scholarly journals The Free Vibration of a Circular Plate Elastically Supported at Some Points

1978 ◽  
Vol 44 (379) ◽  
pp. 895-906
Author(s):  
Toshihiro IRIE ◽  
Gen YAMADA
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Elastically Supported

scholarly journals Free Vibration of Circular Plate Elastically Supported at Some Points

1978 ◽  
Vol 21 (161) ◽  
pp. 1602-1609 ◽  
Author(s):  
Toshihiro IRIE ◽  
Gen YAMADA
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Elastically Supported

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.

Frequencies of a Flexible Circular Plate Attached to the Surface of a Light Elastic Half-Space

1959 ◽  
Vol 26 (1) ◽  
pp. 13-17
Author(s):  
G. N. Bycroft
Keyword(s):  
Free Vibration ◽  
Circular Plate ◽  
Half Space ◽  
Fundamental Frequency ◽  
Elastic Half Space ◽  
Flexible Circular Plate

Abstract The frequencies of free vibration of a thin, flexible, circular plate stuck to the surface of a massless elastic half-space are solved by an application of the Rayleigh-Ritz principle. The approximate fundamental frequency is considered in detail when the plate is clamped, free, or hinged at its periphery. The method of obtaining the higher frequencies, such as those involving nodal diameters, is indicated.

Free Vibration Analysis of a New Polymer Quartz Piezoelectric Crystal Sensor Applied to Identify Chinese Liquors

2017 ◽  
Vol 09 (01) ◽  
pp. 1750015 ◽  
Author(s):  
Qiang Li ◽  
Yu Gu ◽  
Nanfei Wang
Keyword(s):  
Numerical Analysis ◽  
Free Vibration ◽  
Circular Plate ◽  
Mechanical Model ◽  
Numerical Solutions ◽  
Free Vibration Analysis ◽  
Sandwich Composite ◽  
Piezoelectric Crystal ◽  
Absolute Deviation ◽  
Free Vibration Frequency

This paper deals with the analytical and numerical analysis of free vibration in a new polymer piezoelectric crystal sensor. A quartz piezoelectric crystal here serves as the basal material and nonmetallic polymer thin films with perforative central holes as the surface coating according to the principle of quartz crystal microbalance (QCM), based on the Kirchhoff–Love plate model. A mechanical model of the new sensor was built, and its structure was a quartz piezoelectric sandwich composite circular plate with perforative central holes in the surface layers. The form of the electric potential field in the piezoelectric layer was here assumed to be such that the Maxwell static electricity equation is satisfied. The validation of the mechanical model and its analytic method is conducted by comparing the free vibration frequencies of the piezoelectric sandwich composite circular plate produced by the mechanical model’s analytical and numerical analyses performed using ANSYS software. Results show that the first 100 orders of free vibration frequency values of the mechanical model obtained by two methods, the analytical analysis and the numerical analysis, to be fit. The maximum absolute deviation rate ([Formula: see text] between the analytical solutions ([Formula: see text]) and the numerical solutions ([Formula: see text]) was found to be 6.89%. These results are important reference for the design of the new polymer quartz piezoelectric crystal sensors suitable for the identification of Chinese liquors.

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