 Analysis of weak solution of Euler–Bernoulli beam with axial forceBidisha Kundu and Ranjan Ganguli Applied Mathematics and Computation, 2017, vol. 298, issue C, 247-260 Abstract: In this paper, we discuss about the existence and uniqueness of the weak form of the non-uniform cantilever Euler–Bernoulli beam equation with variable axial (tensile and compressive) force. We investigate the reason of the buckling from the coercivity analysis. The frequencies of the beam with tensile force are found by the Galerkin method in the Sobolev space H2 with proper norm. Using this method, a system of ordinary differential equations in time variable is formed and the corresponding mass and stiffness matrices are constructed. A very general form of these matrices, which is very simple and suitable for calculations, is derived here with a standard basis. Numerical results for rotating beams with polynomial stiffness and mass variation, typical of wind turbine and helicopter rotor blades, are obtained. These results match well with the published literature. A new polynomial generating set is found. Using two elements of this set, a formula to find the eigenfrequencies is derived. The proposed approach is easy to implement in symbolic computing software. Keywords: Rotating Euler–Bernoulli beam; Weak formulation; Cantilever beam; Galerkin method; Vibration; Buckling (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:298:y:2017:i:c:p:247-260 DOI: 10.1016/j.amc.2016.11.019 Access Statistics for this article Applied Mathematics and Computation is currently edited by Theodore Simos More articles in Applied Mathematics and Computation from Elsevier |
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