Simulation of the eigenvalue problem for tapered rotating beams by the modified decomposition method

被引：2
作者：
Duan J.-S. [1 ]
Rach R. [2 ]
Wazwaz A.-M. [3 ]
机构：
[1] School of Sciences, Shanghai Institute of Technology, Shanghai
[2] Hartford, MI
[3] Department of Mathematics, Saint Xavier University, Chicago, IL
来源：
International Journal for Computational Methods in Engineering Science and Mechanics | 2022年 / 23卷 / 01期
基金：
中国国家自然科学基金;
关键词：
Adomian decomposition method; centrifugal stiffening; eigenvalue problem; mode shape; Rotating beams;
D O I：
10.1080/15502287.2021.1904461
中图分类号：
学科分类号：
摘要：
The modified decomposition method is applied to analyze the transverse vibrations of tapered rotating beams incorporating both axial centrifugal stiffening and flexible end constraints. Unlike prior analyses relying upon a power series expansion about the left end constraint, we instead expand the solution for the transverse deflection about the interval midpoint, which has significant advantages including an increased rate of convergence and readily adaptation to the Robin-type boundary conditions. The modified decomposition method facilitates systematic solution of the mathematical model including parametric simulations where the boundary conditions can be varied without resolving the original equation. © 2021 Taylor & Francis Group, LLC.
引用
收藏
页码：20 / 28
页数：8
相关论文
共 28 条
  • [1] Naguleswaran S., A direct solution for the transverse vibration of Euler-Bernoulli wedge and cone beams, J. Sound Vibration, 172, 3, pp. 289-304, (1994)
  • [2] Wang G., Wereley N.M., Free vibration analysis of rotating blades with uniform tapers, AIAA j., 42, 12, pp. 2429-2437, (2004)
  • [3] Hodges D.H., Rutkowski M.J., Free-vibration analysis of rotating beams by a variable-order finite-element method, AIAA j., 19, 11, pp. 1459-1466, (1981)
  • [4] Adair D., Jaeger M., Simulation of tapered rotating beams with centrifugal stiffening using the Adomian decomposition method, Appl. Math. Modelling, 40, 4, pp. 3230-3241, (2016)
  • [5] Mao Q., Application of Adomian modified decomposition method to free vibration analysis of rotating beams, Math. Probl. Eng, 2013, pp. 1-10, (2013)
  • [6] Banerjee J.R., Free vibration of centrifugally stiffened uniform and tapered beams using the dynamic stiffness method, J. Sound Vibration, 233, 5, pp. 857-875, (2000)
  • [7] Hsu J.C., Lai H.Y., Chen C.K., Free vibration of non-uniform Euler-Bernoulli beams with general elastically end constraints using Adomian modified decomposition method, J. Sound Vibration, 318, 4-5, pp. 965-981, (2008)
  • [8] Maganti N.V.R., Nalluri M.R., Chordwise bending vibration analysis of functionally graded double-tapered rotating beams, Int. J. Comput. Methods Eng. Sci. Mech, 16, 1, pp. 1-10, (2015)
  • [9] Wang C.M., Zhang H., Gao R.P., Duan W.H., Challamel N., Hencky bar-chain model for buckling and vibration of beams with elastic end restraints, Int. J. Str. Stab. Dyn, 15, 7, (2015)
  • [10] Baroudi D., Giorgio I., Battista A., Turco E., Igumnov L.A., Nonlinear dynamics of uniformly loaded Elastica: Experimental and numerical evidence of motion around curled stable equilibrium configurations, Z. Angew. Math. Mech, 99, 7, pp. 201800121,, (2019)
123