ANALYSIS OF VIBRATING CIRCULAR PLATES HAVING NON-UNIFORM CONSTRAINTS USING THE MODAL PROPERTIES OF FREE-EDGE PLATES: APPLICATION TO BOLTED PLATES

1997 ◽  
Vol 206 (1) ◽  
pp. 23-38 ◽  
Author(s):  
M. Amabili ◽  
R. Pierandrei ◽  
G. Frosali
Keyword(s):  
Free Edge ◽  
Circular Plates ◽  
Modal Properties

scholarly journals ASYMMETRIC NON-LINEAR FORCED VIBRATIONS OF FREE-EDGE CIRCULAR PLATES. PART 1: THEORY

2002 ◽  
Vol 258 (4) ◽  
pp. 649-676 ◽  
Author(s):  
C. TOUZÉ ◽  
O. THOMAS ◽  
A. CHAIGNE
Keyword(s):  
Free Edge ◽  
Forced Vibrations ◽  
Circular Plates ◽  
Non Linear

scholarly journals Effect of Imperfections and Damping on the Type of Nonlinearity of Circular Plates and Shallow Spherical Shells

2008 ◽  
Vol 2008 ◽  
pp. 1-19 ◽  
Author(s):  
Cyril Touzé ◽  
Cédric Camier ◽  
Gaël Favraud ◽  
Olivier Thomas
Keyword(s):  
Normal Modes ◽  
Free Edge ◽  
Nonlinear Normal Modes ◽  
Circular Plates ◽  
Spherical Shells ◽  
Geometric Imperfections ◽  
Softening Behaviour ◽  
Nonlinear Normal ◽  
Deflection Theory ◽  
Large Deflection Theory

The effect of geometric imperfections and viscous damping on the type of nonlinearity (i.e., the hardening or softening behaviour) of circular plates and shallow spherical shells with free edge is here investigated. The Von Kármán large-deflection theory is used to derive the continuous models. Then, nonlinear normal modes (NNMs) are used for predicting with accuracy the coefficient, the sign of which determines the hardening or softening behaviour of the structure. The effect of geometric imperfections, unavoidable in real systems, is studied by adding a static initial component in the deflection of a circular plate. Axisymmetric as well as asymmetric imperfections are investigated, and their effect on the type of nonlinearity of the modes of an imperfect plate is documented. Transitions from hardening to softening behaviour are predicted quantitatively for imperfections having the shapes of eigenmodes of a perfect plate. The role of 2:1 internal resonance in this process is underlined. When damping is included in the calculation, it is found that the softening behaviour is generally favoured, but its effect remains limited.

scholarly journals Forced Vibrations of Circular Plates: From Periodic to Chaotic Motions

2010 ◽  
Author(s):  
Cyril Touze´ ◽  
Olivier Thomas ◽  
Marco Amabili
Keyword(s):  
Internal Resonance ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Free Edge ◽  
Forced Vibrations ◽  
Chaotic Regime ◽  
Circular Plates ◽  
Chaotic Motions ◽  
Resonant Modes ◽  
Transition Scenario

A numerical study of the transition from periodic to chaotic motions in forced vibrations of circular plates, is proposed. A pointwise harmonic forcing of constant excitation frequency Ω and increasing values of the amplitude is considered. Perfect and imperfect circular plates with a free edge are studied within the von Ka´rma´n assumptions for large displacements (geometric non-linearity). The transition scenario is observed for different excitation frequencies in the range of the first eigenfrequencies of the plate. For perfect plate with no specific internal resonance relationships, a direct transition to chaos is at hand. For imperfect plate tuned so as to fulfill specific internal resonance relations, a coupling between internally resonant modes is first observed. The chaotic regime shows an attractor of large dimension, and thus is studied within the framework of wave turbulence.

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