Free vibration analysis of a structural system with a pair of irrational nonlinearities

Siu Kai Lai; B. S. Wu; Y. Y. Lee

doi:10.1016/j.apm.2017.01.017

Free vibration analysis of a structural system with a pair of irrational nonlinearities

Siu Kai Lai, B. S. Wu, Y. Y. Lee

Research output: Journal article publication › Journal article › Academic research › peer-review

8 Citations (Scopus)

Abstract

An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.

Original language	English
Pages (from-to)	997-1007
Number of pages	11
Journal	Applied Mathematical Modelling
Volume	45
DOIs	https://doi.org/10.1016/j.apm.2017.01.017
Publication status	Published - 1 May 2017

Keywords

Analytical approximate solutions
Harmonic balance method
Irrational nonlinearities
Newton's method
Rational approximation

ASJC Scopus subject areas

Modelling and Simulation
Applied Mathematics

More information

10.1016/j.apm.2017.01.017

http://hdl.handle.net/10397/101268

Cite this

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title = "Free vibration analysis of a structural system with a pair of irrational nonlinearities",

abstract = "An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.",

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AU - Lai, Siu Kai

AU - Wu, B. S.

AU - Lee, Y. Y.

PY - 2017/5/1

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N2 - An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.

AB - An alternative method of deriving accurate and simple analytical approximate solutions to a structural dynamical system governed by a pair of strong irrational restoring forces is presented. This system can be used to represent mathematical models in various engineering problems. Prior to solving the problem, a rational approximation of the nonlinear restoring force function is applied to achieve a convergent truncation. Analytical solutions are then obtained using the combination of the harmonic balance method and Newton's method. This approach shows that lower-order analytical procedures can yield highly accurate and exact solutions that are difficult to obtain with an analytical expression.

KW - Analytical approximate solutions

KW - Harmonic balance method

KW - Irrational nonlinearities

KW - Newton's method

KW - Rational approximation

UR - https://www.scopus.com/pages/publications/85019625613

U2 - 10.1016/j.apm.2017.01.017

DO - 10.1016/j.apm.2017.01.017

M3 - Journal article

SN - 0307-904X

VL - 45

SP - 997

EP - 1007

JO - Applied Mathematical Modelling

JF - Applied Mathematical Modelling

ER -

Free vibration analysis of a structural system with a pair of irrational nonlinearities

Abstract

Keywords

ASJC Scopus subject areas

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