caa a22 4500 445361581 CHVBK 20180317142916.0 cr unu---uuuuu 170323e20111101xx s 000 0 eng 10.1007/s11071-011-0150-z doi (NATIONALLICENCE)springer-10.1007/s11071-011-0150-z Stability of nonlinear periodic vibrations of 3D beams [Elektronische Daten] [S. Stoykov, P. Ribeiro] The geometrically nonlinear periodic vibrations of beams with rectangular cross section under harmonic forces are investigated using a p-version finite element method. The beams vibrate in space; hence they experience longitudinal, torsional, and nonplanar bending deformations. The model is based on Timoshenko's theory for bending and assumes that, under torsion, the cross section rotates as a rigid body and is free to warp in the longitudinal direction, as in Saint-Venant's theory. The theory employed is valid for moderate rotations and displacements, and physical phenomena like internal resonances and change of the stability of the solutions can be investigated. Green's nonlinear strain tensor and Hooke's law are considered and isotropic and elastic beams are investigated. The equation of motion is derived by the principle of virtual work. The differential equations of motion are converted into a nonlinear algebraic form employing the harmonic balance method, and then solved by the arc-length continuation method. The variation of the amplitude of vibration in space with the excitation frequency of vibration is determined and presented in the form of response curves. The stability of the solution is investigated by Floquet's theory. Springer Science+Business Media B.V., 2011 Symmetry-breaking bifurcation nationallicence 1:1 internal resonance nationallicence Floquet's theory nationallicence Steady-state response nationallicence Stoykov S. DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal aut Ribeiro P. DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal aut Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 335-353 0924-090X 66:3<335 2011 66 11071 https://doi.org/10.1007/s11071-011-0150-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11071-011-0150-z text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Stoykov S. DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal aut NATIONALLICENCE 700 1- Ribeiro P. DEMec/IDMEC, Faculdade de Engenharia, Universidade do Porto, R. Dr. Roberto Frias, s/n, 4200-465, Porto, Portugal aut NATIONALLICENCE 773 0- Nonlinear Dynamics Springer Netherlands 66/3(2011-11-01), 335-353 0924-090X 66:3<335 2011 66 11071 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer