Study on the Seismic Response of a Portal Frame Structure Based on the Transfer Matrix Method of Multibody System

Abstract

Portal frame structures are widely used in industrial building design but unfortunately are often damaged during an earthquake. As a result, a study on the seismic response of this type of structure is important to both human safety and future building designs. Traditionally, finite element methods such as the ANSYS and MIDAS have been used as the primary methods of computing the response of such a structure during an earthquake; however, these methods yield low calculation efficiencies. In this paper, the mechanical model of a single-story portal frame structure with two spans is constructed based on the transfer matrix method of multibody system (MS-TMM); both the transfer matrix of the components in the model and the total transfer matrix equation of the structure are derived, and the corresponding MATLAB program is compiled to determine the natural period and seismic response of the structure. The results show that the results based on the MS-TMM are similar to those obtained by ANSYS, but the calculation time of the MS-TMM method is only 1/20 of that of the ANSYS method. Additionally, it is shown that the MS-TMM method greatly increases the calculation efficiency while maintaining accuracy.

A Review of the Vibration Analysis Methods for Frame Structures

“…Reference [41] implemented the transfer matrix method of multi-body systems when analyzing portal frames. The investigation successfully achieved computing times that were one-seventh that of ANSYS finite element methods.…”

A simplified method of soft connected battery module for finite element method model of battery pack

“…Hence, the model size is small and can be calculated rapidly. In some research studies, this idea is applied to building structural models in civil engineering field, and its efficiency is far beyond that of FEM model 20‐22 . For the problem of soft‐connected module modeling, the multibody method can not only significantly decline model size, but also maintain the discreteness of the structure, making the simplified model consistent with practical structure.…”

“…For example, in civil engineering, some researchers discretized the continuous structure, and then the multibody dynamic model is used for rapid vibration analysis and earthquake response prediction of building structure. The result shows that multibody model precedes the FEM model apparently in efficiency 19‐22 …”

Free vibrations of planar serial frame structures in the case of axially functionally graded materials

“…A more complex problem is discussed in [2], where elastic joints are introduced at the joints of homogeneous beams of the constant cross-section, while the solutions for equations are compared to the FEM analysis and experimental data. Paper [3] analyzes the portal frame structure, where mass discretization was carried out and a model with a finite number of DOFs was created instead of solving partial differential equations, and the results for such a model were verified by FEM. Coupled partial differential equations are also analytically solved in [4] in the case of planar multi-story frame structures.…”