Reyolando Manoel Lopes Rebello da Fonseca Brasil

Chaos control and sensitivity analysis of a double pendulum arm excited by an RLC circuit based nonlinear shaker

In this paper the dynamical interactions of a double pendulum arm and an electromechanical shaker is investigated. The double pendulum is a three degree of freedom system coupled to an RLC circuit based nonlinear shaker through a magnetic field, and the capacitor voltage is a nonlinear function of the instantaneous electric charge. Numerical simulations show the existence of chaotic behavior for some regions in the parameter space and this behaviour is characterized by power spectral density and Lyapunov exponents. The bifurcation diagram is constructed to explore the qualitative behaviour of the system. This kind of electromechanical system is frequently found in robotic systems, and in order to suppress the chaotic motion, the State-Dependent Riccati Equation (SDRE) control and the Nonlinear Saturation control (NSC) techniques are analyzed. The robustness of these two controllers is tested by a sensitivity analysis to parametric uncertainties.

The dynamic behavior of a parametrically excited time-periodic MEMS taking into account parametric errors:

Micro-electromechanical systems (MEMS) are micro scale devices that are able to convert electrical energy into mechanical energy or vice versa. In this paper, the mathematical model of an electronic circuit of a resonant MEMS mass sensor, with time-periodic parametric excitation, was analyzed and controlled by Chebyshev polynomial expansion of the Picard interaction and Lyapunov-Floquet transformation, and by Optimal Linear Feedback Control (OLFC). Both controls consider the union of feedback and feedforward controls. The feedback control obtained by Picard interaction and Lyapunov-Floquet transformation is the first strategy and the optimal control theory the second strategy. Numerical simulations show the efficiency of the two control methods, as well as the sensitivity of each control strategy to parametric errors. Without parametric errors, both control strategies were effective in maintaining the system in the desired orbit. On the other hand, in the presence of parametric errors, the OLFC technique was more robust.

On non-ideal and non-linear portal frame dynamics analysis using bogoliubov averaging method

We apply the Bogoliubov Averaging Method to the study of the vibrations of an elastic foundation, forced by a Non-ideal energy source. The considered model consists of a portal plane frame with quadratic nonlinearities, with internal resonance 1:2, supporting a direct current motor with limited power. The non-ideal excitation is in primary resonance in the order of one-half with the second mode frequency. The results of the averaging method, plotted in time evolution curve and phase diagrams are compared to those obtained by numerically integrating of the original differential equations. The presence of the saturation phenomenon is verified by analytical procedures.

Potential Application in Energy Harvesting of Intermodal Energy Exchange in a Frame: FEM Analysis

This paper presents a Finite Element Analysis (FEA) of modal energy exchange and harvesting in a simple portal frame structure. We consider both horizontal and vertical support excitations resonant first with the first mode (sway mode) and latter with the second mode (the first symmetrical mode). As 2:1 internal resonance is present between these two modes, the phenomena of mode saturation and energy exchange (modal coupling) may occur. Thus, energy pumped into the system through one of the modes, is partially transferred to the other mode, not directly excited. An evaluation of the energy available for harvesting in each of the considered mode is computed.

A short note on a nonlinear system vibrations under two non-ideal excitations

This paper describes a nonlinear phenomenon in the dynamical behavior of a nonlinearsystem under two non-ideal excitations: the self-synchronization of unbalanced directcurrent motors. The considered model is taken as a Duffing system that is excited by twounbalanced direct current motors with limited power supplies. The results obtained byusing numerical simulations are discussed in details

Nonlinear Dynamics of a Pendulum Excited by a Crank-Shaft-Slider Mechanism

In this analysis, we consider the dynamics of a pendulum under vertical excitation of a crank-shaft-slider mechanism. The nonlinear model approaches that of a classical parametrically excited pendulum when the ratio of the length of the shaft to the radius of the crank is very large. Numerical techniques are employed to investigate the results for different parameters and initial conditions. Lyapunov exponents, bifurcation diagrams, time histories and phase portraits are presented to explore conditions when the pendulum performs or not full rotations. Of special interest are the resonance regions. Rotations together with oscillations and chaos were observed in some resonance zones.Copyright

CREEP IN THE FUNDAMENTAL FREQUENCY AND STABILITY OF A SLENDER WOODEN COLUMN OF COMPOSITE SECTION

A fluencia e um fenomeno que pode ocorrer em estruturas de madeira por ser esse um material viscoelastico. A fluencia pode alterar os parâmetros puramente elasticos determinados nos ensaios iniciais de caracterizacao da madeira, pois o seu comportamento depende da reologia do material, mesmo com um nivel de tensao constante. Matematicamente, a fluencia pode ser caracterizada por modelos onde a deformacao elastica imediata e acrescida de uma deformacao viscosa, resultando em uma funcao temporal. Por essa razao, o calculo da frequencia natural de vibracao e a verificacao da estabilidade de uma coluna esbelta devem incluir os efeitos redutores da rigidez tanto da forca axial quanto da fluencia. O primeiro pode ser considerado por meio da parcela geometrica e o segundo pela introducao, na parcela convencional, de um modulo de elasticidade variavel com o tempo, obtido em relacao ao modelo reologico adotado. Para avaliar os aspectos mencionados, foi realizada uma simulacao numerica, considerando uma peca comprimida por uma forca na extremidade livre equivalente a 10% da forca critica de Euler, mais o seu peso proprio, adotando-se um modelo reologico de tres parâmetros para a variacao do modulo de elasticidade. Os resultados indicaram diferencas de 60% e 50% para a frequencia e para o modulo de elasticidade, alem de definir o instante exato de colapso da coluna em caso de sua inobservância.

Exact Solution of the Elastica with Transverse Shear Effects

A new derivation of Eulers Elastica with transverse shear effects included is presented. The elastic potential energy of bending and transverse shear is set up. The work of the axial compression force is determined. The equation of equilibrium is derived using the variation of the total potential. Using substitution of variables an exact solution is derived. The equation is transcendental and does not have a closed form solution. It is evaluated in a dimensionless form by using a numerical procedure. Finally, numerical examples of laminates made of composite material (fiber reinforced) and sandwich panels are provided.

Control of Slewing Motions of Flexible Structures Using Shape Memory Alloy

This paper presents the position and vibration control of a single flexible slewing structure driven by a DC motor at the slewing axis. The position is controlled over the current applied to the DC motor armature. To control the vibration of the flexible structure Shape Memory Alloys (SMA) are applied to them. The control is made through the State Dependent Ricatti Equations (SDRE) technique which uses sub-optimal control and system local stability search. Numerical simulations and experimental results are presented which demonstrate the effectiveness of the proposed control strategy.Copyright

Vibrations due to Impact in a Non Ideal Mechanical System With a Non-Linear Hertzian Contact Model

This work analyses the post impact behavior of a mechanical system consisting of an oscillator and an unbalanced non–ideal electrical motor. The impact between the mechanical system and a rigid wall is based on the assumption that the impacting bodies undergo local deformations. The method used in the present work is similar to the Discrete Element Method for particle systems modeled with a “soft–sphere” mechanism. The contact forces are modeled using a nonlinear damped Hertzian Spring-Dashpot system. The mathematical model of the mechanical system is represented by a set of nonlinear ordinary differential equations. The transient and steady-state responses are discussed. As the motor is considered a non ideal energy source, the Sommerfeld effect is also analyzed. The impact model is first applied for a single freely falling particle and then in the proposed mechanical system. Non-dimensional expressions for the contact force and numerical simulations of the mechanical system behavior are also presented.Copyright