Open AccessAn Improved Analytical Method for Vibration Analysis of Variable Section Beam
Author(s) -
Jingjing Feng,
Zhengneng Chen,
Shuying Hao,
Kunpeng Zhang
Publication year - 2020
Publication title -
mathematical problems in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.262
H-Index - 62
eISSN - 1026-7077
pISSN - 1024-123X
DOI - 10.1155/2020/3658146
Subject(s) - correctness , variable (mathematics) , vibration , beam (structure) , section (typography) , convergence (economics) , modal , modal analysis , function (biology) , piecewise , mathematics , adomian decomposition method , finite element method , mathematical analysis , algorithm , computer science , structural engineering , differential equation , engineering , physics , acoustics , polymer chemistry , economics , biology , economic growth , operating system , chemistry , evolutionary biology
The variable section structure could be the physical model of many vibration problems, and its analysis becomes more complicated either. It is very important to know how to obtain the exact solution of the modal function and the natural frequency effectively. In this paper, a general analytical method, based on segmentation view and iteration calculation, is proposed to obtain the modal function and natural frequency of the beam with an arbitrary variable section. In the calculation, the section function of the beam is considered as an arbitrary function directly, and then the result is obtained by the proposed method that could have high precision. In addition, the total amount of calculation caused by high-order Taylor expansion is reduced greatly by comparing with the original Adomian decomposition method (ADM). Several examples of the typical beam with different variable sections are calculated to show the excellent calculation accuracy and convergence of the proposed method. The correctness and effectiveness of the proposed method are verified also by comparing the results of the several kinds of the theoretical method, finite element simulation, and experimental method.