A Method of Finding the Principal Modes of Nonlinear Vibration Systems and Their Stabilities

Liu Lian-sheng; Huo Quan-zhong; Huang Ke-lei

Volume 8 Issue 6

Turn off MathJax

Article Contents

Abstract

References

Article Navigation > Applied Mathematics and Mechanics > 1987 > 8(6): 505-512

Liu Lian-sheng, Huo Quan-zhong, Huang Ke-lei. A Method of Finding the Principal Modes of Nonlinear Vibration Systems and Their Stabilities[J]. Applied Mathematics and Mechanics, 1987, 8(6): 505-512.

Citation:

Liu Lian-sheng, Huo Quan-zhong, Huang Ke-lei. A Method of Finding the Principal Modes of Nonlinear Vibration Systems and Their Stabilities[J]. Applied Mathematics and Mechanics, 1987, 8(6): 505-512.

Citation:

Liu Lian-sheng, Huo Quan-zhong, Huang Ke-lei. A Method of Finding the Principal Modes of Nonlinear Vibration Systems and Their Stabilities[J]. Applied Mathematics and Mechanics, 1987, 8(6): 505-512.

PDF( 475 KB)

A Method of Finding the Principal Modes of Nonlinear Vibration Systems and Their Stabilities

1.
Beijing Institute of Aeronautics and Astronautics, Beijing;
2.
Tianjin University, Tianjin

Received Date: 1986-03-24
Publish Date: 1987-06-15

Abstract

Abstract

This paper presents a new method of finding the principal modes of nonlinear vibration systems,by means of which the problem of finding principal modes of nonlinear systems is transferred to the problem of finding real roots of a set of algebraic equations.The method is applicable to various kinds of nonlinear vibration systems with many degrees of freedom,and is simple in calculation.The paper presents another new method of analyzing the stabilities of principal modes of nonlinear systems.

FullText(HTML)

References(6)

References

[1]	Rosenberg,R.M.,Normal modes of nonlinear dual-mode systems,ASME,J,Appl.Mech.,27,E,2(1960),263-268.
[2]	Rosenberg,R.M.,On nonlinear vibrations of systems with many degrees of freedom,Adv.in Appl.Mech.,9,Acad.Press(1966).
[3]	Cooke,C.H.and R.A.Struble,On the existence of periodic solutions and normal mode vibrations of nonlinear systems,Quart.Appl.Math.,24,3(1966),177-193.
[4]	Pecelli,G.and E.S.Thomas,Normal modes,uncoupling,and stability for a class of nonlinear oseillators,Quart.Appl.Math.,37,3(1979),281-301.
[5]	Szemplinska-Stupnicka,W.,The resonant vibration homogeneous non-linear systems,Int.J.Nonl.Mech.,15(1980),407-415.
[6]	Van der Varst,P.G.Th.,On normal mode vibrations of nonlinear conservative systems,Ph.D.Thesis,Eindhoven Univ.of Tech.,Netherland(1982).

Relative Articles

[1]	ZHAI Guoqing, CHEN Qiaoyu, TONG Dongbing, ZHOU Wuneng. Fixed-Time Asymptotic Stability and Energy Consumption Estimation of Nonlinear Systems[J]. Applied Mathematics and Mechanics, 2023, 44(10): 1180-1186. doi: 10.21656/1000-0887.440041
[2]	HU Lijun, ZHAO Kunlei. A Modified Roe Scheme and Stability Analysis[J]. Applied Mathematics and Mechanics, 2020, 41(10): 1110-1124. doi: 10.21656/1000-0887.400388
[3]	HU Li-jun, YUAN Li. Analysis of Numerical Shock Instability and a Hybrid Curing Method[J]. Applied Mathematics and Mechanics, 2015, 36(5): 482-493. doi: 10.3879/j.issn.1000-0887.2015.05.004
[4]	LI Feng-ming, LIU Chun-chuan. Parametric Vibration Stability and Active Control of Nonlinear Beams[J]. Applied Mathematics and Mechanics, 2012, 33(11): 1284-1293. doi: 10.3879/j.issn.1000-0887.2012.11.004
[5]	WANG Hong-li, FENG Jian-feng, SHEN Fei, SUN Jing. Stability and Bifurcation Behaviors Analysis in a Nonlinear Harmful Algal Dynamical Model[J]. Applied Mathematics and Mechanics, 2005, 26(6): 671-676.
[6]	ZHENG Hui-ping, XUE Yu-sheng, CHEN Yu-shu. Quantitative Methodology for the Stability Analysis of Nonlinear Rotor Systems[J]. Applied Mathematics and Mechanics, 2005, 26(9): 1038-1044.
[7]	WU Jun, CHEN Li-qun. Steady-State Responses and Their Stability of Nonlinear Vibration of an Axially Accelerating String[J]. Applied Mathematics and Mechanics, 2004, 25(9): 917-926.
[8]	HE Ji-huan. Linearization and Correction Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 2002, 23(3): 221-228.
[9]	LIU Jun. Research of the Periodic Motion and Stability of Two-Degree-of-Freedom Nonlinear Oscillating Systems[J]. Applied Mathematics and Mechanics, 2002, 23(10): 1093-1100.
[10]	CONG Yu-hao. NGP_G-Stability of Linear Multistep Methods for Systems of Generalized Neutral Delay Differential Equations[J]. Applied Mathematics and Mechanics, 2001, 22(7): 735-742.
[11]	Ji Jinchen, Chen Yushu. Bifurcation in a Parametrically Excited Two-Degree-of-Freedom Nonlinear Oscillating System with 1:2 Internal Resonance[J]. Applied Mathematics and Mechanics, 1999, 20(4): 337-345.
[12]	Liao Shijun, . Homotopy Analysis Method: a New Analytic Method for Nonlinear Problems[J]. Applied Mathematics and Mechanics, 1998, 19(10): 885-890.
[13]	Zhao Lei, Chen Qiu. An Equivalent Nonlinearization Method for Analysing Response of Nonlinear Systems to Random Excitations[J]. Applied Mathematics and Mechanics, 1997, 18(6): 513-521.
[14]	Ye Shou-zhen, Sha Wan-qian. Generalized Transfer Function of Control System and an Improvement on the Decision Method of Movement Stability[J]. Applied Mathematics and Mechanics, 1989, 10(4): 347-357.
[15]	Zhou Zhe-wei. A Kind of Distortion of Mean Velocity Profile in Pipe Poiseuille Flow and Its Stability Behaviour[J]. Applied Mathematics and Mechanics, 1988, 9(1): 73-82.
[16]	Zhao Jun-san. A Criterion for the Stability of Motion of Nonlinear Systems[J]. Applied Mathematics and Mechanics, 1988, 9(11): 1033-1036.
[17]	Wang Xin-zhi, Zhu Tong-xin. A Kind of Nonlinear Oscillations of Single Degree of Non-Autonomy System[J]. Applied Mathematics and Mechanics, 1985, 6(7): 661-669.
[18]	Chen Xiao-lin, Hwang Ling. The Relationship between the Stability and the Optimality of Linear Systems——Another Kind of the Inverse Problem of Linear Optimal Control[J]. Applied Mathematics and Mechanics, 1985, 6(2): 153-160.
[19]	Ling. A Numerical Treatment of the Periodic Solutions of Non-Linear Vibration Systems[J]. Applied Mathematics and Mechanics, 1983, 4(4): 489-506.
[20]	Tang Wen-liang. One Type of Solutions of Conduction of Nervous Pulses and the Stability of Action Potential[J]. Applied Mathematics and Mechanics, 1983, 4(1): 113-121.