Dynamic performance of composite laminate wing beam structures of aeronautical engineering with complex geometrical profiles

Critical aerostructures, such as wings, spars, and propellers, can be considered beam structures with complex geometrical profiles and varying stiffness along the axial direction, complicating their dynamic performance analysis. Therefore, this paper proposes a novel method for the dynamic modeling of composite laminate beams with complex geometrical profiles (CLBCGP). To overcome the difficulty of analytic geometry integration introduced by complex geometrical profiles and the heterogeneous stiffness of laminate composites, the CLBCGP is assumed to be divided into a series of discrete data points uniformly distributed along the axial direction. Meanwhile, a discrete displacement function with variable thickness weighting for CLBCGP is constructed for the first time, and Composite Simpson's numerical integration is imported to calculate the kinetic and potential energies of CLBCGP with arbitrary support in a hygrothermal environment. The governing equation is derived via the Lagrange equation, and then experimental investigations are carried out to confirm the validity of the proposed method. Finally, the stress distribution and dynamic properties of CLBCGP under basic excitation, elastic boundaries, and hygrothermal conditions are systematically investigated. The methodology resolves the numerical divergence of conventional approaches, enabling 2,000th-order calculations with an accuracy of approximately 1e-10, providing a high-precision solution for the dynamics of composite variable-section beams. Concurrently, the methodology is equally efficacious for beams exhibiting markedly nonlinear axial stiffness.