Dynamics of a piecewise-linear oscillator with limited power supply

We discuss dynamics of a vibro-impact system consisting of a cart with an piecewise-linear restoring force, which vibrates under driving by a source with limited power supply. From the point of view of dynamical systems, vibro-impact systems exhibit a rich variety of phenomena, particularly chaotic motion. In our analyzes, we use bifurcation diagrams, basins of attractions, identifying several non-linear phenomena, such as chaotic regimes, crises, intermittent mechanisms, and coexistence of attractors with complex basins of attraction. © 2009 by ASME.

An investigations on local and global behavior of a (SMA) oscillator of 3 - DOF driven by a limited power supply

SMART material systems offer great possibilities in terms of providing novel and economical solutions to engineering problems. The technological advantages of these materials over traditional ones are due to their unique microstructure and molecular properties. Smart materials such as shape memory alloys (SMA), has been used in such diverse areas of engineering science, nowadays. In this paper, we present a numerical investigation of the dynamics interaction of a nonideal structure (NIS). We analyze the phenomenon of the passage through resonance region in the steady state processes. We remarked that this kind of problem can lead to the so-called Sommerfeld effect: steady state frequencies of the DC motor will usually increase as more power (voltage) is given to it in a step-by-step fashion. When a resonance condition with the structure it is reached, the better part of this energy it is consumed to generate large amplitude vibrations of the foundation without sensible change of the motor frequency as before. The results obtained by using numerical simulations are discussed in details. Copyright © 2009 by ASME.

One-dimensional Fermi accelerator model with moving wall described by a nonlinear van der Pol oscillator

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass m, confined to bounce elastically between two rigid walls where one is described by a nonlinear van der Pol type oscillator while the other one is fixed, working as a reinjection mechanism of the particle for a next collision, is carefully made by the use of a two-dimensional nonlinear mapping. Two cases are considered: (i) the situation where the particle has mass negligible as compared to the mass of the moving wall and does not affect the motion of it; and (ii) the case where collisions of the particle do affect the movement of the moving wall. For case (i) the phase space is of mixed type leading us to observe a scaling of the average velocity as a function of the parameter (χ) controlling the nonlinearity of the moving wall. For large χ, a diffusion on the velocity is observed leading to the conclusion that Fermi acceleration is taking place. On the other hand, for case (ii), the motion of the moving wall is affected by collisions with the particle. However, due to the properties of the van der Pol oscillator, the moving wall relaxes again to a limit cycle. Such kind of motion absorbs part of the energy of the particle leading to a suppression of the unlimited energy gain as observed in case (i). The phase space shows a set of attractors of different periods whose basin of attraction has a complicated organization. © 2013 American Physical Society.

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.

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

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

A Laplace transform approach to the quantum harmonic oscillator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Effect of delayed start of light-curing on microtensile bond strengths of two adhesives bonded to dentin

The aim of the present study was to evaluate the microtensile bond strength to dentin (ATBS) of two total-etching adhesives applied with delays of 1-30 s for curing. Fifty extracted molar teeth were used. Occlusal enamel was sectioned to expose flat dentin surface, which was further polished with 600-grit paper for smear layer standardization. The specimens were divided into two groups, G1: Single Bond total-etching adhesive (SB), and G2: Prime & Bond NT total-etching adhesive (PB). Each group was further divided into 5 subgroups according to the delayed light-cure initiation after the adhesive systems application (n=5): Subgroup 1s - 1 s; Subgroup 5s -5 s; Subgroup 10s - 10 s; Subgroup 20s - 20 s; Subgroup 30s - 30 s. Composite resin cones 5 mm height and 10 mm in diameter were fabricated. Specimens were stored in distilled water at 37 degrees C for 24 h and sectioned to obtain 1 x 1 mm(2) transversal specimens. Specimens were thermocycled and mu TBS was measured. Data were submitted to two-way ANOVA (AdhesiveXDelay time) and Tukey's test. The level of significance was set at 5%. The results in mean MPa(+/- SD) for interaction between adhesive and delay time were: PB/1s - 23.82 +/- 2.54a; SB/5s - 19.52 +/- 2.67b; PB/5s - 18.56 +/- 3.06bc; SB/1s - 15.49 +/- 2.69cd; SB/20s - 16.33 +/- 2.55d; SB/10s - 13.88 +/- 1.67d; PB/10s - 11.04 +/- 1.28e; PB/30s - 10.89 +/- 1.31e; PB/20s - 10.24 +/- 2.33e; SB/30s - 9.19 +/- 1.91e. It was concluded that light-cure initiation timing of total-etching adhesives interferes negatively with mu TBS to dentin. (C) 2014 Elsevier Ltd. All rights reserved.

