Non-linear vibrations and stability of an axially moving beam with time-dependent velocity

Öz, H. R.; Pakdemi̇rli̇, Mehmet; Boyacı, Hakan

doi:10.1016/s0020-7462(99)00090-6

Cited by 200 publications

(56 citation statements)

References 22 publications

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“…Based on 1-term Galerkin discretization, Ravindra and Zhu [8] analyzed the chaotic behavior of axially accelerating beams. Oz et al [9] applied the method of multiple scales to determine the steady-state transverse response and the stability of axially accelerating non-linear beams. Hu and Jin [10,11] studied the nonlinear vibration of axially moving cables subjected to transverse loads caused by fluids.…”

Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration of axially moving viscoelastic beams

Yang

Chen

2006

Acta Mech. Solida Sin.

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The non-linear forced vibration of axially moving viscoelastic beams excited by the vibration of the supporting foundation is investigated. A non-linear partial-differential equation governing the transverse motion is derived from the dynamical, constitutive equations and geometrical relations. By referring to the quasi-static stretch assumption, the partial-differential non-linearity is reduced to an integro-partial-differential one. The method of multiple scales is directly applied to the governing equations with the two types of non-linearity, respectively. The amplitude of near-and exact-resonant steady state is analyzed by use of the solvability condition of eliminating secular terms. Numerical results are presented to show the contributions of foundation vibration amplitude, viscoelastic damping, and nonlinearity to the response amplitude for the first and the second mode.KEY WORDS axially moving beam, viscoelasticity, non-linear forced vibration, method of multiple scales

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Section: Introductionmentioning

confidence: 99%

Non-linear forced vibration of axially moving viscoelastic beams

Yang

Chen

2006

Acta Mech. Solida Sin.

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“…The nonlinear partial differential equations of motion are derived assuming that: (1) shear deformation and rotary inertia are neglected, i.e., the Euler-Bernoulli beam theory is employed [26][27][28][29]; (2) the nonlinear behavior is due to the stretching effect of the midplane of the beam; (3) the beam is under a constant pretension p in the axial direction; (4) the cross section of the beam is uniform along the entire length [30,31]; and (5) the rotation of beam cross section is assumed to be small, which neglects the nonlinearities in the curvature-displacement relation [32][33][34][35][36][37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

Ghayesh

Farokhi

2016

Journal of Computational and Nonlinear Dynamics

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The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincare maps, time histories, phase-plane portraits, Poincare sections, and fast Fourier transforms (FFTs). The three-dimensional (3D) nonlinear dynamics of an axially accelerating beam is examined numerically taking into account all of the longitudinal, transverse, and lateral displacements and inertia. Hamilton's principle is employed in order to derive the nonlinear partial differential equations governing the longitudinal, transverse, and lateral motions. These equations are transformed into a set of nonlinear ordinary differential equations by means of the Galerkin discretization technique. The nonlinear global dynamics of the system is then examined by time-integrating the discretized equations of motion. The results are presented in the form of bifurcation diagrams of Poincar e maps, time histories, phase-plane portraits, Poincar e sections, and fast Fourier transforms (FFTs).

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“…For example, Pakdemirli and co-workers [6][7][8][9] examined the vibrations of axially moving strings and beams by means of some perturbation techniques such as the method of multiple timescales and matched asymptotic expansion. Chen and co-workers [10][11][12] employed both analytical and numerical techniques to examine the dynamics of axially moving systems.…”

Section: Introductionmentioning

confidence: 99%

Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

Kazemirad

Ghayesh

Amabili

2013

Shock and Vibration

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Abstract. The thermo-mechanical nonlinear vibrations and stability of a hinged-hinged axially moving beam, additionally supported by a nonlinear spring-mass support are examined via two numerical techniques. The system is subjected to a transverse harmonic excitation force as well as a thermal loading. Hamilton's principle is employed to derive the equations of motion; it is discretized into a multi-degree-freedom system by means of the Galerkin method. The steady state resonant response of the system for both cases with and without an internal resonance between the first two modes is examined via the pseudo-arclength continuation technique. In the second method, direct time integration is employed to construct bifurcation diagrams of Poincaré maps of the system.

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Non-linear vibrations and stability of an axially moving beam with time-dependent velocity

Cited by 200 publications

References 22 publications

Non-linear forced vibration of axially moving viscoelastic beams

Non-linear forced vibration of axially moving viscoelastic beams

Nonlinear Dynamical Behavior of Axially Accelerating Beams: Three-Dimensional Analysis

Thermal Effects on Nonlinear Vibrations of an Axially Moving Beam with an Intermediate Spring-Mass Support

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