A Comparison of the Effects of Nonlinear Damping on the Free Vibration of a Single-Degree-of-Freedom System

This article concerns the free vibration of a single-degree-of-freedom (SDOF) system with three types of nonlinear damping. One system considered is where the spring and the damper are connected to the mass so that they are orthogonal, and the vibration is in the direction of the spring. It is shown that, provided the displacement is small, this system behaves in a similar way to the conventional SDOF system with cubic damping, in which the spring and the damper are connected so they act in the same direction. For completeness, these systems are compared with a conventional SDOF system with quadratic damping. By transforming all the equations of motion of the systems so that the damping force is proportional to the product of a displacement dependent term and velocity, then all the systems can be directly compared. It is seen that the system with cubic damping is worse than that with quadratic damping for the attenuation of free vibration. [DOI: 10.1115/1.4005010]

A simple method for choosing the parameters of a two degree-of-freedom tuned vibration absorber

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

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.

Nonlinear dynamical analysis of an aeroelastic system with multi-segmented moment in the pitch degree-of-freedom

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

The use of nonparametric contrasts in one-way layouts and random block designs

Nonparametric simple-contrast estimates for one-way layouts based on Hodges-Lehmann estimators for two samples and confidence intervals for all contrasts involving only two treatments are found in the literature.Tests for such contrasts are performed from the distribution of the maximum of the rank sum between two treatments. For random block designs, simple contrast estimates based on Hodges-Lehmann estimators for one sample are presented. However, discussions concerning the significance levels of more complex contrast tests in nonparametric statistics are not well outlined.This work aims at presenting a methodology to obtain p-values for any contrast types based on the construction of the permutations required by each design model using a C-language program for each design type. For small samples, all possible treatment configurations are performed in order to obtain the desired p-value. For large samples, a fixed number of random configurations are used. The program prompts the input of contrast coefficients, but does not assume the existence or orthogonality among them.In orthogonal contrasts, the decomposition of the value of the suitable statistic for each case is performed and it is observed that the same procedure used in the parametric analysis of variance can be applied in the nonparametric case, that is, each of the orthogonal contrasts has a chi(2) distribution with one degree of freedom. Also, the similarities between the p-values obtained for nonparametric contrasts and those obtained through approximations suggested in the literature are discussed.

An overview on a nonideal system with three and a half degrees of freedom

The present paper studies a system comprised of two blocks connected by springs and dampers, and a DC motor with limited power supply fixed on a block, characterizing a non-ideal problem. This DC motor exciting the system causes interactions between the motor and the structure supporting it. Because of that, the non-ideal mathematical formulation of the problem has one and a half extra degree of freedom than the ideal one. A suitable choice of physical parameters leads to internal resonance conditions, that is, its natural frequencies are multiple of each other, by a known integer quantity. The purpose here is to study the dynamic behavior of the system using an analytical method based on perturbation techniques. The literature shows that the averaging method is the more flexible method concerning non-ideal problems. Summarizing, an steady state solution in amplitude and phase coordinates was obtained with averaging method showing the dependence of the structure amplitudes with the rotation frequency of the motor. Moreover, this solution shows that on of the amplitude coordinates has influence in the determination of the stationary rotation frequency. The analytical solution obtained shows the presence of the rotation frequency in expressions representing the oscillations of the structure, and the presence of amplitude coordinates in expressions describing the dynamic motion of the DC motor. These characteristics show the influence not only of the motor on structure but also of the response of the structure on dynamical behavior of the motor. Copyright © 2005 by ASME.

Nonlinear dynamic model and simulation of morphing wing profile actuated by shape memory alloys

Morphing aircraft have the ability to actively adapt and change their shape to achieve different missions efficiently. The development of morphing structures is deeply related with the ability to model precisely different designs in order to evaluate its characteristics. This paper addresses the dynamic modeling of a sectioned wing profile (morphing airfoil) connected by rotational joints (hinges). In this proposal, a pair of shape memory alloy (SMA) wires are connected to subsequent sections providing torque by reducing its length (changing airfoil camber). The dynamic model of the structure is presented for one pair of sections considering the system with one degree of freedom. The motion equations are solved using numerical techniques due the nonlinearities of the model. The numerical results are compared with experimental data and a discussion of how good this approach captures the physical phenomena associated with this problem. © The Society for Experimental Mechanics, Inc. 2012.

