Analytical Solutions to the Fundamental Frequency of Arbitrary Laminated Plates under Various Boundary Conditions

在最近的年里，当合成把压成薄片的盘子广泛地在工程被使用，练习例如设计的太空，水兵和大楼，合成把压成薄片的盘子的颤动问题正在变得越来越重要。频率，特别基本频率，处于颤动问题被看作了一个重要因素。在这份报纸，在各种各样的边界条件下面的任意的把压成薄片的盘子的基本频率的一个计算方法被建议。颤动把压成薄片的盘子的微分方程在这份报纸的开始被建立，特长 orthotropic 的频率公式在各种各样的边界条件和反对称的角度厚度下面把盘子压成薄片有简单地支持的边的把压成薄片的盘子被调查。他们被证明正确。为在各种各样的边界条件下面的多层的反对称、任意的把压成薄片的盘子的基本频率的简单算法被一系列典型例子学习。从联合的观点，什么时候把压成薄片的盘子层 N 的数字 > 810，对基本频率的一些联合影响能被忽视。orthotropic 与一样的厚度，但是少些把盘子压成薄片，对使用特长合理计算把压成薄片的盘子的相应基本频率的层。几个例子被进行证明这个结论的正确性。在这份报纸的结束， orthotropic 在基本频率上把压成薄片的特长的层的选择数字的影响被调查。精确性和复杂性被层的数字决定。它对特殊 orthotropic 的层的合适的数字与一样的厚度把压成薄片处于不同边界条件模仿基本频率的使用必要。

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.