Dynamics of nonlinear transversely vibrating beams: Parametric and closed-form solutions

被引：8

作者：

Qin, Yupeng ^{[1
]}

Wang, Zhen ^{[2
,3
]}

Zou, Li ^{[4
,5
]}

机构：

[1] Henan Inst Technol, Sch Sci, Xinxiang 453003, Henan, Peoples R China

[2] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[3] Guangdong Ocean Univ, Sch Ocean Engn, Zhanjiang 524088, Peoples R China

[4] Dalian Univ Technol, Sch Naval Architecture, State Key Lab Struct Anal Ind Equipment, Dalian 116024, Peoples R China

[5] Collaborat Innovat Ctr Adv Ship & Deep Sea Explor, Shanghai 200240, Peoples R China

来源：

APPLIED MATHEMATICAL MODELLING | 2020年 / 88卷

基金：

中国国家自然科学基金;

关键词：

Nonlinear transversely vibrating beams; Periodic vibration; Parametric and closed-form solution; Trigonometric function; Jacobi elliptic function; ENERGY-BALANCE;

D O I：

10.1016/j.apm.2020.06.056

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

Nonlinear transversely vibrating beams, including a uniform beam carrying a lumped mass and a transversely vibrating quintic nonlinear beam, are considered in this paper. Firstly, using trigonometric function, analytical solutions to their Cauchy initial problems are constructed in parametric and closed-form. Secondly, it is found that one has the freedom to choose any periodic function to simulate the periodic vibration theoretically. As an example, we also construct parametric and closed-form solution expressed by Jacobi elliptic function. Thirdly, by comparing the two kinds of derived solutions, it is shown that the Jacobi elliptic function solution can degenerate to the corresponding trigonometric function solution when the modulus tends to zero. Comparison are also made between our derived Jacobi elliptic function solution and other's exact solution, which indicates that the presented parametric solution method is more general. (C) 2020 Elsevier Inc. All rights reserved.

引用

页码：676 / 687

页数：12