Nonlinear stability and bifurcations of an axially accelerating beam with an intermediate spring-support

Ghayesh, Mergen H.,Amabili, Marco Techno-Press 2013 Coupled systems mechanics Vol.2 No.2

The present work aims at investigating the nonlinear dynamics, bifurcations, and stability of an axially accelerating beam with an intermediate spring-support. The problem of a parametrically excited system is addressed for the gyroscopic system. A geometric nonlinearity due to mid-plane stretching is considered and Hamilton's principle is employed to derive the nonlinear equation of motion. The equation is then reduced into a set of nonlinear ordinary differential equations with coupled terms via Galerkin's method. For the system in the sub-critical speed regime, the pseudo-arclength continuation technique is employed to plot the frequency-response curves. The results are presented for the system with and without a three-to-one internal resonance between the first two transverse modes. Also, the global dynamics of the system is investigated using direct time integration of the discretized equations. The mean axial speed and the amplitude of speed variations are varied as the bifurcation parameters and the bifurcation diagrams of Poincare maps are constructed.

Internal resonance and nonlinear response of an axially moving beam: two numerical techniques

Ghayesh, Mergen H.,Amabili, Marco Techno-Press 2012 Coupled systems mechanics Vol.1 No.3

The nonlinear resonant response of an axially moving beam is investigated in this paper via two different numerical techniques: the pseudo-arclength continuation technique and direct time integration. In particular, the response is examined for the system in the neighborhood of a three-to-one internal resonance between the first two modes as well as for the case where it is not. The equation of motion is reduced into a set of nonlinear ordinary differential equation via the Galerkin technique. This set is solved using the pseudo-arclength continuation technique and the results are confirmed through use of direct time integration. Vibration characteristics of the system are presented in the form of frequency-response curves, time histories, phase-plane diagrams, and fast Fourier transforms (FFTs).

Non-linear vibration and stability analysis of an axially moving rotor in sub-critical transporting speed range

Ghayesh, Mergen H.,Ghazavi, Mohammad R.,Khadem, Siamak E. Techno-Press 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.34 No.4

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton's principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation

Ghayesh, M.H.,Khadem, S.E. Techno-Press 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.27 No.1

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

Parametrically excited viscoelastic beam-spring systems: nonlinear dynamics and stability

Ghayesh, Mergen H. Techno-Press 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.40 No.5

The aim of the investigation described in this paper is to study the nonlinear parametric vibrations and stability of a simply-supported viscoelastic beam with an intra-span spring. Taking into account a time-dependent tension inside the beam as the main source of parametric excitations, as well as employing a two-parameter rheological model, the equations of motion are derived using Newton's second law of motion. These equations are then solved via a perturbation technique which yields approximate analytical expressions for the frequency-response curves. Regarding the main parametric resonance case, the local stability of limit cycles is analyzed. Moreover, some numerical examples are provided in the last section.

Parametrically excited viscoelastic beam-spring systems: nonlinear dynamics and stability

Mergen H. Ghayesh 국제구조공학회 2011 Structural Engineering and Mechanics, An Int'l Jou Vol.40 No.5

The aim of the investigation described in this paper is to study the nonlinear parametric vibrations and stability of a simply-supported viscoelastic beam with an intra-span spring. Taking into account a time-dependent tension inside the beam as the main source of parametric excitations, as well as employing a two-parameter rheological model, the equations of motion are derived using Newton’s second law of motion. These equations are then solved via a perturbation technique which yields approximate analytical expressions for the frequency-response curves. Regarding the main parametric resonance case, the local stability of limit cycles is analyzed. Moreover, some numerical examples are provided in the last section.

Non-linear vibration and stability analysis of a partially supported conveyor belt by a distributed viscoelastic foundation

M. H. Ghayesh,S. E. Khadem 국제구조공학회 2007 Structural Engineering and Mechanics, An Int'l Jou Vol.27 No.1

The main source of transverse vibration of a conveyor belt is frictional contact between pulley and belt. Also, environmental characteristics such as natural dampers and springs affect natural frequencies, stability and bifurcation points of system. These phenomena can be modeled by a small velocity fluctuation about mean velocity. Also, viscoelastic foundation can be modeled as the dampers and springs with continuous characteristics. In this study, non-linear vibration of a conveyor belt supported partially by a distributed viscoelastic foundation is investigated. Perturbation method is applied to obtain a closed form analytic solutions. Finally, numerical simulations are presented to show stiffness, damping coefficient, foundation length, non-linearity and mean velocity effects on location of bifurcation points, natural frequencies and stability of solutions.

An analytical solution for nonlinear dynamics of a viscoelastic beam-heavy mass system

Mergen H. Ghayesh,Farbod Alijani,Mohammad A. Darabi 대한기계학회 2011 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.25 No.8

The aim of this study is to develop an approximate analytic solution for nonlinear dynamic response of a simply-supported Kelvin-Voigt viscoelastic beam with an attached heavy intra-span mass. A geometric nonlinearity due to midplane stretching is considered and Newton’s second law of motion along with Kelvin-Voigt rheological model, which is a two-parameter energy dissipation model, are employed to derive the nonlinear equations of motion. The method of multiple timescales is applied directly to the governing equations of motion, and nonlinear natural frequencies and vibration responses of the system are obtained analytically. Regarding the resonance case, the limit-cycle of the response is formulated analytically. A parametric study is conducted in order to highlight the influences of the system parameters. The main objective is to examine how the vibration response of a plain (i.e. without additional adornment) beam is modified by the presence of a heavy mass, attached somewhere along the beam length.

Non-linear vibration and stability analysis of an axially moving rotor in sub-critical transporting speed range

Mergen H. Ghayesh,Mohammad R. Ghazavi,Siamak E. Khadem 국제구조공학회 2010 Structural Engineering and Mechanics, An Int'l Jou Vol.34 No.4

Parametric and forced non-linear vibrations of an axially moving rotor both in non-resonance and near-resonance cases have been investigated analytically in this paper. The axial speed is assumed to involve a mean value along with small harmonic fluctuations. Hamilton’s principle is employed for this gyroscopic system to derive three coupled non-linear equations of motion. Longitudinal inertia is neglected under the quasi-static stretch assumption and two integro-partial-differential equations are obtained. With introducing a complex variable, the equations of motion is presented in the form of a single, complex equation. The method of multiple scales is applied directly to the resulting equation and the approximate closed-form solution is obtained. Stability boundaries for the steady-state response are formulated and the frequency-response curves are drawn. A number of case studies are considered and the numerical simulations are presented to highlight the effects of system parameters on the linear and nonlinear natural frequencies, mode shapes, limit cycles and the frequency-response curves of the system.

Dynamical behaviour of electrically actuated microcantilevers

Farokhi, Hamed,Ghayesh, Mergen H. Techno-Press 2015 Coupled systems mechanics Vol.4 No.3

The current paper aims at investigating the nonlinear dynamical behaviour of an electrically actuated microcantilever. The microcantilever is excited by a combination of AC and DC voltages. The nonlinear equation of motion of the microcantilever is obtained by means of force and moment balances. A high-dimensional Galerkin scheme is then applied to reduce the equation of motion to a discrete model. A numerical technique, based on the pseudo-arclength continuation method, is used to solve the discretized model. The electrostatic deflection of the microcantilever and static pull-in instabilities, due to the DC voltage, are analyzed by plotting the so-called DC voltage-deflection curves. At the simultaneous presence of the DC and AC voltages, the nonlinear dynamical behaviour of the microcantilever is analyzed by plotting frequency-response and force-response curves.