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

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

Fingerprint

ASJC Scopus subject areas

Mechanics of Materials
Mechanical Engineering
Applied Mathematics

Cite this

Caughey, T. K., Vakakis, A., & Sivo, J. M. (1990). Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems. International Journal of Non-Linear Mechanics, 25(5), 521-533. https://doi.org/10.1016/0020-7462(90)90016-3

@article{32cee7bd2827470a87a7ac67939cabc9,

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.",

author = "Caughey, {T. K.} and A. Vakakis and Sivo, {J. M.}",

year = "1990",

doi = "10.1016/0020-7462(90)90016-3",

language = "English (US)",

volume = "25",

pages = "521--533",

journal = "International Journal of Non-Linear Mechanics",

issn = "0020-7462",

publisher = "Elsevier Limited",

number = "5",

}

TY - JOUR

T1 - Analytical study of similar normal modes and their bifurcations in a class of strongly non-linear systems

AU - Caughey, T. K.

AU - Vakakis, A.

AU - Sivo, J. M.

PY - 1990

Y1 - 1990

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=0025638281&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025638281&partnerID=8YFLogxK

U2 - 10.1016/0020-7462(90)90016-3

DO - 10.1016/0020-7462(90)90016-3

M3 - Article

AN - SCOPUS:0025638281

VL - 25

SP - 521

EP - 533

JO - International Journal of Non-Linear Mechanics

JF - International Journal of Non-Linear Mechanics

SN - 0020-7462

IS - 5

ER -

Access to Document

10.1016/0020-7462(90)90016-3