Одељење за механику, 19. април 2017.

Наредни састанак Семинара биће одржан у среду, 19. априла 2017. у сали 301ф Математичког института САНУ са почетком у 18 часова.

Предавач: Dr. Fotios Georgiades, Senior Lecturer, School of Engineering, College of Science, University of Lincoln, United Kingdom


Since the 1960s, the dynamics of L-shaped coupled beams has been of interest because of their relative structural simplicity. It is among the simplest ‘composite’ elastic structures. It is derived all the equations of motion of an L-Shaped beam structure, and it is showed the importance of rotary inertia terms. The equations are decoupled in two motions, namely the in -plane bending and out-of-plane bending with torsion. A theoretical and numerical modal analysis has been performed and it is examined the effect of the orientation of the secondary beam (oriented in two ways) and also the shear effects. Parametric study of natural frequencies for various parameters of the L-Shaped beam showed stiffening and softening effects. Also in case that the length of secondary beam is less than 10% of the length of the primary beam, then the system behaves like cantilever beam with tip mass. Modelling of geometric nonlinearities indicates that the in-plane with out-of-plane motions are coupled together and has to be considered both planes even in examining up to 2nd order nonlinearities. Noted, so far in the literature of the L-Shaped beam structures with geometric nonlinearities the out-of-plane motions has been neglected. Although the two elastic beams are connected, the equations of motion form a self-adjoint system, therefore the projection of the dynamics in the infinite basis of the underlying linear system, lead to the modal equations with only nonlinear coupling and then well-known dimension reduction methods can be applied e.g. center manifolds. This work, paves the way for examination of dynamics in case of geometric nonlinearities of L-Shaped Beam structures, since it is almost impossible using commercial finite element software to perform nonlinear dynamic analysis e.g. the determination of Nonlinear Normal Modes as periodic orbits of millions of DOFs. Also, this work paves the way for analytical modelling and dynamic analysis of more complicated elastic structures e.g. a full airplane model.

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