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.

Chaotic oscillations of a shallow cylindrical shell with a concentrated mass under periodic excitation

2004 ◽  
Vol 82 (31-32) ◽  
pp. 2607-2619 ◽  
Author(s):  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Mitsuru Oya ◽  
Takao Yamaguchi
Keyword(s):  
Cylindrical Shell ◽  
Periodic Excitation ◽  
Chaotic Oscillations ◽  
Concentrated Mass ◽  
Shallow Cylindrical Shell

Chaotic Oscillations of a Post-Buckled Beam Constrained by an Axial Spring: Part 2 — Analysis

2004 ◽  
Author(s):  
Shinichi Maruyama ◽  
Ken-ichi Nagai ◽  
Takao Yamaguchi ◽  
Kazuaki Hoshi
Keyword(s):  
Principal Component Analysis ◽  
Lyapunov Exponent ◽  
Principal Component ◽  
Component Analysis ◽  
Degree Of Freedom ◽  
Chaotic Oscillations ◽  
Harmonic Response ◽  
Chaotic Response ◽  
Buckled Beam ◽  
Modes Of Vibration

To compare with corresponding experiment, analytical results are presented on chaotic oscillations of a post-buckled beam constrained by an axial spring. The beam with an initial deflection is clamped at both ends. The beam is compressed to a post-buckled configuration by the axial spring. Then, the beam is subjected to both accelerations of gravity and periodic lateral excitation. Basic equations of motion includes geometrical nonlinearity of deflection and in-plane displacement. Applying the Galerkin procedure to the basic equation and using the mode shape function proposed by the author, a set of nonlinear ordinary differential equations is obtained with a multiple-degree-of-freedom system. Linear natural frequency due to the axial compression and restoring force of the post-buckled beam are obtained. Next, periodic responses of the beam are inspected by the harmonic balance method. Chaotic responses are obtained by the numerical integration of the Runge-Kutta-Gill method. Chaotic time responses are inspected by the Fourier spectra, the Poincare´ projections, the maximum Lyapunov exponents. Contribution of the number of modes of vibration to the chaos is also discussed by the principal component analysis. Chaotic response is generated within the sub-harmonic resonance responses of 1/2 and 1/3 orders. The maximum Lyapunov exponent corresponded to the sub-harmonic response of 1/2 order is greater than that of the sub-harmonic response of 1/3 order. By the inspection of the Lyapunov exponent on the chaotic response and the analysis with the multiple-degree-of-freedom system, more than three modes of vibration contribute to the chaos. Using the principal component analysis to the chaotic responses at multiple positions of the beam, the lowest mode of vibration contributes dominantly. Higher modes of vibration contribute to the chaos with small amount of amplitude.

Dynamic Response of a Cylindrical Shell Panel to Explosive Loading

1991 ◽  
Vol 113 (3) ◽  
pp. 273-278 ◽  
Author(s):  
D. Redekop ◽  
P. Azar
Keyword(s):  
Cylindrical Shell ◽  
Dynamic Response ◽  
Numerical Solutions ◽  
Free Field ◽  
Nonlinear Behavior ◽  
Explosive Loading ◽  
Shell Panel ◽  
Linear And Nonlinear ◽  
Nonlinear Geometric ◽  
Steel Cylindrical Shell

The dynamic response of steel cylindrical shell panels subjected to external free-field air-blast loading is investigated. The cases of rectangular and square panels having hinged and immovable boundary conditions are considered. Approximate theoretical solutions are presented for linear and nonlinear geometric behavior. Numerical solutions are given for linear, nonlinear geometric and general nonlinear behavior. Results from the theoretical and numerical solutions are compared for several panel rise cases, and conclusions are drawn.

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

NUMERICAL SOLUTIONS OF 2D AND 3D SLAMMING PROBLEMS

2021 ◽  
Vol 153 (A2) ◽  
Author(s):  
Q Yang ◽  
W Qiu
Keyword(s):  
Free Surface ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Type Equation ◽  
The Body ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Highly Nonlinear ◽  
2D And 3D

Slamming forces on 2D and 3D bodies have been computed based on a CIP method. The highly nonlinear water entry problem governed by the Navier-Stokes equations was solved by a CIP based finite difference method on a fixed Cartesian grid. In the computation, a compact upwind scheme was employed for the advection calculations and a pressure-based algorithm was applied to treat the multiple phases. The free surface and the body boundaries were captured using density functions. For the pressure calculation, a Poisson-type equation was solved at each time step by the conjugate gradient iterative method. Validation studies were carried out for 2D wedges with various deadrise angles ranging from 0 to 60 degrees at constant vertical velocity. In the cases of wedges with small deadrise angles, the compressibility of air between the bottom of the wedge and the free surface was modelled. Studies were also extended to 3D bodies, such as a sphere, a cylinder and a catamaran, entering calm water. Computed pressures, free surface elevations and hydrodynamic forces were compared with experimental data and the numerical solutions by other methods.

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