Análise do comportamento dinâmico não-linear de estruturas sob excitação de suportes não-ideal.

Abstract

In this work we study the dynamical nonlinear behavior of plane frame under non ideal support excitation, being this applicable to civil structures derived from it. In this sense, a building can be considered as a contiguous series of frames. Simple physical models that are applicable to civil or mechanical structures with increasing difficulty degree are solved individually, with the use of differential Lagrange's equations to determine the system's equations of motion. Qualitative analysis of each problem allows the determination of the values that the physical parameters can take. Each model provides a simple set of parameters, which are being progressively used in numerical integrations. On systems with limited power supply, there is an interaction between the structure's and the energy source's movement; mathematically an extra equation of motion is coupled to its corresponding excitement's free system. Because in plane frames of high slenderness the axial loads induce large displacements, it is important to consider the structure's geometric nonlinearity. In this case, in order to identify system's degrees of freedom, the structure must be discretized. In the problems' analysis, we seek the steady state, in which the structure's amplitudes vary slowly with time and the power supply works with constant frequency.