000013107 001__ 13107
000013107 005__ 20161114160327.0
000013107 04107 $$aeng
000013107 046__ $$k2009-06-22
000013107 100__ $$aSapountzakis E., J.
000013107 24500 $$aNonlinear nonuniform torsional vibrations of bars by bem

000013107 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013107 260__ $$bNational Technical University of Athens, 2009
000013107 506__ $$arestricted
000013107 520__ $$2eng$$aIn this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant crosssection taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement – small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post- buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an “average” axial displacement of the cross section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the Analog Equation Method, a BEM based method, leading to a system of nonlinear Differential – Algebraic Equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental modeshape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the Direct Iteration Technique (DIT), with a geometrically linear fundamental modeshape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.

000013107 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013107 653__ $$ashear stresses, bar, boundary element method, nonuniform torsion, nonlinear vibrations, torsional vibrations Abstract. In this paper a boundary element method is developed for the nonuniform torsional vibration problem of bars of arbitrary doubly symmetric constant crosssection taking into account the effect of geometrical nonlinearity. The bar is subjected to arbitrarily distributed or concentrated conservative dynamic twisting and warping moments along its length, while its edges are supported by the most general torsional boundary conditions. The transverse displacement components are expressed so as to be valid for large twisting rotations (finite displacement – small strain theory), thus the arising governing differential equations and boundary conditions are in general nonlinear. The resulting coupling effect between twisting and axial displacement components is considered and torsional vibration analysis is performed in both the torsional pre- or post- buckled state. A distributed mass model system is employed, taking into account the warping, rotatory and axial inertia, leading to the formulation of a coupled nonlinear initial boundary value problem with respect to the variable along the bar angle of twist and to an “average” axial displacement of the cross section of the bar. The numerical solution of the aforementioned initial boundary value problem is performed using the Analog Equation Method, a BEM based method, leading to a system of nonlinear Differential – Algebraic Equations (DAE), which is solved using an efficient time discretization scheme. Additionally, for the free vibrations case, a nonlinear generalized eigenvalue problem is formulated with respect to the fundamental modeshape at the points of reversal of motion after ignoring the axial inertia to verify the accuracy of the proposed method. The problem is solved using the Direct Iteration Technique (DIT), with a geometrically linear fundamental modeshape as a starting vector. The validity of negligible axial inertia assumption is examined for the problem at hand.

000013107 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013107 720__ $$aSapountzakis E., J.$$iTsipiras V., J.
000013107 8560_ $$ffischerc@itam.cas.cz
000013107 8564_ $$s649211$$uhttps://invenio.itam.cas.cz/record/13107/files/CD143.pdf$$yOriginal version of the author's contribution as presented on CD, section: Advances in structural vibrations - i (MS).
000013107 962__ $$r13074
000013107 980__ $$aPAPER