Fiber-reinforced composite laminates can be tailored to produce structural elastic couplings that optimize their response in dynamic environments. It is therefore essential that the free vibration characteristics of structural elements fabricated from fiber-reinforced composites be accurately modeled and investigated. In this work, an analytical wave-based approach is extended to study the in-plane vibrations of nonsymmetrically laminated cross-ply L-shaped frames. The proposed theory accounts for the effects of shear deformation, rotary inertia, and the elastic coupling between in-plane bending and longitudinal deformations. The reflection matrices at the boundaries, together with the reflection and transmission matrices at the corner joint of the L-shaped frame are derived. A traveling wave approach is then used to systematically assemble the small-order matrices into a single expression that can be used to efficiently calculate the exact natural frequencies. An expression for evaluating the mode shapes of the frame for general boundary conditions is also given. The application of the wave-based method is illustrated through several numerical examples and the results are validated using independent finite element models. As part of the numerical analysis, the influence of the number of cross-ply layers on the natural frequencies is investigated.

可以定制纤维增强复合层压板以生产结构弹性联轴器，以优化其在动态环境中的响应。因此，对由纤维增强复合材料制成的结构元件的自由振动特性进行准确建模和研究至关重要。在这项工作中，一种基于分析波的方法被扩展到研究非对称层压交叉层 L 形框架的平面内振动。所提出的理论考虑了剪切变形、旋转惯性以及平面内弯曲和纵向变形之间的弹性耦合的影响。导出边界处的反射矩阵，以及 L 形框架拐角处的反射和透射矩阵。然后使用行波方法将小阶矩阵系统地组合成单个表达式，该表达式可用于有效地计算精确的自然频率。还给出了用于评估一般边界条件框架模态振型的表达式。通过几个数值例子说明了基于波浪的方法的应用，并使用独立的有限元模型验证了结果。作为数值分析的一部分，研究了交叉层数对固有频率的影响。通过几个数值例子说明了基于波浪的方法的应用，并使用独立的有限元模型验证了结果。作为数值分析的一部分，研究了交叉层数对固有频率的影响。通过几个数值例子说明了基于波浪的方法的应用，并使用独立的有限元模型验证了结果。作为数值分析的一部分，研究了交叉层数对固有频率的影响。