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.

On an Optimal Linear Control of a Chaotic Non-Ideal Duffing System

In this work, we use a nonlinear control based on Optimal Linear Control. We used as mathematical model a Duffing equation to model a supporting structure for an unbalanced rotating machine with limited power (non-ideal motor). Numerical simulations are performed for a set control parameter (depending on the voltage of the motor, that is, in the static and dynamic characteristic of the motor) The interaction of the non-ideal excitation with the structure may lead to the occurrence of interesting phenomena during the forward passage through the several resonance states of the system. Chaotic behavior is obtained for values of the parameters. Then, the proposed control strategy is applied in order to regulate the chaotic behavior, in order to obtain a periodic orbit and to decrease its amplitude. Both methodologies were used in complete agreement between them. The purpose of the paper is to give suggestions and recommendations to designers and engineers on how to drive this kind of system through resonance.

Non-linear analysis of reinforced concrete plates by the boundary element method and continuum damage mechanics

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

Quenching in a non-ideal mechanical system and the Averaging Method

In this paper, for the first time, a quenching result in a non-ideal system is rigorously obtained. In order to do this a new mechanical hypothesis is assumed, it means that the moment of inertia of the rotating parts of the energy source is big. From this is possible to use the Averaging Method. © 2012 American Institute of Physics.

Reactive power dispatch and planning using a non-linear branch-and-bound algorithm

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

On the performance of a dual-mode non-linear vibration energy harvesting device

The research trend for harvesting energy from the ambient vibration sources has moved from using a linear resonant generator to a non-linear generator in order to improve on the performance of a linear generator; for example, the relatively small bandwidth, intolerance to mistune and the suitability of the device for low-frequency applications. This article presents experimental results to illustrate the dynamic behaviour of a dual-mode non-linear energy-harvesting device operating in hardening and bi-stable modes under harmonic excitation. The device is able to change from one mode to another by altering the negative magnetic stiffness by adjusting the separation gap between the magnets and the iron core. Results for the device operating in both modes are presented. They show that there is a larger bandwidth for the device operating in the hardening mode compared to the equivalent linear device. However, the maximum power transfer theory is less applicable for the hardening mode due to occurrence of the maximum power at different frequencies, which depends on the non-linearity and the damping in the system. The results for the bi-stable mode show that the device is insensitive to a range of excitation frequencies depending upon the input level, damping and non-linearity.

Thermodynamic analysis of a non linear lattice

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

On local analysis of oscillations of a non-ideal and non-linear mechanical model

It is of major importance to consider non-ideal energy sources in engineering problems. They act on an oscillating system and at the same time experience a reciprocal action from the system. Here, a non-ideal system is studied. In this system, the interaction between source energy and motion is accomplished through a special kind of friction. Results about the stability and instability of the equilibrium point of this system are obtained. Moreover, its bifurcation curves are determined. Hopf bifurcations are found in the set of parameters of the oscillating system.

On non-linear dynamics and control designs applied to the ideal and non-ideal variants of the Fitzhugh-Nagumo (FN) mathematical model

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

On non-linear dynamics and an optimal control synthesis of the action potential of membranes (ideal and non-ideal cases) of the Hodgkin-Huxley (HH) mathematical model

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

Design and management optimization of trickle irrigation systems using non-linear programming

A non-linear model is presented which optimizes the lay-out, as well as the design and management of trickle irrigation systems, to achieve maximum net benefit. The model consists of an objective function that maximizes profit at the farm level, subject to appropriate geometric and hydraulic constraints. It can be applied to rectangular shaped fields, with uniform or zero slope. The software used is the Gams-Minos package. The basic inputs are the crop-water-production function, the cost function and cost of system components, and design variables. The main outputs are the annual net benefit and pipe diameters and lengths. To illustrate the capability of the model, a sensitivity analysis of the annual net benefit for a citrus field is evaluated with respect to irrigated area, ground slope, micro-sprinkler discharge and shape of the field. The sensitivity analysis suggests that the greatest benefit is obtained with the smallest microsprinkler discharge, the greatest area, a square field and zero ground slope. The costs of the investment and energy are the components of the objective function that had the greatest effect in the 120 situations evaluated. (C) 1996 Academic Press Limited

