Fracture analysis of one-dimensional hexagonal quasicrystals: Researches of a finite dimension rectangular plate by boundary collocation method

2017 ◽  
Vol 31 (5) ◽  
pp. 2373-2383 ◽  
Author(s):  
Cheng Jiaxing ◽  
Dongfa Sheng ◽  
Pengpeng Shi
Keyword(s):  
Rectangular Plate ◽  
Collocation Method ◽  
Finite Dimension ◽  
Fracture Analysis ◽  
One Dimensional ◽  
Boundary Collocation Method

scholarly journals Feedback stabilization of one-dimensional parabolic systems related to formations

2015 ◽  
Vol 63 (1) ◽  
pp. 295-303
Author(s):  
H. Sano
Keyword(s):  
Finite Dimension ◽  
Time Derivative ◽  
Parabolic Systems ◽  
Feedback Stabilization ◽  
Boundary Values ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Neumann Type ◽  
Sturm Liouville ◽  
Output Operator

Abstract This paper is concerned with the problem of stabilizing one-dimensional parabolic systems related to formations by using finitedimensional controllers of a modal type. The parabolic system is described by a Sturm-Liouville operator, and the boundary condition is different from any of Dirichlet type, Neumann type, and Robin type, since it contains the time derivative of boundary values. In this paper, it is shown that the system is formulated as an evolution equation with unbounded output operator in a Hilbert space, and further that it is stabilized by using an RMF (residual mode filter)-based controller which is of finite-dimension. A numerical simulation result is also given to demonstrate the validity of the finite-dimensional controller

scholarly journals Forced quasi-periodic oscillations in strongly dissipative systems of any finite dimension

2019 ◽  
Vol 21 (07) ◽  
pp. 1850064 ◽  
Author(s):  
Guido Gentile ◽  
Alessandro Mazzoccoli ◽  
Faenia Vaia
Keyword(s):  
Potential Energy ◽  
Finite Dimension ◽  
Dissipative Systems ◽  
Diophantine Condition ◽  
Frequency Vector ◽  
Periodic Forcing ◽  
One Dimensional ◽  
Forcing Term ◽  
Degeneracy Condition ◽  
The One

We consider a class of singular ordinary differential equations describing analytic systems of arbitrary finite dimension, subject to a quasi-periodic forcing term and in the presence of dissipation. We study the existence of response solutions, i.e. quasi-periodic solutions with the same frequency vector as the forcing term, in the case of large dissipation. We assume the system to be conservative in the absence of dissipation, so that the forcing term is — up to the sign — the gradient of a potential energy, and both the mass and damping matrices to be symmetric and positive definite. Further, we assume a non-degeneracy condition on the forcing term, essentially that the time-average of the potential energy has a strict local minimum. On the contrary, no condition is assumed on the forcing frequency; in particular, we do not require any Diophantine condition. We prove that, under the assumptions above, a response solution always exists provided the dissipation is strong enough. This extends results previously available in the literature in the one-dimensional case.

Application of boundary collocation method to two-dimensional wave propagation

2015 ◽  
Vol 29 (4) ◽  
pp. 579-587 ◽  
Author(s):  
Xue-ling Cao ◽  
Ya-ge You ◽  
Song-wei Sheng ◽  
Wen Peng ◽  
Yin Ye
Keyword(s):  
Wave Propagation ◽  
Collocation Method ◽  
Two Dimensional ◽  
Boundary Collocation Method ◽  
Dimensional Wave

Boundary collocation method vs fem for some harmonic 2-d problems

1989 ◽  
Vol 33 (1) ◽  
pp. 155-168 ◽  
Author(s):  
J.A. Kołodziej ◽  
M. Kleiber
Keyword(s):  
Collocation Method ◽  
Boundary Collocation Method
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