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.

Large amplitude vibrations of heated Timoshenko beams with delamination

2015 ◽  
Vol 230 (1) ◽  
pp. 88-101 ◽  
Author(s):  
Emil Manoach ◽  
Jerzy Warminski ◽  
Anna Warminska
Keyword(s):  
Large Amplitude ◽  
Previous Analysis ◽  
Geometrically Nonlinear ◽  
Timoshenko Beams ◽  
Shear Forces ◽  
Temperature Changes ◽  
Normal Forces ◽  
Amplitude Vibration ◽  
Large Amplitude Vibration ◽  
Large Amplitude Vibrations

In this work, the large amplitude vibration of a heated Timoshenko composite beam having delamination is studied. The model of delamination considers the contact interaction between sublaminates including normal forces, shear forces, and additional damping due to the interaction of sublaminates. This work is an extension of the previous analysis based on a model of the dynamic behavior of a beam with delamination considering additionally the nonlinearities due to large displacements and temperature changes. Numerical calculations are performed in order to estimate the influence of the delamination, the geometrically nonlinear terms, and elevated temperature on the response of the beam.

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.

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