Experiments and analysis on chaotic vibrations of a shallow cylindrical shell-panel

2007 ◽  
Vol 305 (3) ◽  
pp. 492-520 ◽  
Author(s):  
K. Nagai ◽  
S. Maruyama ◽  
T. Murata ◽  
T. Yamaguchi
Keyword(s):  
Cylindrical Shell ◽  
Shallow Cylindrical Shell ◽  
Chaotic Vibrations ◽  
Shell Panel

Chaotic Oscillations of a Shallow Cylindrical Shell-Panel With a Concentrated Elastic-Support

2000 ◽  
Author(s):  
Takao Yamaguchi ◽  
Ken-ichi Nagai
Keyword(s):  
Cylindrical Shell ◽  
Numerical Solutions ◽  
Harmonic Balance Method ◽  
Type Equation ◽  
Inertia Force ◽  
Chaotic Oscillations ◽  
Shallow Cylindrical Shell ◽  
Chaotic Response ◽  
Modes Of Vibration ◽  
Shell Panel

Abstract This paper presents numerical solutions on chaotic oscillations of a shallow cylindrical shell-panel excited by a periodic acceleration. The shell with rectangular boundary is simply supported along all edges, and the center of the shell is supported by an elastic spring. The Donnell-Mushtari-Vlasov type equation is used with the modification of an inertia force. The governing equation is reduced to a nonlinear differential equation of a multi-degree-of-freedom system by the Bubnov-Galerkin procedure. To estimate regions of the chaotic response, periodic solutions of steady state response are first calculated by the harmonic balance method. Next, time evolutions of the chaotic motion are obtained numerically by the Runge-Kutta-Gill method. The chaotic response accompanied with a dynamic snap-through is identified both by means of Lyapunov exponents and Poincaré projections. For the shell with a spring, the Lyapunov dimension is smaller than for the case without the spring. Multiple modes of vibration contributes to the generation of chaos, in paticular, the higher modes of vibration are significant.

Magnetostrictive Microactuations and Modal Sensitivities of Thin Magnetoelastic Shells

2008 ◽  
Vol 130 (1) ◽  
Author(s):  
W. K. Chai ◽  
H. S. Tzou ◽  
S. M. Arnold ◽  
H.-J. Lee
Keyword(s):  
Cylindrical Shell ◽  
Transverse Mode ◽  
Control Force ◽  
Control Actions ◽  
Spatially Distributed ◽  
Longitudinal Bending ◽  
Shell Panel ◽  
Magnetostrictive Actuator ◽  
Membrane Bending ◽  
Control Forces

This study is to evaluate distributed microscopic actuation characteristics and control actions of segmented magnetostrictive actuator patches laminated on a flexible cylindrical shell panel. A mathematical model and its modal domain governing equations of the cylindrical shell panel laminated with distributed magnetostrictive actuator patches are presented first, followed by the formulation of distributed magnetostrictive control forces and microcontrol actions including circumferential membrane∕bending and longitudinal bending control components. Transverse mode shape functions with simply supported boundary conditions are used in the modal control force expressions and the microcontrol action analyses. Control effectives and spatial characteristics of distributed actuators depend on applied magnetic fields and on geometrical (e.g., spatial segmentation, location, and shape) and material (i.e., various actuator materials) properties. Spatially distributed magnetoelectromechanical actuation characteristics contributed by circumferential membrane∕bending and longitudinal bending control actions are investigated. Distributed control forces and microactuations of a magnetostrictive actuator patch at various locations are analyzed, and modal-dependent spatial control effectiveness is evaluated.

scholarly journals A Single and Double Mode Approach to Chaotic Vibrations of a Cylindrical Shell with Large Deflection

2004 ◽  
Vol 11 (5-6) ◽  
pp. 533-546 ◽  
Author(s):  
Liming Dai ◽  
Qiang Han ◽  
Mingzhe Dong
Keyword(s):  
Cylindrical Shell ◽  
Large Deflection ◽  
Single Mode ◽  
Order Mode ◽  
Governing Equations ◽  
Chaotic Vibrations ◽  
Nonlinear Dynamic Equations ◽  
Different Types ◽  
Mode Method ◽  
Research Show

The chaotic vibrations of a cylindrical shell of large deflection subjected to two-dimensional exertions are studied in the present research. The dynamic nonlinear governing equations of the cylindrical shell are derived on the basis of single and double mode models established. Two different types of nonlinear dynamic equations are obtained with varying dimensions and loading parameters. The criteria for chaos are determined via Melnikov function for the single mode model. The chaotic motion of the cylindrical shell is investigated and the comparison between the single and double mode models is carried out. Results of the research show that the single mode method usually used may lead to incorrect conclusions under certain conditions. Double mode or higher order mode methods should be used in these cases.

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