Non-linear vibration of a travelling beam

Chakraborty, Goutam; Mallik, Asok K.; Hatwal, H.

doi:10.1016/s0020-7462(98)00017-1

Cited by 72 publications

(44 citation statements)

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“…The industrial applications of moving materials classified as axially travelling stringlike, beamlike structures are numerous [1][2][3][4] such as magnetic tapes drives, band saws, power transmission belts, robot arms, serpentine belts and aerial cable tramways. The purpose of the current research paper is to investigate the linear instability of the beam.…”

Section: Introductionmentioning

confidence: 99%

The Linear Stability of the Responses of Axially Moving Beams Supported by an Intermediate Spring

Köstekci

2016

MATEC Web Conf.

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Section: Introductionmentioning

confidence: 99%

The Linear Stability of the Responses of Axially Moving Beams Supported by an Intermediate Spring

Köstekci

2016

MATEC Web Conf.

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“…The second author and co-workers [35][36][37][38][39] used the method of multiple timescales to study the nonlinear dynamics and vibrations of stationary beams with intermediate adornments. In contrast, there are rather limited studies regarding the vibrations of axially moving systems with intermediate elements [40][41][42][43][44][45][46]. In these studies, intermediate elements are mostly considered as elastic springs, where the inertia of these adornments has been neglected.…”

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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“…In the absence of these constraints, exact, closed form solutions for the vibration of gyroscopic systems are available through Laplace transform methods [4] and modal analysis and Green's function methods [5]. Similar solution methods are developed for gyroscopic systems with linear constraints by dividing the system into two contiguous regions divided at the point of the linear constraint [6][7][8].…”

Section: Introductionmentioning

confidence: 99%

Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints

Brake

Wickert

2010

Journal of Sound and Vibration

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To cite this version:M.R. Brake, J.A. Wickert. Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints. Journal of Sound and Vibration, Elsevier, 2010, 329 (7) A method for the modal analysis of continuous gyroscopic systems with nonlinear constraints is developed. This method assumes that the nonlinear constraint can be expressed as a piecewise linear force-deflection profile located at an arbitrary position within the domain. Using this assumption, the mode shapes and natural frequencies are first found for each state, then a mapping method based on the inner product of the mode shapes is developed to map the displacement of the system between the in-contact and out-of-contact states. To illustrate this method, a model for the vibration of a traveling string in contact with a piecewise-linear constraint is developed as an analog of the interaction between magnetic tape and a guide in data storage systems. Five design parameters of the guide are considered: flange clearance, flange stiffness, symmetry of the force-deflection profile in terms of flange stiffness and offset, and the guide's position along the length of the string. There are critical bifurcation thresholds, below which the system exhibits no chaotic behavior and is dominated by period one, symmetric behavior, and above which the system contains asymmetric, higher periodic motion with windows of chaotic behavior. These bifurcation thresholds are particularly pronounced for the transport speed, flange clearance, symmetry of the force deflection profile, and guide position. The stability of the system is sensitive to the system's velocity, and, compared to stationary systems, more mode shapes are needed to accurately model the dynamics of the system.

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Non-linear vibration of a travelling beam

Cited by 72 publications

References 0 publications

The Linear Stability of the Responses of Axially Moving Beams Supported by an Intermediate Spring

The Linear Stability of the Responses of Axially Moving Beams Supported by an Intermediate Spring

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

Modal analysis of a continuous gyroscopic second-order system with nonlinear constraints

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