Influence of the Parameterization in the Interval Solution of Elastic Beams

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.

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Remedy to Overestimation of Classical Interval Analysis: Analysis of Beams with Uncertain Boundary Conditions

Shock and Vibration ◽

10.1155/2013/521374 ◽

2013 ◽

Vol 20 (1) ◽

pp. 143-156 ◽

Cited By ~ 3

Author(s):

Isaac Elishakoff ◽

Clément Soret

Keyword(s):

Boundary Conditions ◽

Interval Analysis ◽

Natural Frequencies ◽

Mass Density ◽

Static Problem ◽

Interval Parameter ◽

Dynamic Behaviors ◽

Stiffness Coefficients ◽

Interval Variables ◽

Uncertain Boundary

This study investigates both the static and dynamic behaviors for the uniform beam supported at its ends by rotational supports. The stiffness coefficients of these supports are treated as interval variables. It is first demonstrated on the static problem that the classical interval analysis may lead to overestimation of the response. The paper introduces a remedy for this "ill" of the classical interval analysis. The artificial interval parameter is introduced and the extrema of the static displacements and natural frequencies are determined. Finally, the hybrid case of uncertain boundary conditions and uncertain mass density is treated with attendant interesting results.

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Closed-form solutions for the coupled deflection of anisotropic Euler–Bernoulli composite beams with arbitrary boundary conditions

Thin-Walled Structures ◽

10.1016/j.tws.2021.107479 ◽

2021 ◽

Vol 161 ◽

pp. 107479 ◽

Cited By ~ 1

Author(s):

Pedram Khaneh Masjedi ◽

Olga Doeva ◽

Paul M. Weaver

Keyword(s):

Boundary Conditions ◽

Closed Form ◽

Composite Beams ◽

Arbitrary Boundary ◽

Closed Form Solutions ◽

Arbitrary Boundary Conditions

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Quantum square-well with logarithmic central spike

Modern Physics Letters A ◽

10.1142/s0217732318500098 ◽

2018 ◽

Vol 33 (02) ◽

pp. 1850009 ◽

Cited By ~ 2

Author(s):

Miloslav Znojil ◽

Iveta Semorádová

Keyword(s):

Perturbation Theory ◽

Boundary Conditions ◽

Closed Form ◽

Wave Functions ◽

Change Of Variables ◽

State Dependent ◽

Square Well ◽

Strength Formula ◽

Schrödinger Perturbation ◽

Dependent Interaction

Singular repulsive barrier [Formula: see text] inside a square-well is interpreted and studied as a linear analog of the state-dependent interaction [Formula: see text] in nonlinear Schrödinger equation. In the linearized case, Rayleigh–Schrödinger perturbation theory is shown to provide a closed-form spectrum at sufficiently small [Formula: see text] or after an amendment of the unperturbed Hamiltonian. At any spike strength [Formula: see text], the model remains solvable numerically, by the matching of wave functions. Analytically, the singularity is shown regularized via the change of variables [Formula: see text] which interchanges the roles of the asymptotic and central boundary conditions.

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Interval solution and robust validation of uncertain elastic beams

Safety, Reliability, Risk and Life-Cycle Performance of Structures and Infrastructures ◽

10.1201/b16387-67 ◽

2014 ◽

pp. 445-452

Author(s):

S Gabriele ◽

C Valente ◽

M de Angelis

Keyword(s):

Elastic Beams ◽

Interval Solution

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The Krylov problem in the case of a beam on Vlasov inertial foundation

AUTOBUSY – Technika Eksploatacja Systemy Transportowe ◽

10.24136/atest.2018.165 ◽

2018 ◽

Vol 19 (6) ◽

pp. 728-736

Author(s):

Wacław Szcześniak ◽

Magdalena Ataman

Keyword(s):

Closed Form ◽

Compressive Force ◽

Elastic Beam ◽

Forced Vibrations ◽

Critical Force ◽

Winkler Foundation ◽

Static Deflection ◽

Numerical Examples ◽

Moving Force ◽

Axial Forces

The paper deals with vibrations of the elastic beam caused by the moving force traveling with uniform speed. The function defining the pure forced vibrations (aperiodic vibrations) is presented in a closed form. Dynamic deflection of the beam caused by moving force is compared with the static deflection of the beam subjected to the force , and compressed by axial forces . Comparing equations (9) and (13), it can be concluded that the effect on the deflection of the speed of the moving force is the same as that of an additional compressive force . Selected problems of stability of the beam on the Winkler foundation and on the Vlasov inertial foundation are discussed. One can see that the critical force of the beam on Vlasov foundation is greater than in the case of Winkler's foundation. Numerical examples are presented in the paper

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