Finite Element Analysis Of An Axially Moving Beam, Part II: Stability Analysis

Stylianou, M.; Tabarrok, B.

doi:10.1006/jsvi.1994.1498

Cited by 64 publications

(27 citation statements)

References 0 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Further, after q i (t) and r i (t) are solved, Eq. (53) can be recast as [15,16] and Theodore et al [19]. During the beam extension in Fig.…”

Section: Analysis Of Dynamic Stabilizationmentioning

confidence: 99%

“…Zhu and Ni [14] presented the linear dynamics of a cantilever beam with an arbitrarily varying length where the tension from their axially moving acceleration was incorporated; they also studied the dynamic stability from the energy viewpoint. Base on the finite element method, Stylianou and Tabarrok [15,16] investigated the axially moving slender beam; their numerical results specified that the beam would be stabilized in extension and unstabilized in retraction. The dynamics and control of a translating flexible beam with a tip mass at one end emerging from or retracting into a rigid base was proposed by Tadikonda and Baruh [17]; they exploited the eigenfunctions of a cantilever beam to obtain closed-form expressions for several domain integrals that arise in the model, which showed that the coupling effect of elastic and translational motions is very important to the beam control.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Wang

Zhong

et al. 2010

Acta Mech

View full text Add to dashboard Cite

The nonlinear free vibration of an axially translating viscoelastic beam with an arbitrarily varying length and axial velocity is investigated. Based on the linear viscoelastic differential constitutive law, the extended Hamilton's principle is utilized to derive the generalized third-order equations of motion for the axially translating viscoelastic Bernoulli-Euler beam. The coupling effects between the axial motion and transverse vibration are assessed under various prescribed time-varying velocity fields. The inertia force arising from the longitudinal acceleration emerges, rendering the coupling terms between the axial beam acceleration and the beam flexure. Semi-analytical solutions for the governing PDE are obtained through the separation of variables and the assumed modes method. The modified Galerkin's method and the fourth-order RungeKutta method are employed to numerically analyze the resulting equations. Further, dynamic stabilization is examined from the system energy standpoint for beam extension and retraction. Extensive numerical simulations are presented to illustrate the influences of varying translating velocities and viscoelastic parameters on the underlying dynamic responses. The material viscosity always dissipates energy and helps stabilize the transverse vibration.

show abstract

“…Further, after q i (t) and r i (t) are solved, Eq. (53) can be recast as [15,16] and Theodore et al [19]. During the beam extension in Fig.…”

Section: Analysis Of Dynamic Stabilizationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Wang

Zhong

et al. 2010

Acta Mech

View full text Add to dashboard Cite

show abstract

“…Marynowski and Kapitaniak [14] investigated the nonlinear dynamics of an axially moving viscoelastic beam by introducing a three-parameter Zener internal damping in the beam model; they used the Galerkin scheme along with Runge-Kutta method to solve the equations numerically. A finite element approach was used by Stylianou and Tabarrok [15], who analyzed the stability of an axially moving beam. Chakraborty and Mallik [16] examined the stability of an axially moving beam analytically by means of the method of multiple scales.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Farokhi

Ghayesh

Hussain

2015

Journal of Vibration and Acoustics

View full text Add to dashboard Cite

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).

show abstract

“…Stylianou and Tabarrok [12,13] used finite element formulation to consider translational and rotary inertia effects of the tip mass and made a stability analysis. Borglund [14] considered the stability and optimal design of a beam subject to forces induced by fluid flow through attached pipes with a tip mass by using finite element formulation.…”

Section: Introductionmentioning

confidence: 99%

Current Research on the Vibration and Stability of Axially Moving Materials

Öz¹

2003

Journal of Sound and Vibration

View full text Add to dashboard Cite

Finite Element Analysis Of An Axially Moving Beam, Part II: Stability Analysis

Cited by 64 publications

References 0 publications

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Dynamic analysis of an axially translating viscoelastic beam with an arbitrarily varying length

Three-Dimensional Nonlinear Global Dynamics of Axially Moving Viscoelastic Beams

Current Research on the Vibration and Stability of Axially Moving Materials

Contact Info

Product

Resources

About