The effects of large vibration amplitudes on the mode shapes and natural frequencies of thin elastic structures part I: Simply supported and clamped-clamped beams

Benamar, Rhali; Bennouna, M.; White, Robert G.

doi:10.1016/0022-460x(91)90630-3

Cited by 103 publications

(88 citation statements)

References 5 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This approach to considered particular problem is more adequate than very popular modal ones because the influence of more then one mode of vibration can be taken into account in an easy way. As shown in many papers (see, for example references [19][20][21][22]), the interaction of two or more modes of vibration could be very important if nonlinear systems are considered. Moreover, beams with the non-uniform spatial distribution of the beam bending stiffness, the mass per unit length or the cross-section characteristic dimension can be modelled more accurately.…”

Section: Description Of Computational Modelmentioning

confidence: 99%

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

Lewandowski

2002

Journal of Sound and Vibration

View full text Add to dashboard Cite

Section: Description Of Computational Modelmentioning

confidence: 99%

Non-Linear Steady State Vibrations of Beams Excited by Vortex Shedding

Lewandowski

2002

Journal of Sound and Vibration

View full text Add to dashboard Cite

“…(18) and (19) as a perturbation of that of Eqs. (13) and (14) as (26) (27) and combining with Eqs. (18) and (19), one obtains…”

Section: Small Damping Approximationmentioning

confidence: 99%

“…Section 3 describes the proposed non-linear modal analysis of the forced response of non-linear systems, and Section 4 closes on a few conclusions. Several definitions of non-linear normal modes of vibrations have been proposed in the past for nonlinear structural systems (see, in particular, references [15][16][17][18][19][20][21][22][23][24][25][26][27]. In most cases, the system is assumed to be conservative, so that, essentially, modal motions are periodic and, in the configuration space, all coordinates are parametrized by only one of them.…”

Section: Introductionmentioning

confidence: 99%

Non-linear modal analysis of the forced response of structural systems

Boivin¹,

Pierre²,

Shaw³

1996

Dynamics Specialists Conference

View full text Add to dashboard Cite

A non-linear modal analysis procedure is presented for the forced response of non-linear structural systems. It utilizes the notion of invariant manifolds in the phase space, which was recently used to define non-linear normal modes and the corresponding non-linear modal analysis for unforced vibratory systems. For harmonic forcing, a similar procedure could be formulated, simply by augmenting the size of the free vibration problem. However, in order to accommodate general, non-harmonic external excitations, the invariant manifolds associated with the unforced system are used herein for the forced response analysis. The procedure allows one to generate reduced-order models for the forced analysis of structural systems. Although strictly speaking the invariance property is violated, good results are obtained for the case study considered. In particular, it is found that fewer non-linear modes than linear modes are needed to perform a forced modal analysis with the same accuracy. For systems with small and/or diagonal damping, approximate invariant manifolds are determined, which are shown to yield good results for both the unforced and forced responses.

show abstract

“…This assumption has been shown both theoretically and experimentally to be inaccurate for beams in references [27,28], and for homogeneous and laminated plates in reference [29]. A theoretical model based on Hamilton's principle and spectral analysis was developed by Benamar et al in order to adapt the Rayleigh}Ritz linear eigenvalue problem to non-linear problems of thin straight structures [30]. This model was applied to simply supported and fully clamped beams and extended to rectangular isotropic and laminated plates [31,32].…”

Section: Introductionmentioning

confidence: 99%