In aerospace and automotive industries, structural designs are required to meet specific weight limits whilst maintaining strength and stiffness. The material of choice for such applications is fiber-reinforced composites because of their high strength-to-weight and stiffness-to-weight ratios. Composite materials used in these applications are often subjected to random dynamic loads and if the excitation sources are large enough, excessive vibration can lead to unwanted noise levels and fatigue failure. A commonly used design tool for modeling the vibration transmission and power flow in structures excited by random forces is statistical energy analysis. In order to incorporate fiber-reinforced composites within a statistical energy analysis methodology, a detailed understanding of how the modal energy levels vary when excited by a broadband random excitation source is needed. In this paper, analytical expressions are derived for the modal energy levels of a fiber-reinforced composite beam coupled in bending and torsion subjected to spatial white noise or the so-called rain-on-the-roof loading. It is shown that the modal energy levels of the fiber-reinforced composite beam are markedly nonuniform across the modal spectrum. This finding is in contrast with the well-known classical result that an isotropic beam subjected to the same type of excitation is characterized by a uniform modal energy spectrum, a result sometimes referred to as the equipartition of energy. The equipartition of energy forms the basis of statistical energy analysis and the results of this work indicate that fiber-reinforced composite beams cannot be reliably included into a conventional statistical energy analysis methodology. It is also shown that the mechanism responsible for the nonuniform modal energy distribution is related to the physical process by which power is transmitted across the boundaries. Simulations are also carried out to illustrate that the distribution characteristics of the modal energy are identical for a range of classical boundary conditions.

在航空航天和汽车工业中，要求结构设计满足特定的重量限制，同时又要保持强度和刚度。此类应用的首选材料是纤维增强复合材料，因为它们具有高的强度重量比和刚度重量比。这些应用中使用的复合材料通常会承受随机的动态载荷，如果激励源足够大，则过度的振动会导致不希望的噪音水平和疲劳破坏。用于对随机力激发的结构中的振动传递和功率流进行建模的常用设计工具是统计能量分析。为了将纤维增强复合材料纳入统计能量分析方法中，需要对宽带随机激发源激发时模态能级如何变化的详细理解。在本文中，导出了在空间白噪声或所谓的屋顶雨水荷载作用下，弯曲和扭转耦合的纤维增强复合梁的模态能级的解析表达式。结果表明，纤维增强复合材料梁的模态能级在模态谱上明显不均匀。该发现与众所周知的经典结果相反，经典的结果是，经受相同类型激发的各向同性光束的特征在于均匀的模态能谱，该结果有时称为能量均分。能量的均分构成了统计能量分析的基础，这项工作的结果表明，纤维增强的复合梁不能可靠地包含在常规统计能量分析方法中。还表明，负责非均匀模态能量分配的机制与功率跨边界传输的物理过程有关。还进行了仿真，以说明对于一系列经典边界条件，模态能量的分布特性是相同的。还表明，负责非均匀模态能量分配的机制与跨边界传输功率的物理过程有关。还进行了仿真，以说明对于一系列经典边界条件，模态能量的分布特性是相同的。还表明，负责非均匀模态能量分配的机制与跨边界传输功率的物理过程有关。还进行了仿真，以说明对于一系列经典边界条件，模态能量的分布特性是相同的。