered as an important factor in vibration problem. In this paper, a calculation method of the fundamental frequency of arbitrary laminated plates under various boundary conditions is proposed. The vibration differential equation of the laminated plates is established at the beginning of this paper and the frequency formulae of specialty orthotropic laminated plates under various boundary conditions and antisymmetric angle-ply laminated plates with simply-supported edges are investigated. They are proved to be correct. Simple algorithm of the fundamental frequency for multilayer antisymmetric and arbitrary laminated plates under various boundary conditions is studied by a series of typical examples. From the perspective of coupling, when the number of laminated plates layers N > 8–10, some coupling influence on the fundamental frequency can be neglected. It is reasonable to use specialty orthotropic laminated plates with the same thickness but less layers to calculate the corresponding fundamental frequency of laminated plates. Several examples are conducted to prove correctness of this conclusion. At the end of this paper, the influence of the selected number of layers of specialty orthotropic laminates on the fundamental frequency is investigated. The accuracy and complexity are determined by the number of layers. It is necessary to use proper number of layers of special orthotropic laminates with the same thickness to simulate the fundamental frequency in different boundary conditions.

Keywords

laminated plates / arbitrary orientation / analytical solutions / fundamental frequency / boundary conditions