Eigenvalue analysis of graphene plates embedded into the elastic Pasternak foundation

Subsynchronous Oscillation problems caused by HVDC system are studied and analyzed intensively in this paper based on eigenvalue analysis method. By establishing the small signal linearized model of a typical HVDC system, subsynchronous oscillation characteristics of the system with or without SSDC are obtained. Further more, the influence of SSDC parameters to the system subsynchronous oscillation characteristic can be illustrated clearly. This is significant for SSDC design in order to achieve a satisfied restraining effect. Comparing with more accurate electromagnetic transient simulation results, the consistency of the two methods is verified and it can be demonstrated that eigenvalue analysis method is adequate for studying subsynchronous oscillations.

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On the effective buckling length of framed columns using eigenvalue analysis.

Doboku Gakkai Ronbunshu ◽

10.2208/jscej.1994.489_157 ◽

1994 ◽

pp. 157-166 ◽

Cited By ~ 3

Author(s):

Kuniei Nogami ◽

Kazuyuki Yamamoto

Keyword(s):

Eigenvalue Analysis ◽

Buckling Length

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A Quasi-Greens Function Method for the Bending Problem of Simply Supported Polygonal Shallow Spherical Shells on Pasternak Foundation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.353-356.3215 ◽

2013 ◽

Vol 353-356 ◽

pp. 3215-3219

Author(s):

Shan Qing Li ◽

Hong Yuan

Keyword(s):

Function Method ◽

Homogeneous Boundary Condition ◽

Fredholm Integral Equations ◽

Pasternak Foundation ◽

Boundary Equation ◽

Spherical Shells ◽

Simply Supported ◽

Suitable Form ◽

Greens Function ◽

Good Agreement

The quasi-Greens function method (QGFM) is applied to solve the bending problem of simply supported polygonal shallow spherical shells on Pasternak foundation. A quasi-Greens function is established by using the fundamental solution and the boundary equation of the problem. And the function satisfies the homogeneous boundary condition of the problem. Then the differential equation of the problem is reduced to two simultaneous Fredholm integral equations of the second kind by the Greens formula. The singularity of the kernel of the integral equation is overcome by choosing a suitable form of the normalized boundary equation. The comparison with the ANSYS finite element solution shows a good agreement, and it demonstrates the feasibility and efficiency of the proposed method.

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Three-Dimensional Vibration Analysis of Rectangular Thick Plates on Pasternak Foundation with Arbitrary Boundary Conditions

Shock and Vibration ◽

10.1155/2017/3425298 ◽

2017 ◽

Vol 2017 ◽

pp. 1-10 ◽

Cited By ~ 2

Author(s):

Huimin Liu ◽

Fanming Liu ◽

Xin Jing ◽

Zhenpeng Wang ◽

Linlin Xia

Keyword(s):

Boundary Conditions ◽

Admissible Function ◽

Three Dimensional ◽

Future Research ◽

Pasternak Foundation ◽

Arbitrary Boundary ◽

Thick Plates ◽

Arbitrary Boundary Conditions ◽

Ritz Procedure ◽

Three Dimensional Elasticity

This paper presents the first known vibration characteristic of rectangular thick plates on Pasternak foundation with arbitrary boundary conditions on the basis of the three-dimensional elasticity theory. The arbitrary boundary conditions are obtained by laying out three types of linear springs on all edges. The modified Fourier series are chosen as the basis functions of the admissible function of the thick plates to eliminate all the relevant discontinuities of the displacements and their derivatives at the edges. The exact solution is obtained based on the Rayleigh–Ritz procedure by the energy functions of the thick plate. The excellent accuracy and reliability of current solutions are demonstrated by numerical examples and comparisons with the results available in the literature. In addition, the influence of the foundation coefficients as well as the boundary restraint parameters is also analyzed, which can serve as the benchmark data for the future research technique.

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