A two-parameter multiple shooting method and its application to the natural vibrations of non-prismatic multi-segment beams  

作　　者：R.HOŁUBOWSKI K.JARCZEWSKA 

机构地区：[1]Faculty of Civil Engineering,Wroc law University of Science and Technology,Wroc law 50-370,Poland

出　　处：《Applied Mathematics and Mechanics(English Edition)》2023年第12期2243-2252,共10页应用数学和力学（英文版）

摘　　要：This paper presents an enhanced version of the standard shooting method that enables problems with two unknown parameters to be solved.A novel approach is applied to the analysis of the natural vibrations of Euler-Bernoulli beams.The proposed algorithm,named as two-parameter multiple shooting method,is a new powerful numerical tool for calculating the natural frequencies and modes of multi-segment prismatic and non-prismatic beams with different boundary conditions.The impact of the axial force and additional point masses is also taken into account.Due to the fact that the method is based directly on the fourth-order ordinary differential equation,the structures do not have to be divided into many small elements to obtain an accurate enough solution,even though the geometry is very complex.To verify the proposed method,three different examples are considered,i.e.,a three-segment non-prismatic beam,a prismatic column subject to non-uniformly distributed compressive loads,and a two-segment beam with an additional point mass.Numerical analyses are carried out with the software MATHEMATICA.The results are compared with the solutions computed by the commercial finite element program SOFiSTiK.Good agreement is achieved,which confirms the correctness and high effectiveness of the formulated algorithm.

关 键 词：two-parameter multiple shooting method two-point boundary value problem natural vibration non-prismatic beam multi-segment beam 

分 类 号：O327[理学—一般力学与力学基础]