Fiber-reinforced composites are used in many weight critical applications owing to their high strength-to-weight and stiffness-to-weight ratios. In certain applications, fiber-reinforced composites are subjected to broadband excitation sources that act over a significant portion of the audible frequency range leading to the response of a large number of higher order structural modes. In predicting the response levels of such systems, regardless of whether it is modeled in isolation or using a statistical energy analysis framework, it becomes necessary to quantify the number of resonant modes available to receive and store energy within a frequency band. Conventionally, the mode count and modal density are two parameters used for this purpose. Generally, the analysis of the mode count and modal density of anisotropic fiber-reinforced composite structures have received considerably less attention compared to their isotropic metallic counterparts, and as a result a number of key analytical formulations are yet to be derived and investigated. In this work, the modal distribution and density of nonsymmetric cross-ply laminated composite beams coupled in bending and longitudinal extension are analyzed. A wave approach is used to derive an expression for the mode count of the beam having generalized boundary conditions. Using numerical examples and nonlinear regression analysis, simplified expressions are then obtained for the average mode count function of the beam for different boundary conditions. An analytical expression for the modal density is obtained by taking the differential of the average mode count function with respect to frequency. The wave approach employed in this study is validated based on comparison with results from past literature in addition to finite element simulations. The expression for the modal density is also validated using a finite element model and is shown to be independent of boundary conditions.
Laminated composite stiffened shallow spherical panels with cutouts under free vibration – A finite element approach