Solvability of the clamped Euler-Bernoulli beam equation

被引：16

作者：

Baysal, Onur ^{[1
,2
]}

Hasanov, Alemdar ^{[3
]}

机构：

[1] Bahcesehir Coll, Sci & Technol High Sch, Izmir, Turkey

[2] Univ Sao Paulo, Escola Politecn, Sao Paulo, Brazil

[3] Dogus Univ, Dept Mech Engn, Istanbul, Turkey

来源：

APPLIED MATHEMATICS LETTERS | 2019年 / 93卷

关键词：

Euler-Bernoulli beam; Weak solution; Existence; Uniqueness; VIBRATION;

D O I：

10.1016/j.aml.2019.02.006

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this study, solvability of the initial boundary value problem for general form Euler-Bernoulli beam equation which includes also moving point-loads is investigated. The complete proof of an existence and uniqueness properties of the weak solution of the considered equation with Dirichlet type boundary conditions is derived. The method used here is based on Galerkin approximation which is the main tool for the weak solution theory of linear evolution equations as well as in derivation of a priori estimate for the approximate solutions. All steps of the proposed technique are explained in detail. (C) 2019 Elsevier Ltd. All rights reserved.

引用

页码：85 / 90

页数：6

共 50 条

[31] Analytical Study of Sandwich Structures using Euler-Bernoulli Beam Equation
Xue, Hui
Khawaja, H.
[J]. ICNPAA 2016 WORLD CONGRESS: 11TH INTERNATIONAL CONFERENCE ON MATHEMATICAL PROBLEMS IN ENGINEERING, AEROSPACE AND SCIENCES, 2017, 1798
[32] Inverse Problem for the Time-Fractional Euler-Bernoulli Beam Equation
Tekin, Ibrahim
Yang, He
[J]. MATHEMATICAL MODELLING AND ANALYSIS, 2021, 26 (03) : 503 - 518
[33] Well-posedness and stability for a nonlinear Euler-Bernoulli beam equation
Deng, Panyu
Zheng, Jun
Zhu, Guchuan
[J]. COMMUNICATIONS IN ANALYSIS AND MECHANICS, 2024, 16 (01): : 193 - 216
[34] A dynamic Euler-Bernoulli beam equation frictionally damped on an elastic foundation
Heibig, Arnaud
Petrov, Adrien
[J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2022, 64
[35] Polynomial and analytic stabilization of a wave equation coupled with an Euler-Bernoulli beam
Ammari, Kais
Nicaise, Serge
[J]. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 2009, 32 (05) : 556 - 576
[36] Logarithmic stability in determining two coefficients in a dissipative wave equation. Extensions to clamped Euler-Bernoulli beam and heat equations
Ammari, Kais
Choulli, Mourad
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2015, 259 (07) : 3344 - 3365
[37] Modeling a Clamped Boring Bar using Euler-Bernoulli Beam Models with Various Boundary Conditions
Smirnova, T.
Akesson, H.
Claesson, I.
Hakansson, L.
Lagoe, T.
[J]. MATHEMATICAL MODELING OF WAVE PHENOMENA, 2009, 1106 : 149 - +
[38] The Floquet theory of the periodic Euler-Bernoulli equation
Papanicolaou, VG
Kravvaritis, D
[J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 1998, 150 (01) : 24 - 41
[39] EXACT SEMIINTERNAL CONTROL OF AN EULER-BERNOULLI EQUATION
KIM, JU
[J]. SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 1992, 30 (05) : 1001 - 1023
[40] Motion Planning for a Damped Euler-Bernoulli Beam
Meurer, Thomas
Schroeck, Johannes
Kugi, Andreas
[J]. 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC), 2010, : 2566 - 2571

← 1 2 3 4 5 →