Conservative linear models for the vibrating string and rod free to slide, at one end point, on a vertical guide

被引：2

作者：

Frontini, M ^{[1
]}

Gotusso, L ^{[1
]}

机构：

[1] Politecn Milan, Dipartimento Matemat, I-20133 Milan, Italy

来源：

COMPUTERS & MATHEMATICS WITH APPLICATIONS | 1998年 / 35卷 / 06期

关键词：

differential equations; difference equations; discrete models; conservative models; linear elasticity;

D O I：

10.1016/S0898-1221(98)00016-9

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The motion of a linear vibrating string, or rod, fixed in one point and free to slide on a vertical guide in the other one, is studied. Only transversal vibrations are considered. The motion is simulated by a discrete conservative model. In order to prove that the total energy is conserved, a matrix form of the potential and kinetic energy is used. The same technique may be used to simplify the proof of energy conservation theorem given by the authors in a previous paper. The numerical method related to the model turns out to be unconditionally stable. Some examples of the motion simulated by the model are given.

引用

页码：41 / 50

页数：10

共 5 条

[1] The vibrating string and rod free to slide, at both end points, on a vertical guide
Frontini, M
Gotusso, L
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2000, 40 (2-3) : 277 - 290
[2] Linear and nonlinear models for the vibrating string and the vibrating rod
Gotusso, L
Veneziani, A
ADVANCES IN DIFFERENCE EQUATIONS-BOOK, 1997, : 245 - 252
[3] Discrete conservative model for the linear vibrating string and rod
Frontini, M.
Gotusso, L.
Computers and Mathematics with Applications, 1997, 33 (10): : 53 - 65
[4] A discrete conservative model for the linear vibrating string and rod
Frontini, M
Gotusso, L
COMPUTERS & MATHEMATICS WITH APPLICATIONS, 1997, 33 (10) : 53 - 65
[5] Discrete conservative models for the simulation of the motion of a vibrating string or rod
Frontini, M
Gotusso, L
NUMERICAL ANALYSIS: METHODS AND MATHEMATICAL SOFTWARE, SUPPLEMENT, 2000, 46 : 293 - 304

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