Interval solution and robust validation of uncertain elastic beams

2014 ◽  
pp. 445-452
Author(s):  
S Gabriele ◽  
C Valente ◽  
M de Angelis
Keyword(s):  
Elastic Beams ◽  
Interval Solution

scholarly journals Influence of the Parameterization in the Interval Solution of Elastic Beams

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Stefano Gabriele ◽  
Valerio Varano
Keyword(s):  
Boundary Conditions ◽  
Closed Form ◽  
Interval Analysis ◽  
Elastic Beam ◽  
Elastic Beams ◽  
Analysis Theory ◽  
Set Intersection ◽  
Interval Solution ◽  
Uncertain Boundary

We are going to analyze the interval solution of an elastic beam under uncertain boundary conditions. Boundary conditions are defined as rotational springs presenting interval stiffness. Developments occur according to the interval analysis theory, which is affected, at the same time, by the overestimation of interval limits (also known as overbounding, because of the propagation of the uncertainty in the model). We suggest a method which aims to reduce such an overestimation in the uncertain solution. This method consists in a reparameterization of the closed form Euler-Bernoulli solution and set intersection.

scholarly journals Tolerance Modelling of Vibrations and Stability for Periodic Slender Visco-Elastic Beams on a Foundation with Damping. Revisiting

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 3939
Author(s):  
Jarosław Jędrysiak
Keyword(s):  
Mathematical Modelling ◽  
System Of Differential Equations ◽  
Governing Equations ◽  
Asymptotic Homogenization ◽  
Elastic Beams ◽  
Oscillating Coefficients ◽  
Constant Coefficients ◽  
Tolerance Modelling ◽  
Tolerance Method ◽  
Modelling Approach

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.

Computer Simulation for Active Control of Vibration in Beam Structures

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.

Large deflection of curved elastic beams made of Ludwick type material

2017 ◽  
Vol 38 (7) ◽  
pp. 909-920 ◽  
Author(s):  
Hua Liu ◽  
Yi Han ◽  
Jialing Yang
Keyword(s):  
Large Deflection ◽  
Type Material ◽  
Elastic Beams
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