A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case

Özhan, B. Burak; Pakdemi̇rli̇, Mehmet

doi:10.1016/j.jsv.2009.04.009

Cited by 37 publications

(2 citation statements)

References 18 publications

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“…The first order approximate solution of Eq.6 can be solved by using the multiple scales method [5,6] and the assumptions are given below.…”

Section: Primary Resonance Analysismentioning

confidence: 99%

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

Jiang

Zhao²

2013

AMM

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In this paper, the vibration equation of the structure-soil nonlinear interaction system was qualitatively analyzed by using the modern dynamic theory. Based on the multilinear kinematic hardening mode, the nonlinear finite element method was applied for the solution of the horizontal and torsional stiffness between the foundation and soil interaction system. And a mechanical model of the structure-soil nonlinear interaction system was established. The Lagrange energy method is used to build the coupling vibration equation of the structural horizontal displacement and torsion. The Primary resonance of the structure-soil nonlinear interaction system was studied by using the multiple scales method. By analyzing the nonlinear coupling interaction between different structures and soil, the coupling effect of structure system was revealed by appearing energy transfer from high order horizontal vibration to low order torsional vibration, and also the vibration characteristics and the behavior of energy transfer were obtained.

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“…The first order approximate solution of Eq.6 can be solved by using the multiple scales method [5,6] and the assumptions are given below.…”

Section: Primary Resonance Analysismentioning

confidence: 99%

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

Jiang

Zhao²

2013

AMM

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show abstract

“…Hatami et al [13] examined free vibration of moving laminated composite plates using semi-analytical finite strip method. Ö zhan and Pakdemirli [14] examined the primary resonance of an axially moving beam by developing a general solution procedure for this class of systems. In a series of papers by the author and co-investigators [15][16][17][18][19], the sub-and super-critical dynamics and stability of an axially moving beam were investigated analytically and numerically.…”

Section: Introductionmentioning

confidence: 99%

Coupled longitudinal–transverse dynamics of an axially accelerating beam

Ghayesh

2012

Journal of Sound and Vibration

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A New Spatial and Temporal Incremental Harmonic Balance Method for Obtaining Steady-State Responses of a One-Dimensional Continuous System

Wang¹,

Zhu²

2020

Advanced Structured Materials

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A general solution procedure for the forced vibrations of a continuous system with cubic nonlinearities: Primary resonance case

Cited by 37 publications

References 18 publications

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

Research on Horizontal Displacement and Torsion Coupling Effect of Structure-Soil System

Coupled longitudinal–transverse dynamics of an axially accelerating beam

A New Spatial and Temporal Incremental Harmonic Balance Method for Obtaining Steady-State Responses of a One-Dimensional Continuous System

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