Dynamic Behaviors of Composite-Laminated Concentrically Stiffened Rectangular Plates by Substructure Modal Synthesis

Existing numerical analysis methods often incur high computational costs when directly solving multi-degree-of-freedom systems due to computer capacity limitations. To address this issue, this paper took the composite laminated concentrically stiffened rectangular plate as the research object. The modal synthesis method was employed to reduce the degrees of freedom of the model, enabling the solution of complex dynamic characteristics. In the research process, the domain decomposition theory was used to divide the research object into plate and rib substructures. Based on the spectral Chebyshev method, the substructure dynamic model of the composite laminated rectangular plate was constructed. Subsequently, the function expressions of the complex load excitation on each substructure were derived, and the fixed modal synthesis method was introduced to construct the spectral Chebyshev reduced model of the substructures. According to the artificial spring theory equivalent, the interface force, and the whole reduction model of the composite laminated concentrically stiffened rectangular plate were obtained by assembling the substructure models. The time–domain and frequency–domain dynamic behaviors of composite laminated concentrically stiffened rectangular plates are yielded by solving the whole reduced model. The novelty of this work lies in combining the spectral Chebyshev method with the modal synthesis method. The established reduced model no longer depended on mesh quality and required fewer matrix dimensions and computation time compared to the whole model, while still achieving sufficiently accurate results. Additionally, based on the reduced model, an effective parametric study scheme was proposed to analyze the impact of dimensions and material properties of rib substructures on the dynamic behaviors of the composite laminated concentrically stiffened rectangular plate. These findings can be used to guide the optimal design of laminated concentrically stiffened rectangular plates in engineering practice.