On energy transfer between linear and nonlinear oscillators

In this paper energy transfer in a dissipative mechanical system is analysed. Such system is composed of a linear and a nonlinear oscillator with a nonlinearizable cubic stiffness. Depending on initial conditions, we find energy transfer either from linear to nonlinear oscillator (energy pumping) or from nonlinear to linear. Such results are valid for two different potentials. However, under resonance and absence of external excitation, if the mass of the nonlinear oscillator is adequately small then the linear oscillator always loses energy. Our approach uses rigorous Regular Perturbation Theory. Besides, we have included the case of two linear oscillators under linear or cubic interactions. Comparisons with the earlier case are made. (c) 2008 Elsevier Ltd. All rights reserved.

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.

Wave reflection at the end of a waveguide supported by a nonlinear spring

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

DYNAMICS AT INFINITY of A CUBIC CHUA'S SYSTEM

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cubic approximation for the transverse displacement in BEM for elastic plates analysis

This work presents an application for the plate analysis formulation by BEM where 3 boundary equations are used, written for the transverse displacement w and the normal and tangential derivatives partial derivativew/partial derivativen and partial derivativew/partial derivatives. In this extension, the transverse displacement w is approximated by a cubic polynomial and, as a consequence, partial derivativew/partial derivatives has a quadratic approximation. This alternative BEM formulation improves the analysis of thin plates, when compared to the formulation using the linear approximation for the displacements, mainly in the obtaining of the bending moments at the boundary of the plate. The implementation of this proposal to the computational codes is simple. (C) 2004 Published by Elsevier Ltd.

Force and displacement transmissibility of a nonlinear isolator with high-static-low-dynamic-stiffness

Engineers often face the challenge of reducing the level of vibrations experienced by a given payload or those transmitted to the support structure to which a vibrating source is attached. In order to increase the range over which vibrations are isolated, soft mounts are often used in practice. The drawback of this approach is the static displacement may be too large for reasons of available space for example. Ideally, a vibration isolator should have a high-static stiffness, to withstand static loads without too large a displacement, and at the same time, a low dynamic stiffness so that the natural frequency of the system is as low as possible which will result in an increased isolation region. These two effects are mutually exclusive in linear isolators but can be overcome if properly configured nonlinear isolators are used. This paper is concerned with the characterisation of such a nonlinear isolator comprising three springs, two of which are configured to reduce the dynamic stiffness of the isolator. The dynamic behaviour of the isolator supporting a lumped mass is investigated using force and displacement transmissibility, which are derived by modelling the dynamic system as a single-degree-of-freedom system. This results in the system dynamics being approximately described by the Duffing equation. For a linear isolator, the dynamics of the system are the same regardless if the source of the excitation is a harmonic force acting on the payload (force transmissibility) or a harmonic motion of the base (displacement transmissibility) on which the payload is mounted. In this paper these two expressions are compared for the nonlinear isolator and it is shown that they differ. A particular feature of the displacement transmissibility is that the response is unbounded at the nonlinear resonance frequency unless the damping in the isolator is greater than some threshold value, which is not the case for force transmissibility. An explanation for this is offered in the paper. (C) 2011 Elsevier Ltd. All rights reserved.

An experimental switchable stiffness device for shock isolation

The development of an experimental switching stiffness device fcr shock isolation is presented. The system uses magnetic forces to exert a restoring force, which results in an effective stiffness that is used to isolate a payload. When the magnetic force is turned on and off, a switchable stiffness is obtained. Characterization of the physical properties of the device is presented. They are estimated in terms of the percentage stiffness change and effective damping ratio when switched between two constant stiffness states. Additionally, the setup is used to implement a control strategy to reduce the shock response and minimize residual vibration. The system was found to be very effective for shock isolation. The response is reduced by around 50 percent compared with passive isolation showing good correlation with theoretical predictions, and the effective damping ratio in the system following the shock was increased from about 4.5 percent to 13 percent. (c) 2012 Elsevier Ltd. All rights reserved.

DEA and DSC study of cubic silsesquioxane epoxy resin nanocomposites

Non-isothermal dielectric analysis (DEA) and differential scanning calorimetry (DSC) techniques were used to study the epoxy nanocomposites prepared by reacting 1,3,5,7,9,11,13,15-octa[dimethylsiloxypropylglycidylether] pentaciclo [9.5.1.1(3,9).1(5,15).1(7,13)] octasilsesquioxane (ODPG) with methylenedianiline (MDA). Loss factor (epsilon) and activation energy were calculated by DEA. The relationships between the loss factor, the activation energy, the structure of the network, and the mechanical properties were investigated. Activation energies determined by DEA and DSC, heat of polymerization, fracture toughness and tensile modulus show the same profile for mechanical properties with respect to ODPG content.

Changes in the stiffness of demineralized dentin following application of tooth whitening agents

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

Cubic interaction term for Schnabl's solution using Pade approximants

We evaluate the cubic interaction term in the action of open bosonic string field theory for Schnabl's solution written in terms of Bernoulli numbers. This computation provides us with new evidence for the fact that the string field equation of motion is satisfied when it is contracted with the solution itself.

Generating Erler-Schnabl-type solution for the tachyon vacuum in cubic superstring field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Regularizing cubic open Neveu-Schwarz string field theory

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Cubic interactions and quantum criticality in dimerized antiferromagnets

In certain Mott-insulating dimerized antiferromagnets, triplet excitations of the paramagnetic phase display both three-particle and four-particle interactions. When such a magnet undergoes a quantum phase transition into a magnetically ordered state, the three-particle interaction becomes part of the critical theory provided that the lattice ordering wave vector is zero. One microscopic example is the staggered-dimer antiferromagnet on the square lattice, for which deviations from O(3) universality have been reported in numerical studies. Using both symmetry arguments and microscopic calculations, we show that a nontrivial cubic term arises in the relevant order-parameter quantum field theory, and we assess its consequences using a combination of analytical and numerical methods. We also present finite-temperature quantum Monte Carlo data for the staggered-dimer antiferromagnet which complement recently published results. The data can be consistently interpreted in terms of critical exponents identical to that of the standard O(3) universality class, but with anomalously large corrections to scaling. We argue that the cubic interaction of critical triplons, although irrelevant in two spatial dimensions, is responsible for the leading corrections to scaling due to its small scaling dimension.

On energy transfer between vibrating systems under linear and nonlinear interactions

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

Joint Experimental and Theoretical Analysis of Order Disorder Effects in Cubic BaZrO3 Assembled Nanoparticles under Decaoctahedral Shape

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