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Stability of a gradient elastic beam compressed by non‐conservative forces
Author(s) -
Lazopoulos K.A.,
Lazopoulos A.K.
Publication year - 2010
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.200900231
Subject(s) - beam (structure) , elasticity (physics) , mechanics , conservative force , linear elasticity , action (physics) , classical mechanics , mathematics , physics , mathematical analysis , finite element method , optics , thermodynamics , quantum mechanics
The critical loads for five non‐conservative problems are defined under the context of gradient elasticity theory of a beam. The first problem deals with the stability of a gradient elastic beam compressed by a follower force (Beck's problem) and the second deals with the stability of a gradient elastic beam compressed by a force with a fixed line of action (Rent's problem). The governing dynamic equation with the boundary conditions is formulated on the bases of simple linear elasticity theory with the beam mass concentrated on the moving end. Also the case with uniform distribution of the mass along the beam will be considered. Further the effect of an additional conservative force acting on the moving end of the beam will also be discussed. Numerical applications indicate that although the surface energy term does not have a substantial effect, the intrinsic length due to gradient elasticity is of major importance. In fact, it increases of the critical load.