Paper Info
Title
A priori estimates for the general dynamic Euler-Bernoulli beam equation: Supported and cantilever beams.
Abstract
This work is a further development of weak solution theory for the general Euler–Bernoulli beam equation ρ(x)utt+μ(x)ut+r(x)uxxxx−(Tr(x)ux)x=F(x,t) defined in the finite dimension domain ΩT≔(0,l)×(0,T)⊂R2, based on the energy method. Here r(x)=EI(x), E>0 is the elasticity modulus and I(x)>0 is the moment of inertia of the cross-section, ρ(x)>0 is the mass density of the beam, μ(x)>0 is the damping coefficient and Tr(x)≥0 is the traction force along the beam. Two benchmark initial boundary value problems with mixed boundary conditions, corresponding to supported and cantilever beams, are analyzed. For the weak and regular weak solutions of these problems a priori estimates are derived under the minimal conditions. These estimates in particular imply the uniqueness of the solutions of both problems.
Year
DOI
Venue
2019
10.1016/j.aml.2018.07.038
Applied Mathematics Letters
Keywords
Field
DocType
Euler–Bernoulli beam equation,Weak and regular weak solution,A priori estimates,Uniqueness
Elastic modulus,Boundary value problem,Uniqueness,Moment of inertia,Mathematical analysis,Weak solution,Euler's formula,Beam (structure),Mathematics,Bernoulli's principle
Journal
Volume
ISSN
Citations 
87
0893-9659
0
PageRank 
References 
Authors
0.34
2
2
Name
Order
Citations
PageRank
Alemdar Hasanov100.34
Hiromichi Itou201.01