On the dynamic behaviour of a mass supported by a parallel combination of a spring and an elastically connected damper

This paper presents a consistent and concise analysis of the free and forced vibration of a mass supported by a parallel combination of a spring and an elastically supported damper (a Zener model). The results are presented in a compact form and the physical behaviour of the system is emphasised. This system is very similar to the conventional single-degree-of freedom system (sdof)-(Voigt model), but the dynamics can be quite different depending on the system parameters. The usefulness of the additional spring in series with the damper is investigated, and optimum damping values for the system subject to different types of excitation are determined and compared.There are three roots to the characteristic equation for the Zener model; two are complex conjugates and the third is purely real. It is shown that it is not possible to achieve critical damping of the complex roots unless the additional stiffness is at least eight times that of the main spring. For a harmonically excited system, there are some possible advantages in using the additional spring when the transmitted force to the base is of interest, but when the displacement response of the system is of interest then the benefits are marginal. It is shown that the additional spring affords no advantages when the system is excited by white noise. (c) 2007 Elsevier Ltd. All rights reserved.

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.

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.

Bose-Einstein condensation thermodynamics of a trapped gas with attractive interaction

We study the Bose-Einstein condensation of an interacting gas with attractive interaction confined in a harmonic trap using a semiclassical two-fluid mean-field model. The condensed state is described by the converged numerical solution of the Gross-Pitaevskii equation. By solving the system of coupled equations of this model iteratively we obtain the converged results for the temperature dependencies of the condensate fraction, chemical potential, and internal energy for the Bose-Einstein condensate of Li-7 atoms. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Suppression of vibrations in strongly nonhomogeneous 2DOF systems

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

Analytical study of the nonlinear behavior of a shape memory oscillator: Part I-primary resonance and free response at low temperatures

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Effect of addition of MTES on the structure of siloxane-PPG nanocomposites

Hybrid transparent and flexible siloxane-polypropyleneglycol (PPG) materials with covalent bonds between the inorganic (siloxane) and organic (polymeric) phases were prepared by sol-gel process. In order to improve the quality of the mechanical properties of these materials, different amounts of methyltriethoxysilane (MTES) were added to the initial sol. The effect of MTES addition on the structure of the composites was studied by Small-Angle X-Ray Scattering (SAXS) and Si-29 Nuclear Magnetic Resonance (Si-29 NMR). In absence of MTES, SAXS spectra exhibit a peak that is assigned to spatial correlation due to short range order between the siloxane clusters embedded in the polymeric phase. The experimental results indicate that, for low MTES concentrations ([MTES]/[O] less than or equal to 0.8, O: ether-type oxygen of PPG), the silicon species resulting from hydrolysis and condensation of MTES fill the open spaces between polymeric chains, interacting with the ether-type oxygens. For larger MTES content ([MTES]/[O] greater than or equal to 0.8), the number of free ether-type oxygen sites avalaible for reaction with such silicon species is not large enough. Consequently, a fraction of silicon species resulting from MTES addition graft to siloxane clusters formed by hydrolysis and condensation of the hybrid precursor. For all MTES concentrations the condensation degree of the siloxane phase, determined from Si-29 NMR spectroscopy, is high (> 69%), as expected under neutral pH synthesis conditions.

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.

New possibilities for the gauging of chiral bosons

We study a new mechanism for the electromagnetic gauging of chiral bosons showing that new possibilities emerge for the interacting theory of chiral scalars. We introduce a chirally coupled gauge field necessary to mod out the degree of freedom that obstructs gauge invariance in a system of two opposite chiral bosons soldering them together.

On the effects of system parameters on the response of a harmonically excited system consisting of weakly coupled nonlinear and linear oscillators

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 having linear and cubic restoring forces. The effects of the system parameters on the shape of the frequency-response curve are investigated, in particular those yielding the appearance and disappearance of outer and inner detached resonance curves. In contrast to the case when the linear stiffness of the attachment is zero, it is found that multivaluedness occurs at low frequencies as the resonant peak bends to the right. It is also found that as the coefficient of the linear term increases, the range of parameters yielding detached curves reduces. Compared to the case when the attached system has no linear stiffness term, this range of parameters corresponds to smaller values of the damping and nonlinear coefficients. Approximate analytical expressions for the jump-up and jump-down frequencies of the system under investigation are also derived. (C) 2011 Elsevier Ltd. All rights reserved.

Effects of Antibacterial Agents on Dental Pulps of Monkeys Mechanically Exposed and Contaminated.