On non-linear dynamics and a periodic control design applied to the potential of membrane action

The Fitzhugh-Nagumo (fn) mathematical model characterizes the action potential of the membrane. The dynamics of the Fitzhugh-Nagumo model have been extensively studied both with a view to their biological implications and as a test bed for numerical methods, which can be applied to more complex models. This paper deals with the dynamics in the (FH) model. Here, the dynamics are analyzed, qualitatively, through the stability diagrams to the action potential of the membrane. Furthermore, we also analyze quantitatively the problem through the evaluation of Floquet multipliers. Finally, the nonlinear periodic problem is controlled, based on the Chebyshev polynomial expansion, the Picard iterative method and on Lyapunov-Floquet transformation (L-F transformation).

Non-linear boundary element analysis of floor slabs reinforced with rectangular beams

In this work, a numerical model to perform non-linear analysis of building floor structures is proposed. The presented model is derived from the Kirchhoff-s plate bending formulation of the boundary element method (BENI) for zoned domains, in which the plate stiffness is modified by the presence of membrane effects. In this model, no approximation of the generalized forces along the interface is required and the compatibility and equilibrium conditions along interfaces are imposed at the integral equation level. In order to reduce the number of degrees of freedom, the Navier Bernoulli hypothesis is assumed to simplify the strain field for the thin sub-regions (rectangular beams). The non-linear formulation is obtained from the linear formulation by incorporating initial internal force fields, which are approximated by using the well-known cell sub-division. Then, the non-linear solution of algebraic equations is obtained by using the concept of the consistent tangent operator. The Von Mises criterion is adopted to govern the elasto-plastic material behaviour checked at points along the plate thickness and along the rectangular beam element axes. The numerical representations are accurately obtained by either computing analytically the element integrals or performing the numerical integration accurately using an appropriate sub-elementation scheme. (C) 2007 Elsevier Ltd. All rights reserved.

On non-linear and non-ideal interactions in two vibrating problems

In practical situations, the dynamics of the forcing function on a vibrating system cannot be considered as given a priori, and it must be taken as a consequence of the dynamics of the whole system. In other words, the forcing source has limited power, as that provided by a DC motor for an example, and thus its own dynamics is influenced by that of the vibrating system being forced. This increases the number of degrees of freedom of the problem, and it is called a non-ideal problem. In this work, we considerer two non-ideal problems analyzed by using numerical simulations. The existence of the Sommerfeld effect was verified, that is, the effect of getting stuck at resonance (energy imparted to the DC motor being used to excite large amplitude motions of the supporting structure). We considered two kinds of non-ideal problem: one related to the transverse vibrations of a shaft carrying two disks and another to a piezoceramic bar transducer powered by a vacuum tube generated by a non-ideal source Copyright © 2007 by ASME.

A note on non-linear phenomena in a non-ideal oscillator, with a snap-through truss absorber, including parameter uncertainties

This work considers the vibrating system that consists of a snap-through truss absorber coupled to an oscillator under excitation of an electric motor with an eccentricity and limited power, characterizing a non-ideal oscillator. It is aimed to use the non-linearity and quasi-zero stiffness of absorber (snap-through truss absorber) to obtain a significantly attenuation the jump phenomenon. There is also an interest to exhibit the reduction of Sommerfeld effect, to confirm the saturation phenomenon occurrence and show the power transfer in a non-linear structure, evidencing the pumping energy. As shown by simulations in this work, this absorber allows the energy pumping before and during the jump phenomenon, decreasing the higher amplitudes of considered system. Additionally, the occurrence of saturation phenomenon due use of snap-through truss absorber is verified. The analysis of parameter uncertainties was introduced. Sensitivity of system with parametric errors demonstrated a trustable system. © IMechE 2012.