In-plane and out-of-plane vibration analysis of laminated composite frames with warping effects

This paper addresses the free vibration analysis of a general planar frame structure, consisting of an assembly of laminated composite beam members. A mathematical model is established for the beams by introducing a novel displacement field, which encompasses the influence of shear deformation, rotary inertia, material coupling, warping phenomenon, as well as in-plane and out-of-plane deformations. By incorporating these various factors, a comprehensive representation of the beam's behavior is achieved. The continuity equations for displacements and rotations of two adjacent members are formulated to derive the equations for the entire frame structure. The assembled equations are solved using the Finite Element Method (FEM). The numerical results obtained are compared with existing results in the literature and new results from 3D models in ANSYS. The present results for torsional modes are closer to the ANSYS results than the results of previous studies. An extensive analysis is performed to investigate the impact of various parameters, including stacking sequence, frame angle, relative frame length, and anisotropy ratios on the system response.