The purpose of this study was to compare the effectiveness of antibacterial agents and mineral trioxide aggregate in the healing of bacterial contaminated primate pulps. Study Design: The experiment required four adult male primates (Cebus opella) with 48 teeth prepared with buccal penetrartions into the pulpal tissues. The preparations (Cebus opella) with 48 teeth prepared with buccal penetrations into the exposed to cotton pellets soaked in a bacterial mixture consisting of microorganisms normally found in human pulpal abscesses obtained from the Endodontic Clinic of UNESP. Following bacterial inoculation (30 minute exposure), the pulpal tissue was immediately treated with either sterile saline, Cipro HC Otic solution (12), diluted Buckley formecresol solution (12) or Otosporin otic solution (12) for 5 minutes. After removal of the pellet, hemostasis was obtained and a ZOE base applied to the DFC treated pulps and the non-treated controls (12). After hemostasis, the other exposed pulps were covered with mineral trioxide aggregate (ProRoot). The pulpal bases were all covered with a RMGI (Fuji II LC). The tissue samples were collected at one day, two days, one week and over four weeks (34 days). Results: Following perfusion fixation, the samples were demineralized, sectioned, stained and histologically graded. After histologic analysis, presence of neutrophilic infiltrate and areas of hemorrhage with hyperemia were observed . The depth of the neutrophilic infiltrate depended on the agent or material used. The pupal tissue treated with Otic suspensions demonstrated significantly less inflammation (Kruskal Wallis non parametric analysis, H=9.595 with 1 degree of freedom; P=0.0223) than the formocresol and control groups. The hard tissue bridges formed over the exposure sites were more organized in the MTA treatment groups than in the control and ZOE groups (Kruskal Wallis non parametric analysis, H=18.291 with 1 degree of freedom; P=0.0004). Conclusions: Otic suspensions and MTA are effective in treating bacterial infected pulps and stimulate the production of a hard tissue bridge over the site of the exposure.

Selection of environmental temperature by the yellow scorpion Tityus serrulatus Lutz & Mello, 1922 (Scorpiones, Buthidae)

The preferred temperature of the yellow scorpion Tityus serrulatus was investigated since its dispersion is a matter of concern. Adult T. serrulatus, weighing 1.24 ± 0.20 g (mean + sd) and with a standard length of 59.3 ± 2.5 mm, were used. A metallic corridor (120 cm long, 5 cm large and 10 cm high) with thermal gradient ranging from 0°C to 40°C was used. Tityus serrulatus chose and stayed in temperatures ranging from 14° C to 38°C when safe conditions were offered (dark and thigmotactic stimuli). The number of animals that remained in the 11°C-20°C, 21°C-30°C, and 31°C-40°C temperature zones were 8, 8, and 9, respectively. The chi-square test (degree of freedom = 2) showed that differences were not significant (p>0.05). Some animals moved to lower temperature areas (less than 8°C) when the corridor was completely illuminated and thigmotactic stimuli were absent, which led the animals to present a torpor state. It is concluded that T. serrulatus does not select a specific environmental temperature. Associated with the capacity of temporally surviving at low temperatures, this species seems to be highly adaptable to different thermal zones.

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.

Point vibration measurements for the detection of shallow-buried objects

A major UK initiative, entitled 'Mapping the Underworld', is seeking to address the serious social, environmental and economic consequences arising from an inability to locate accurately and comprehensively the buried utility service infrastructure without resorting to extensive excavations. Mapping the Underworld aims to develop and prove the efficacy of a multi-sensor device for accurate remote buried utility service detection, location and, where possible, identification. One of the technologies to be incorporated in the device is low-frequency vibro-acoustics, and application of this technique for detecting buried infrastructure is currently being investigated. Here, the potential for making a number of simple point vibration measurements in order to detect shallow-buried objects, in particular plastic pipes, is explored. Point measurements can be made relatively quickly without the need for arrays of surface sensors, which can be expensive, time-consuming to deploy, and sometimes impractical in congested areas. At low frequencies, the ground behaves as a simple single-degree-of-freedom (mass-spring) system with a well-defined resonance, the frequency of which will depend on the density and elastic properties of the soil locally. This resonance will be altered by the presence of a buried object whose properties differ from the surrounding soil. It is this behavior which can be exploited in order to detect the presence of a buried object, provided it is buried at a sufficiently shallow depth. The theoretical background is described and preliminary measurements are made both on a dedicated buried pipe rig and on the ground over a domestic waste pipe. Preliminary findings suggest that, for shallow-buried pipes, a measurement of this kind could be a quick and useful adjunct to more conventional methods of buried pipe detection. © 2012 Elsevier Ltd. All rights reserved.

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of- freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not. © 2012 Elsevier Ltd.