Identificação de parâmetros modais utilizando apenas as respostas da estrutura: identificação estocástica de subespaço e decomposição no domínio da frequência

Pós-graduação em Engenharia Mecânica - FEIS

Análise modal baseada apenas na resposta: decomposição no domínio da frequência

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

Simulação numérica do escoamento em difusores radiais com discos frontais fixos e móveis

Pós-graduação em Engenharia Mecânica - FEIS

Iniciação ao estudo da dinâmica de rotação de um satélite em variáves de Andoyer

The dynamics of the rotation of a satellite is an old and classical problem, specially in the Euler formalism. However, with these variables, even in torque free motion problem, the integrability of the system is far from trivial, mainly when the three moments of the inertia are not equal. Another disadvantage occurs when the inclinations between some plans are null or close to zero, so the nodes become undetermined. In this work, we propose the use of modern Andoyer's variables. These are a set of canonical variables and therefore some significant advantages can be obtained when dealing with perturbation methods. On other the hand, the integrability of the torque free motion becomes very clear, as the system is reduced to a problem of one degree of freedom. The elimination of the singularities mentioned above, can be solved very easily, with Pincaré-type variables. In this work we give the background concepts of the Andoyer's variables and the disturbing potential is obtained for the rotational dynamics of a satellite perturbed by a planet. In the case when A = B (moments of inertia) and due to the current variables, the averaged system is trivially obtained through very simple integrations

Influence of light guide tip used in the photo-activation on degree of conversion and hardness of one nanofilled dental composite

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Degree of conversion and molecular weight of one denture base and three reline resins submitted post-polymerization treatments

The effect of post-polymerization treatments (MW-microwave irradiatron and WB-water-bath) on the degree of conversion (DC) of three reline resins (Ufi Gel hard-U, Kooliner-K, and Tokuso Rebase Fast-T) and one denture base resin (Lucitone 550-L), submitted to two polymerization cycles (LS-short and LL-long), was evaluated by using FT-Raman spectroscopy (n = 5). The molecular weight (Mw) of the powder of all materials and of K polymerized specimens (control; MW; and WB; n = 3) was analyzed using GPC. DC data were analyzed using Kruskal-Wallis test (α = .05). For control specimens, there were no significant differences between U (68%) and LL (77%) and among LL, K (81%), and T (84%). LS (92%) had the highest DC (P<0.05). Only material K exhibited an increased DC after WB (P<0.05). All powders had Mw from 4.0 × 105 to 6.5 × 105 and narrow Mw distributions (2.1 to 3.6). Polymerization and post-polymerization produced K specimens with Mw similar to that of K powder.

Robust broadband vibration control of a flexible structure using an electrical dynamic absorber

This paper presents a simple but practical feedback control method to suppress the vibration of a flexible structure in the frequency range between 10 Hz and 1 kHz. A dynamic vibration absorber is designed for this, which has a natural frequency of 100 Hz and a normalized bandwidth (twice the damping ratio) of 9.9. The absorber is realized electrically by feeding back the structural acceleration at one position on the host structure to a collocated piezoceramic patch actuator via an analog controller consisting of a second-order lowpass filter. This absorber is equivalent to a single degree-of-freedom mechanical oscillator consisting of a serially connected mass-spring-damper system. A first-order lowpass filter is additionally used to improve stability at very high frequencies. Experiments were conducted on a free-free beam embedded with a piezoceramic patch actuator and an accelerometer at its center. It is demonstrated that the single absorber can simultaneously suppress multiple vibration modes within the control bandwidth. It is further shown that the control system is robust to slight changes in the plant. The method described can be applied to many other practical structures, after retuning the absorber parameters for the structure under control.

Infrared spectroscopy: a tool for determination of the degree of conversion in dental composites

Infrared spectroscopy is one of the most widely used techniques for measurement of conversion degree in dental composites. However, to obtain good quality spectra and quantitative analysis from spectral data, appropriate expertise and knowledge of the technique are mandatory. This paper presents important details to use infrared spectroscopy for determination of the conversion degree.