On the dynamic behaviour of a nonlinear system weakly connected to a linear single degree-of-freedom system

This paper discusses the dynamic behaviour of a nonlinear two degree-of-freedom system consisting of a harmonically excited linear oscillator weakly connected to a nonlinear attachment that behaves as a hardening Duffing oscillator. A system which behaves in this way could be a shaker (linear system) driving a nonlinear isolator. The mass of the nonlinear system is taken to be much less than that in the linear system and thus the nonlinear system has little effect on the dynamics of the linear system. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the linear system such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the linear system. It is shown that for some values of the system parameters a complicated frequency response curve for the nonlinear system can occur; closed detached curves can appear as a part of the overall amplitude-frequency response. The reason why these detached curves appear is presented and approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are given.

Development of a simplified transmission line model directly in the phase domain

A transmission line digital model is developed direct in the phase and time domains. The successive modal transformations considered in the three-phase representation are simplified and then the proposed model can be easily applied to several operation condition based only on the previous knowing of the line parameters, without a thorough theoretical knowledge of modal analysis. The proposed model is also developed based on lumped elements, providing a complete current and voltage profile at any point of the transmission system. This model makes possible the modeling of non-linear power devices and electromagnetic phenomena along the transmission line using simple electric circuit components, representing a great advantage when compared to several models based on distributed parameters and inverse transforms. In addition, an efficient integration method is proposed to solve the system of differential equations resulted from the line modeling by lumped elements, thereby making possible simulations of transient and steady state using a wide and constant integration step. © 2012 IEEE.

On certain new exact solutions of a diffusive predator-prey system

We construct exact solutions for a system of two coupled nonlinear partial differential equations describing the spatio-temporal dynamics of a predator-prey system where the prey per capita growth rate is subject to the Allee effect. Using the G'/G expansion method, we derive exact solutions to this model for two different wave speeds. For each wave velocity we report three different forms of solutions. We also discuss the biological relevance of the solutions obtained. © 2012 Elsevier B.V.

Estudo dos métodos de solução da equação de Fokker-Planck linear e não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Controle semi-ativo de vibrações usando lógica nebulosa e fluido magnetoreológico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Multiple Determinants of Anuran Richness and Occurrence in an Agricultural Region in South-Eastern Brazil

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Bifurcations Leading to Nonlinear Oscillations in a 3D Piecewise Linear Memristor Oscillator

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Comportamento dinâmico de suspensão eletromecânica: análise da resposta devido ao amortecimento e à rigidez não linear

Pós-graduação em Engenharia Elétrica - FEB

Model updating of the non-linear vibrating structures through Volterra series and proper orthogonal decomposition

Classical procedures for model updating in non-linear mechanical systems based on vibration data can fail because the common linear metrics are not sensitive for non-linear behavior caused by gaps, backlash, bolts, joints, materials, etc. Several strategies were proposed in the literature in order to allow a correct representative model of non-linear structures. The present paper evaluates the performance of two approaches based on different objective functions. The first one is a time domain methodology based on the proper orthogonal decomposition constructed from the output time histories. The second approach uses objective functions with multiples convolutions described by the first and second order discrete-time Volterra kernels. In order to discuss the results, a benchmark of a clamped-clamped beam with an pre-applied static load is simulated and updated using proper orthogonal decomposition and Volterra Series. The comparisons and discussions of the results show the practical applicability and drawbacks of both approaches.

Non-destructive linear model for leaf area estimation in Vernonia ferruginea Less

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

A virtual experiment for the detection of specific features in the frequency response of a coupled nonlinear and linear oscillator

This paper presents an investigation into some practical issues that may be present in a real experiment, when trying to validate the theoretical frequency response curve of a two degree-of-freedom nonlinear system consisting of coupled linear and nonlinear oscillators. Some specific features, such as detached resonance curves, have been theoretically predicted in multi degree-of-freedom nonlinear oscillators, when subject to harmonic excitation, and the system parameters have been shown to be fundamental in achieving such features. When based on a simplified model, approximate analytical expression for the frequency response curves may be derived, which may be validated by the numerical solutions. In a real experiment, however, the practical achievability of such features was previously shown to be greatly affected by small disturbances induced by gravity and inertia, which led to some solutions becoming unstable which had been predicted to be stable. In this work a practical system configuration is proposed where such effects are reduced so that the previous limitations are overcome. A virtual experiment is carried out where a detailed multi-body model of the oscillator is assembled and the effects on the system response are investigated.

Non-parametric identification of a non-linear buckled beam using discrete-time Volterra Series

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Análise dinâmica não-linear de um sistema não-ideal, utilizando amortecedor magneto-reológico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Dinâmica não linear e controle de um sistema vibratório modelado com memória de forma e, excitado por fontes de energia do tipo ideal e não ideal

Pós-graduação em Engenharia Mecânica - FEB

On abstract differential equations with nonlocal conditions involving the temporal derivative of the solution

In this paper we discuss the existence of solutions for a class of abstract differential equations with nonlocal conditions for which the nonlocal term involves the temporal derivative of the solution. Some concrete applications to parabolic differential equations with nonlocal conditions are considered. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.