A New Method for Analyzing Dynamic Characteristics of Generalized Planar Frame Structures Under Complex Conditions

This paper presents a novel method for analyzing the vibration characteristics of planar frame structure composed of straight beams with arbitrary shapes. The method is based on the first-order shear theory, which takes into account the shear deformation and cross-sectional rotational inertia of the beams. On the one hand, an improved Fourier series method (IFSM) is employed to approximate the displacement function of the straight beam, and the displacements are determined by using the Rayleigh–Ritz method. On the other hand, the displacements of the curved beam are obtained by using the finite element method (FEM), which are then combined with the IFSM for the analysis of coupled nodes of straight and curved beams. This results in a computational method for calculating the vibration characteristics of complex planar frame structures with concentrated masses, straight and curved beams, arbitrary boundary conditions, and any connection form of nodes. The applicability of the proposed method is demonstrated through numerical examples, including planar frame structure with arbitrary shapes composed of straight beams, different cross-sectional shapes, and combinations of beam with various cross-sectional shapes, as well as planar frame structures with straight and curved beams. The results of the proposed method are validated by comparing them with those obtained from literature or finite element software ABAQUS. The numerical examples show that the proposed method combining the IFSM with FEM has the advantages of high accuracy, good convergence, and strong applicability for calculating the vibration characteristics of planar frame structures.