scholarly journals Behavior of a Flat Solid in a Container with Liquid Subject to Large Amplitude Vibration

2016 ◽  
Vol 2016 ◽  
pp. 1-11
Author(s):  
Victor Kozlov ◽  
Olga Vlasova
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Lift Force ◽  
Stable State ◽  
The Body ◽  
Body Density ◽  
Dimensionless Amplitude ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Inertia Forces

We experimentally study the behavior of a flat body in the oscillating container with liquid. The body density is much more than the density of liquid. The body oscillates with large amplitude under the action of inertia forces. It is found that under the vibration the body lifts up and goes to quasi-steady suspended state at some distance from the container bottom. The lift force is measured by a method of dynamic suspension of a body in the gravity field. It is found that the dimensionless repulsion lift force depends on the dimensionless amplitude of the body oscillations; it reduces with the amplitude and is in agreement with the theoretical model in the limit of small amplitude. Qualitatively new regimes of body behavior are found in the supercritical region. With an increase of the vibration intensity, the body gets a stable state in the middle of the container height and then moves on to the container ceiling.

Large Amplitude Free Vibration Study of Square Plates under Different Boundary Conditions Through a Static Analysis

2004 ◽  
Vol 10 (7) ◽  
pp. 1009-1028 ◽  
Author(s):  
K. N. Saha ◽  
D. Misra ◽  
G. Pohit ◽  
S. Ghosal
Keyword(s):  
Boundary Conditions ◽  
Large Amplitude ◽  
Static Problem ◽  
Mode Shapes ◽  
Linear Combinations ◽  
Isotropic Plates ◽  
Dimensionless Amplitude ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Comparison Of The Results

The free v ibration problem of thin isotropic plates incorporating the effect. of geometric non-linearity is studied by developing a specific numerical methodology. The problem is formulated by using a variational method. The large amplitude vibration problem is addressed by solving the corresponding static problem first through an iterative schemne using a relaxation parameter. Subsequently. with the resulting displacement field, the dynamic problem is solved as a standard eigenvalue problem. The assumed deflection field, required for the analysis, is constituted through linear combinations of beam vibration modes corresponding to the specific boundary conditions of the plate. Typical results for the square plates, in the form of backbone curves, have been furnished in the dimensionless amplitude-frequency plane. Two different combinations of the boundary conditions for the purpose are chosen following an earlier benchmark work. Much insight on large amplitude dynamic behavior of the plate is obtained through the vibration mode shapes. presented for each case. A comparison of the results of the reduced problem with those of earlier studies indicates excellent agreement.

Large Amplitude Vibration of a Circular Plate With Concentric Rigid Mass

1972 ◽  
Vol 39 (2) ◽  
pp. 577-583 ◽  
Author(s):  
D. C. Chiang ◽  
S. S. H. Chen
Keyword(s):  
Circular Plate ◽  
Large Amplitude ◽  
Small Amplitude ◽  
Natural Frequencies ◽  
Elliptic Functions ◽  
Amplitude Vibration ◽  
Rigid Mass ◽  
Large Amplitude Vibration ◽  
Large Amplitude Vibrations ◽  
Special Case

Simplified nonlinear governing differential equations proposed by Berger and extended by Nash and Modeer are applied to obtain natural frequencies of a circular plate with concentric rigid part at its center in large amplitude vibrations. A modified Galerkin technique is used to derive a nonlinear differential equation of which the solution is given in terms of elliptic functions. The small amplitude vibration is treated as a special case of large amplitude vibration, while the free, large amplitude vibration of a flat circular plate is studied as a special case of large amplitude vibration of a circular plate with a concentric mass. The numerical results show that the effect of added concentric rigid mass to a circular plate is significant.

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