Journal ArticleDOI
Two mode sub-harmonic and harmonic vibrations of a non-linear beam forced by a two mode harmonic load.
R. Van Dooren,R. Bouc +1 more
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TLDR
In this paper, the non-linear transverse vibrations of a uniform beam with ends restrained to remain a fixed distance apart and forced by a two mode function which is harmonic in time, are studied by a corresponding two mode approach.Abstract:
The non-linear transverse vibrations of a uniform beam with ends restrained to remain a fixed distance apart and forced by a two mode function which is harmonic in time, are studied by a corresponding two mode approach. The existence of sub-harmonic response of order 1 3 and harmonic response in the sub-harmonic resonance region of the forcing frequency is proved. Approximate solutions are found by Urabe's numerical method applied to Galerkin's procedure and by an analytical harmonic balance-perturbation method. Error bounds of the Galerkin approximations are given.read more
Citations
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Galerkin's Procedure for Nonlinear Periodic Systems (関数方程式の近似解法研究会報告集)
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.
Journal ArticleDOI
Non-linear vibrations of a clamped beam with initial deflection and initial axial displacement, Part I: Theory
N. Yamaki,A. Mori +1 more
TL;DR: In this article, the effects of both initial deflection and initial axial displacement on the static deflection as well as the lower natural frequencies were analyzed for non-linear vibrations of a clamped beam under uniformly distributed periodic lateral loading.
Dissertation
Vibrations forcées de structures minces, élastiques, non linéaires
TL;DR: Le travail presente dans ce memoire est une contribution a l'etude des vibrations non lineaires de structures minces, par des approches numeriques et experimentales, d'un outil numerique qui permet de traiter une large classe of structures.
Journal ArticleDOI
HIA: A Hybrid Integral Approach to model incompressible isotropic hyperelastic materials—Part 1: Theory
A. Nguessong Nkenfack,A. Nguessong Nkenfack,Tibi Beda,Zhi-Qiang Feng,Zhi-Qiang Feng,François Peyraut +5 more
TL;DR: In this article, a new constitutive model for rubber-like materials is proposed, which adds to the 8-chain density introduced by Arruda and Boyce, two phenomenological components: an original part made of an integral density and an interleaving constraint part represented by a logarithmic function.
Journal ArticleDOI
Non-linear, steady-state analysis of multispan beams by the finite element method
TL;DR: In this paper, the Von Karman theory, the total Lagrangian formulation and the Ritz method are used to study the steady-state, harmonic response of geometrically non-linear multispan beams subjected to harmonic forces.
References
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Journal ArticleDOI
Galerkin's procedure for nonlinear periodic systems
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.
Galerkin's Procedure for Nonlinear Periodic Systems (関数方程式の近似解法研究会報告集)
TL;DR: In this paper, it was shown that Galerkin's procedure is always available for twice continuously differentiable periodic differential systems if a periodic solution is restricted to an isolated periodic solution.
Journal ArticleDOI
Numerical computation of nonlinear forced oscillations by Galerkin's procedure
Minoru Urabe,Allen Reiter +1 more
TL;DR: In this paper, the Galerkin's procedure can be used to obtain an isolated periodic solution lying inside the region of definition of X(x,t) and its derivative with respect to x and t. In the present paper, the practical numerical method is described and some numerical examples are presented.
Journal ArticleDOI
Stability of large amplitude forced motion of a simply supported beam
Joe G. Eisley,James A. Bennett +1 more
TL;DR: In this article, the stability of the unforced modes when a single mode is forced is investigated and it is concluded that the approximation of single mode response is not always valid because of the possible instability of higher modes.
Journal ArticleDOI
Non-linear response of a beam to periodic loading
H.R. Busby,V.I. Weingarten +1 more
TL;DR: In this article, the steady state response of a non-linear beam under periodic excitation is investigated and the nonlinearity is attributed to the membrane tension effect which is induced in the beam when the deflection is not small in comparison to its thickness.
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