Fractional calculus - A different approach to the analysis of viscoelastically damped structures

Bagley, Ronald L.; Torvik, Peter J.

doi:10.2514/3.8142

Cited by 1,046 publications

(455 citation statements)

References 8 publications

Supporting

Mentioning

430

Contrasting

Unclassified

Order By: Relevance

“…So, it should be modeling accurately. Several models are presented in the literature [4,5] but the majority of them are fairly straight forward to describe the really characteristics of the viscoelastic materials. One effective and useful model is the (GHM) viscoelastic model which expresses the shear modulus in the Laplace domain, as a sum of mini-oscillators as given as follows:…”

Section: Viscoelastic Modelmentioning

confidence: 99%

Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

Zghal

Bouazizi

Bouhaddi

2014

MATEC Web of Conferences

View full text Add to dashboard Cite

Abstract. The present paper deals with the analysis of the dynamic behavior of viscoelastic sandwich structures with localized nonlinearities. The Golla-Hughes Mac Tavish (GHM) viscoelastic model is used and the finite elements procedure is established to derive both linear and non-linear equations of motion. This model increase the order of the differential equations of motion through the addition of dissipative coordinates, which complicate further the numerical resolution with the addition of local nonlinearities in the junctions of the assembled structures. Hence, a reduced-order model is proposed to enhance the control of the dynamic behavior of such structures incorporating viscoelastic materials especially for structures with large finite element model.

show abstract

Section: Viscoelastic Modelmentioning

confidence: 99%

Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

Zghal

Bouazizi

Bouhaddi

2014

MATEC Web of Conferences

View full text Add to dashboard Cite

show abstract

“…It is worth noting that a related modelling technique used to model non-viscous effects is fractional damping (see for example [12] and references therein). Bagley and Torvik [11], Torvik and Bagley [13], Gaul et al [14] and Maia et al [15] have considered damping modelling in terms of fractional derivatives of the displacements. The resulting equation has a convolution integral form similar to equation (1).…”

Section: Introductionmentioning

confidence: 99%

On the interaction of exponential non-viscous damping with symmetric nonlinearities

Sieber

Wagg

Adhikari

2008

Journal of Sound and Vibration

View full text Add to dashboard Cite

This paper studies the interaction between non-viscous damping and nonlinearities for nonlinear oscillators with reflection symmetry. The non-viscous damping function is an exponential damping model which adds a decaying memory property to the damping term of the oscillator. We consider the case of softening and hardening behaviour in the frequency response of the system. Numerical simulations of the Duffing oscillator show a significant enhancement of the resonance peaks for increasing levels of non-viscous damping parameter in the hardening case, but not in the softening case.This can be explained in the general context by an energy balance analysis of the undamped unforced oscillator, which shows that for hardening nonlinearities the growth of damping with the energy level is an order of magnitude smaller in the exponential case than in the viscous case.

show abstract

“…The mathematical formulation of the FC theory can be addressed in Refs. [1][2][3][4][5] and applications, such as viscoelasticity, biology, signal processing, diffusion, modeling and control, can be found in [6][7][8][9][10]. In spite of its popularity, FC requires some efforts towards the development and adoption of standard tools often adopted in system analysis and control.…”

Section: Introductionmentioning

confidence: 99%

Root locus of fractional linear systems

Machado

2011

Communications in Nonlinear Science and Numerical Simulation

View full text Add to dashboard Cite

show abstract

Fractional calculus - A different approach to the analysis of viscoelastically damped structures

Cited by 1,046 publications

References 8 publications

Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

Reduced-order model for non-linear dynamic analysis of viscoelastic sandwich structures in time domain

On the interaction of exponential non-viscous damping with symmetric nonlinearities

Root locus of fractional linear systems

Contact Info

Product

Resources

About