Inlays Made From a Hybrid Material: Adaptation and Bond Strengths

The aim of this study was to evaluate the internal fit, marginal adaptation, and bond strengths of inlays made of computer-aided design/computer-aided manufacturing feldspathic ceramic and polymer-infiltrated ceramic. Twenty molars were randomly selected and prepared to receive inlays that were milled from both materials. Before cementation, internal fit was achieved using the replica technique by molding the internal surface with addition silicone and measuring the cement thicknesses of the pulpal and axial walls. Marginal adaptation was measured on the occlusal and proximal margins of the replica. The inlays were then cemented using resin cement (Panavia F2.0) and subjected to two million thermomechanical cycles in water (200 N load and 3.8-Hz frequency). The restored teeth were then cut into beams, using a lathe, for microtensile testing. The contact angles, marginal integrity, and surface patterns after etching were also observed. Statistical analysis was performed using two-way repeated measures analysis of variance (p<0.05), the Tukey test for internal fit and marginal adaptation, and the Student t-test for bond strength. The failure types (adhesive or cohesive) were classified on each fractured beam. The results showed that the misfit of the pulpal walls (p=0.0002) and the marginal adaptation (p=0.0001) of the feldspathic ceramic were significantly higher when compared to those of the polymer-infiltrated ceramic, while the bond strength values of the former were higher when compared to those of the latter. The contact angle of the polymer-infiltrated ceramic was also higher. In the present study, the hybrid ceramic presented improved internal and marginal adaptation, but the bond strengths were higher for the feldspathic ceramic.

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.

Variational and perturbative schemes for a spiked harmonic oscillator

A variational analysis of the spiked harmonic oscillator Hamiltonian operator - d2/dx2 + x2 + l(l + 1)/x2 + λ|x| -α, where α is a real positive parameter, is reported in this work. The formalism makes use of the functional space spanned by the solutions of the Schrödinger equation for the linear harmonic oscillator Hamiltonian supplemented by a Dirichlet boundary condition, and a standard procedure for diagonalizing symmetric matrices. The eigenvalues obtained by increasing the dimension of the basis set provide accurate approximations for the ground state energy of the model system, valid for positive and relatively large values of the coupling parameter λ. Additionally, a large coupling perturbative expansion is carried out and the contributions up to fourth-order to the ground state energy are explicitly evaluated. Numerical results are compared for the special case α = 5/2. © 1989 American Institute of Physics.

The Morse oscillator generalised from supersymmetry

Using the factorisation method in supersymmetric quantum mechanics the author determines new potentials from the Morse oscillator. This method is applied although the ladder operators are not used.

Approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2

An approximate analytic expression for the eigenenergies of the anharmonic oscillator V(x)=Ax6+Bx2 is introduced, starting from particular analytic solutions which are valid when certain relations between the parameters A and B are held. © 1995 The American Physical Society.

Algebraic solution of an anisotropic ring-shaped oscillator

Using an algebraic technique related to the SO (2, 1) group we construct the Green function for the potential ar2 + b(r sin θ)-2 + c(r cos θ)-2 + dr2 sin2θ + er2 cos2θ. The energy spectrum and the normalized wave functions are also obtained. © 1990.