Application of a Set of Completed System of Orthogonal Functions in L2[a,b] Space on the Vibration Analysis of Annular Plates

2011 ◽  
Vol 42 (11) ◽  
pp. 25-29
Author(s):  
WeiDong Wang ◽  
Gang Cheng ◽  
Quan Cheng
Keyword(s):  
Integral Equation ◽  
Free Vibration ◽  
High Precision ◽  
Green's Function ◽  
Vibration Analysis ◽  
Annular Plate ◽  
Integral Equation Method ◽  
Equation Method ◽  
Orthogonal Functions ◽  
Annular Plates

A type of complete systems of orthogonal functions in L2[a,b] space is introduced into the construction of Green's function of annular plate. A brief and effective method is derived to study the free vibration of annular plates by using the integral equation method. The results obtained not only reveal its briefness and high precision, but also provide a reliable premise for the vibration analysis of more complex annular plates.

Integral Equation Method for Free Vibration of Annular Plates with Elastic Supports

2011 ◽  
Vol 52-54 ◽  
pp. 573-577
Author(s):  
Gang Cheng ◽  
Wei Dong Wang ◽  
Quan Cheng
Keyword(s):  
Integral Equation ◽  
Eigenvalue Problem ◽  
Free Vibration ◽  
Infinite Order ◽  
Integral Equation Method ◽  
Free Vibrations ◽  
Equation Method ◽  
Orthogonal Functions ◽  
Elastic Supports ◽  
Annular Plates

Annular plates are commonly found in the fields of engineering. The present study is concerned with the integral equation method for the free vibrations of annular plates with elastic supports. A set of complete systems of orthogonal functions, which is constructed by Bessel functions of the first and the second kind is used to construct the Green's function of annular plates. The eigenvalue problem of free vibration of annular plates with Elastic Supports is transformed into the eigenvalue problem of integral equation. And then, the problem of integral equation is transformed into a standard eigenvalue problem of a matrix with infinite order. Numerical example shows the significant advantages of the present method.

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.

scholarly journals Multiple Scattering Using Parallel Volume Integral Equation Method: Interaction of SH Waves with Multiple Multilayered Anisotropic Elliptical Inclusions

2015 ◽  
Vol 2015 ◽  
pp. 1-48 ◽  
Author(s):  
Jungki Lee ◽  
Hyechang Lee ◽  
Hogwan Jeong
Keyword(s):  
Integral Equation ◽  
Multiple Scattering ◽  
Green's Function ◽  
Wave Scattering ◽  
Integral Equation Method ◽  
Equation Method ◽  
Volume Integral ◽  
Volume Integral Equation ◽  
Parallel Volume ◽  
Volume Integral Equation Method

The parallel volume integral equation method (PVIEM) is applied for the analysis of elastic wave scattering problems in an unbounded isotropic solid containing multiple multilayered anisotropic elliptical inclusions. This recently developed numerical method does not require the use of Green’s function for the multilayered anisotropic inclusions; only Green’s function for the unbounded isotropic matrix is needed. This method can also be applied to solve general two- and three-dimensional elastodynamic problems involving inhomogeneous and/or multilayered anisotropic inclusions whose shape and number are arbitrary. A detailed analysis of the SH wave scattering is presented for multiple triple-layered orthotropic elliptical inclusions. Numerical results are presented for the displacement fields at the interfaces for square and hexagonal packing arrays of triple-layered elliptical inclusions in a broad frequency range of practical interest. It is necessary to use standard parallel programming, such as MPI (message passing interface), to speed up computation in the volume integral equation method (VIEM). Parallel volume integral equation method as a pioneer of numerical analysis enables us to investigate the effects of single/multiple scattering, fiber packing type, fiber volume fraction, single/multiple layer(s), multilayer’s shape and geometry, isotropy/anisotropy, and softness/hardness of the multiple multilayered anisotropic elliptical inclusions on displacements at the interfaces of the inclusions.

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