Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

doi:10.1007/s10483-024-3125-8

Applied Mathematics and Mechanics (English Edition) ›› 2024, Vol. 45 ›› Issue (6): 983-1000.doi: https://doi.org/10.1007/s10483-024-3125-8

收稿日期:2024-01-18 出版日期:2024-06-03 发布日期:2024-06-01

Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

Xiaoyang SU¹^,²^,³, Tong HU¹, Wei ZHANG¹^,²^,³^,*(), Houjun KANG¹^,²^,³, Yunyue CONG¹^,²^,³, Quan YUAN¹

¹ School of Civil Engineering and Architecture, Guangxi University, Nanning 530004, China
² Scientific Research Center of Engineering Mechanics, Guangxi University, Nanning 530004, China
³ State Key Laboratory of Featured Metal Materials and Life-Cycle Safety for Composite Structures, Guangxi University, Nanning 530004, China

Received:2024-01-18 Online:2024-06-03 Published:2024-06-01
Contact: Wei ZHANG E-mail:sandyzhang9@163.com
Supported by:
the National Natural Science Foundation of China(12302007);the National Natural Science Foundation of China(12372006);the National Natural Science Foundation of China(12202109);the Specific Research Project of Guangxi for Research Bases and Talents(AD23026051);Project supported by the National Natural Science Foundation of China (Nos. 12302007, 12372006, and 12202109) and the Specific Research Project of Guangxi for Research Bases and Talents (No. AD23026051)

摘要/Abstract

Abstract:

Functionally graded materials (FGMs) are a novel class of composite materials that have attracted significant attention in the field of engineering due to their unique mechanical properties. This study aims to explore the dynamic behaviors of an FGM stepped beam with different boundary conditions based on an efficient solving method. Under the assumptions of the Euler-Bernoulli beam theory, the governing differential equations of an individual FGM beam are derived with Hamilton's principle and decoupled via the separation-of-variable approach. Then, the free and forced vibrations of the FGM stepped beam are solved with the transfer matrix method (TMM). Two models, i.e., a three-level FGM stepped beam and a five-level FGM stepped beam, are considered, and their natural frequencies and mode shapes are presented. To demonstrate the validity of the method in this paper, the simulation results by ABAQUS are also given. On this basis, the detailed parametric analyses on the frequencies and dynamic responses of the three-level FGM stepped beam are carried out. The results show the accuracy and efficiency of the TMM.

Key words: transfer matrix method (TMM), free vibration, forced vibration, functionally graded material (FGM), stepped beam

中图分类号:

00A71

. [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 983-1000.

Xiaoyang SU, Tong HU, Wei ZHANG, Houjun KANG, Yunyue CONG, Quan YUAN. Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions[J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(6): 983-1000.

图/表 24

参考文献 28

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Transfer matrix method for free and forced vibrations of multi-level functionally graded material stepped beams with different boundary conditions

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