Free vibrations of a circular plate with attached concentrated mass, spring and dashpot

1967 ◽  
Vol 4 (3) ◽  
pp. 273-287
Author(s):  
N. Gajendar
Keyword(s):  
Circular Plate ◽  
Free Vibrations ◽  
Concentrated Mass ◽  
Mass Spring

An Integral Equation Method for Free Vibration of Circular Plate with Concentrated Mass at Arbitrary Positions

2011 ◽  
Vol 255-260 ◽  
pp. 1830-1835 ◽  
Author(s):  
Gang Cheng ◽  
Quan Cheng ◽  
Wei Dong Wang
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Green’S Function ◽  
Circular Plate ◽  
Green's Function ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Concentrated Mass

The paper concerns on the free vibrations of circular plate with arbitrary number of the mounted masses at arbitrary positions by using the integral equation method. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first kind, is used to construct the Green's function of circular plates firstly. Then the eigenvalue problem of free vibration of circular plate carrying oscillators and elastic supports at arbitrary positions is transformed into the problem of integral equation by using the superposition theorem and the physical meaning of the Green’s function. And then the eigenvalue problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical examples are presented.

Free Vibrations of Constrained Beams

1952 ◽  
Vol 19 (4) ◽  
pp. 471-477
Author(s):  
Winston F. Z. Lee ◽  
Edward Saibel
Keyword(s):  
Natural Frequencies ◽  
Degree Of Approximation ◽  
Free Vibrations ◽  
Frequency Equation ◽  
Continuous Beam ◽  
Concentrated Mass ◽  
Simple Manner ◽  
Natural Modes ◽  
Modes Of Vibration ◽  
Rigid Supports

Abstract A general expression is developed from which the frequency equation for the vibration of a constrained beam with any combination of intermediate elastic or rigid supports, concentrated masses, and sprung masses can be found readily. The method also is extended to the case where the constraint is a continuous elastic foundation or uniformly distributed load of any length. This method requires only the knowledge of the natural frequencies and natural modes of the beam supported at the ends in the same manner as the constrained beam but not subjected to any of the constraints between the ends. The frequency equation is obtained easily and can be solved to any desired degree of approximation for any number of modes of vibration in a quick and simple manner. Numerical examples are given for a beam with one concentrated mass, for a beam with one sprung mass, and a continuous beam with one sprung mass.

A PASSIVE STATE SIMULATION OF AN ANAL SPHINCTER USING SIMMECHANICS

2018 ◽  
Vol 18 (06) ◽  
pp. 1850059
Author(s):  
BLANCA N. RIOS ATAXCA ◽  
CARLOS D. GARCÍA BELTRÁN ◽  
JOSÉ M. RODRÍGUEZ LELIS ◽  
VÍCTOR H. OLIVARES PEREGRINO ◽  
FLORENCIO DE LA CONCHA BERMEJILLO ◽  
...  
Keyword(s):  
Initial Conditions ◽  
Radial Force ◽  
The Body ◽  
Passive State ◽  
Sphincter Muscle ◽  
Human Beings ◽  
Concentrated Mass ◽  
Mechanical Oscillations ◽  
Spring System ◽  
Mass Spring

Nowadays, different mechanical artificial sphincters can be found implanted in human beings, trying to overcome a deficiency in the performance of the natural one. However, they do not take into account the natural anal sphincter’s (AS) dimensions, and autonomous response; they also lack in basic contraction and relaxation properties. In this paper, by addressing the AS behavior, an AS model designed with Matlab/SimMechanics is shown. The model comprises bodies of concentrated mass interconnected by springs. The mass–spring system is arranged in concentric rings where every concentrated mass is interconnected by a spring. Each spring takes specific stiffness, which varies with length, in accordance to an experimental curve. The system described can be loaded or unloaded, describing then the muscle behavior. Each element that forms the model of rings is subject to displacements caused by forces of traction and compression, when a radial force is applied from the center towards the inner ring. The springs of the inner ring experience forces of traction, whereas the springs that connect the body of the inner ring with the outer ring perpendicularly are submitted to compression forces.The data used in the proposed model corresponded to dimensions of the humanAS: width, height, rigidity, stress, tension, basically obtaining an initial deformation behavior according to the sphincter in the passive state. The model remained stable with some mechanical oscillations due to the elastic elements; by modifying one of the parameters, the behavior became unstable and unmanageable. It was verified that it is a sensitive model when modifying the initial conditions that the concrete data requires in case of reproducing the sphincter muscle with particular dimensions.

Vibrating circular plate carrying a concentrated mass: Comparison of results

1990 ◽  
Vol 138 (2) ◽  
pp. 335-336 ◽  
Author(s):  
M.J. Maurizi ◽  
P.A.A. Laura ◽  
D.V. Bambill ◽  
C. Rossit
Keyword(s):  
Circular Plate ◽  
Concentrated Mass ◽  
Comparison Of Results ◽  
Mass Comparison

Effects of a Concentrated Mass on Chaotic Vibrations of a Clamped Circular Plate With Initial Deformation

2011 ◽  
Author(s):  
Kenji Okada ◽  
Ken-ichi Nagai ◽  
Shinichi Maruyama ◽  
Takao Yamaguchi
Keyword(s):  
Circular Plate ◽  
Fourier Spectrum ◽  
Principal Component ◽  
Frequency Region ◽  
Initial Deformation ◽  
Periodic Excitation ◽  
Contribution Ratio ◽  
Concentrated Mass ◽  
Chaotic Vibrations ◽  
Maximum Lyapunov Exponents

Experimental results are presented on effects of a concentrated mass on chaotic vibrations of a clamped circular plate. The plate has initial deformation due to initial deflection and initial in-plane compressive constraint at the boundary. The concentrated mass is attached on the center of the plate. Under periodic excitation, non-periodic responses with dynamic snap-through are generated on the plates. The responses are inspected by the Fourier spectrum, the Poincare´ projection, the maximum Lyapunov exponents and the principal component analysis. The non-periodic responses are found to be chaotic responses. The lowest mode of vibration shows the largest contribution ratio. When the concentrated mass is attached on the plate, the region of the response is shifted to the lower frequency. Furthermore, the width of the frequency region is decreased. The contribution ratio of the lowest mode slightly increases.

Sign in / Sign up

Export Citation Format

Share Document