Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems

T. K. Caughey; A. Vakakis; J. M. Sivo

doi:10.1016/0020-7462(90)90016-3

Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems

T. K. Caughey, A. Vakakis, J. M. Sivo

Research output: Contribution to journal › Article › peer-review

Abstract

The concept of similar normal mode is used to study the free oscillations of a class of strongly non-linear, two degree of freedom undamped systems. By using the so-called balancing diagrams, the bifurcations of normal modes can be conveniently studied for different forms of stiffness non-linearities. Consequently, the stability of the resulting free motions is analytically examined and the theoretical results are checked by numerical integration of the equations of motion.

Original language	English (US)
Pages (from-to)	521-533
Number of pages	13
Journal	International Journal of Non-Linear Mechanics
Volume	25
Issue number	5
DOIs	https://doi.org/10.1016/0020-7462(90)90016-3
State	Published - 1990
Externally published	Yes

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

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title = "Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems",

abstract = "The concept of similar normal mode is used to study the free oscillations of a class of strongly non-linear, two degree of freedom undamped systems. By using the so-called balancing diagrams, the bifurcations of normal modes can be conveniently studied for different forms of stiffness non-linearities. Consequently, the stability of the resulting free motions is analytically examined and the theoretical results are checked by numerical integration of the equations of motion.",

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AB - The concept of similar normal mode is used to study the free oscillations of a class of strongly non-linear, two degree of freedom undamped systems. By using the so-called balancing diagrams, the bifurcations of normal modes can be conveniently studied for different forms of stiffness non-linearities. Consequently, the stability of the resulting free motions is analytically examined and the theoretical results are checked by numerical integration of the equations of motion.

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