Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam

Ghayesh, Mergen H.; Kafiabad, Hossein A.; Reid, Tyler

doi:10.1016/j.ijsolstr.2011.10.007

Cited by 98 publications

(30 citation statements)

References 47 publications

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“…The nonlinear partial differential equations of motion are derived under the following assumptions: (1) the Euler-Bernoulli beam theory [26][27][28] is employed neglecting the effect of shear deformation and rotary inertia; (2) the stretching effect of the midplane of the beam (which is caused due to large deflections) is the source of geometric nonlinearity [29][30][31][32][33][34]; (3) the material, not partial, time derivative is used in the viscoelastic constitutive relation; (4) the beam is under a pretension p in the axial direction; (5) the cross section of the beam is uniform along the entire length; (6) the rotation of beam cross section is assumed to be small [35]; and (7) the axial speed is constant [36].…”

Section: Continuous and Reduced-order Modelsmentioning

confidence: 99%

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Farokhi

Ghayesh

Hussain

2015

Journal of Vibration and Acoustics

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The three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincaré sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the threedimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT). Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic BeamsThe three-dimensional nonlinear global dynamics of an axially moving viscoelastic beam is investigated numerically, retaining longitudinal, transverse, and lateral displacements and inertia. The nonlinear continuous model governing the motion of the system is obtained by means of Hamilton's principle. The Galerkin scheme along with suitable eigenfunctions is employed for model reduction. Direct time-integration is conducted upon the reduced-order model yielding the time-varying generalized coordinates. From the time histories of the generalized coordinates, the bifurcation diagrams of Poincar e sections are constructed by varying either the forcing amplitude or the axial speed as the bifurcation parameter. The results for the three-dimensional viscoelastic model are compared to those of a three-dimensional elastic model in order to better understand the effect of the internal energy dissipation mechanism on the dynamical behavior of the system. The results are also presented by means of time histories, phase-plane diagrams, and fast Fourier transforms (FFT).

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Section: Continuous and Reduced-order Modelsmentioning

confidence: 99%

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Farokhi

Ghayesh

Hussain

2015

Journal of Vibration and Acoustics

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“…The literature concerning the dynamics of axially moving beams with constant axial speed is quite large [9][10][11]. For example, Sze et al [12] and Huang et al [13] investigated the subcritical resonant dynamic response of an axially moving beam by means of the incremental harmonic balance method.…”

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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“…Hatami et al (2007Hatami et al ( , 2009 considered prescribed above problems for 2D plates. Recently, Ghayesh et al (2012Ghayesh et al ( , 2013, Yang et al (2012), and Saksa (2012) studied the dynamic stability of elastic and viscoelastic plates under deterministic loads. In many industrial applications, especially when the moving plate passes through a cooling fluid, the resultant distributed lateral force due to solid structure interaction displays random behavior (Asnafi, 2011).…”

Section: Introductionmentioning

confidence: 99%

The Effect of Material Property on the Critical Velocity of Randomly Excited Nonlinear Axially Travelling Functionally Graded Plates

Abedi

Asnafi

Beheshaein

2016

Lat. Am. j. solids struct.

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In this paper, the critical axial speeds of three types of sigmoid, power law and exponential law functionally graded plates for both isotropic and orthotropic cases are obtained via a completely analytic method. The plates are subjected to lateral white noise excitation and show evidence of large deformations. Due to randomness, the conventional deterministic methods fail and a statistical approach must be selected. Here, the probability density function is evaluated analytically for prescribed plates and used to investigate the critical axial velocity of them. Specifically the effect of inplane forces, mean value of lateral load and the material property on the critical axial speed are studied and discussed for both isotropic and orthotropic functionally graded plates. Since the governing equation is transformed to a non dimensional format, the results can be used for a wide range of plate dimensions. It is shown that the material heterogeneity palys an essential and significant role in increasing or decreasing the critical speed of both isotropic and orthotropic functionally graded plates.

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Sub- and super-critical nonlinear dynamics of a harmonically excited axially moving beam

Cited by 98 publications

References 47 publications

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

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

The Effect of Material Property on the Critical Velocity of Randomly Excited Nonlinear Axially Travelling Functionally Graded Plates

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