Pardies’ essays on the catenary and on elastic beams (1673)

The mathematical modelling of certain problems of vibrations and stability for periodic slender visco-elastic beams is presented in this note. To consider these problems and take into account the effect of the microstructure, the tolerance modelling approach is proposed. Using this technique, the equation with non-continuous, periodic, highly oscillating coefficients is replaced by a system of differential equations with constant coefficients. Moreover, these governing equations describe the effect of the microstructure on the overall behavior of the beams under consideration. The tolerance modelling can lead to equations of two different tolerance models—the standard and the general, under weakened assumptions. This averaging tolerance method was assessed by comparison with the asymptotic homogenization, the governing equations of which omit this effect. My considerations were limited to proposing and presenting only mathematical models describing investigated beams. In a simple analytical example, the application of the presented average models is shown.

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Free vibration of layered magneto-electro-elastic beams by SS-DSC approach

Composite Structures ◽

10.1016/j.compstruct.2015.01.048 ◽

2015 ◽

Vol 125 ◽

pp. 96-103 ◽

Cited By ~ 25

Author(s):

Libo Xin ◽

Zhendong Hu

Keyword(s):

Free Vibration ◽

Elastic Beams

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Discussion of “Variational Considerations for Elastic Beams and Shells”

Journal of the Engineering Mechanics Division ◽

10.1061/jmcea3.0000334 ◽

1962 ◽

Vol 88 (5) ◽

pp. 179-183

Author(s):

A.R. Oliver

Keyword(s):

Elastic Beams

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Computer Simulation for Active Control of Vibration in Beam Structures

Volume 3C: 15th Biennial Conference on Mechanical Vibration and Noise — Vibration Control, Analysis, and Identification ◽

10.1115/detc1995-0683 ◽

1995 ◽

Author(s):

Masa. Tanaka ◽

T. Matsumoto ◽

L. Huang

Keyword(s):

Inverse Problem ◽

Active Control ◽

Inverse Analysis ◽

Taylor Series Expansion ◽

Integral Equation Method ◽

Unknown Parameters ◽

Bending Vibration ◽

Linear System Of Equations ◽

Elastic Beams ◽

The Laplace Transform

Abstract This paper is concerned with an inverse problem of the active control of non-steady dynamic vibration in elastic beams. A simulation technique based on the boundary element method and the extended Kalman filter or a new filter theory is successfully applied to the inverse problem. The Laplace-transform integral equation method is used for the solution of dynamic bending vibration in elastic beams. Through a Taylor series expansion, the linear system of equations is derived for modification of the unknown parameters, and it is solved iteratively so that an appropriate norm is minimized. The usefulness of the proposed method of inverse analysis is demonstrated through numerical computation of a few examples.

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