Passive vibration isolation using axially loaded curved beams

A nonlinear spring element of a vibration isolator should ideally possess high static and low dynamic stiffness. A buckled beam may be a good candidate to fulfil this requirement provided its internal resonance frequencies are high enough to achieve a wide frequency range of isolation. If a straight beam is used, there is a singularity in the force-displacement characteristic. To smooth this characteristic and eliminate the singularity at the buckling point, beams with initial constant curvature along their length are investigated here as an alternative to the buckled straight beam. Their force displacement characteristics are compared with different initial curvature and with a straight buckled beam. The minimum achievable dynamic stiffness with its corresponding static stiffness is compared for different initial curvatures. A case study is considered where the beams are optimized to isolate a one kilogram mass and to achieve a natural frequency of 1 Hz, considering small amplitudes of vibration. Resonance frequencies of the optimized beams for different curvature are presented. It is shown that an order of magnitude reduction in stiffness compared with a linear spring is achievable, while the internal resonance frequencies of the curved beam are high enough to achieve an acceptable frequency range of isolation.

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.

On the effects of mistuning a force-excited system containing a quasi-zero-stiffness vibration isolator

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Isolamento passivo de vibrações aleatórias atuantes sobre equipamentos eletrônicos aeronaúticos embarcados

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

An investigation of a two-stage nonlinear vibration isolation system

This paper investigates the most desirable configuration of a two-stage nonlinear vibration isolation system, in which the isolators contain hardening geometric stiffness nonlinearity and linear viscous damping. The force transmissibility of the system is used as the measure of the effectiveness of the isolation system. The hardening nonlinearity is achieved by placing horizontal springs onto the suspended and intermediate masses, which are supported by vertical springs. It is found that nonlinearity in the upper stage has very little effect and thus serves little purpose. The nonlinearity in the lower stage, however, has a profound effect, and can significantly improve the effectiveness of the isolation system. Further, it is found that it is desirable to have high damping in the upper stage and very low damping in the lower stage. © 2012 Elsevier Ltd.

Active vibration control at machinery feet

The unmitigated transmission of undesirable vibration can result in problems by way of causing human discomfort, machinery and equipment failure, and affecting the quality of a manufacturing process. When identifiable transmission paths are discernible, vibrations from the source can be isolated from the rest of the system and this prevents or minimises the problems. The approach proposed here for vibration isolation is active force cancellation at points close to the vibration source. It uses force feedback for multiple-input and multiple-output control at the mounting locations. This is particularly attractive for rigid mounting of machine on relative flexible base where machine alignment and motions are to be restricted. The force transfer function matrix is used as a disturbance rejection performance specification for the design of MIMO controllers. For machine soft-mounted via flexible isolators, a model for this matrix has been derived. Under certain conditions, a simple multiplicative uncertainty model is obtained that shows the amount of perturbation a flexible base has on the machine-isolator-rigid base transmissibility matrix. Such a model is very suitable for use with robust control design paradigm. A different model is derived for the machine on hard-mounts without the flexible isolators. With this model, the level of force transmitted from a machine to a final mounting structure using the measurements for the machine running on another mounting structure can be determined. The two mounting structures have dissimilar dynamic characteristics. Experiments have verified the usefulness of the expression. The model compares well with other methods in the literature. The disadvantage lies with the large amount of data that has to be collected. Active force cancellation is demonstrated on an experimental rig using an AC industrial motor hard-mounted onto a relative flexible structure. The force transfer function matrix, determined from measurements, is used to design H and Static Output Feedback controllers. Both types of controllers are stable and robust to modelling errors within the identified frequency range. They reduce the RMS of transmitted force by between 30?80% at all mounting locations for machine running at 1340 rpm. At the rated speed of 1440 rpm only the static gain controller is able to provide 30?55% reduction at all locations. The H controllers on the other hand could only give a small reduction at one mount location. This is due in part to the deficient of the model used in the design. Higher frequency dynamics has been ignored in the model. This can be resolved by the use of a higher order model that can result in a high order controller. A low order static gain controller, with some tuning, performs better. But it lacks the analytical framework for analysis and design.

Analysis of TMJ vibration sounds before and after use of two types of occlusal splints

Temporomandibular joint (TMJ) sounds are important and common physical signs of temporomandibular disorders (TMD). The aim of this study was to evaluate the influence of the effect of the use of occlusal bite splints (stabilizing and repositioning) on the sounds produced in the TMJ, by means of the electrovibratography (EVG). Thirty-one patients with TMD from the Dental School of Ribeirão Preto, University of São Paulo, Brazil were selected for this study. Group 1 (n=23) wore stabilizing bite splints and Group 2 (n=8) used anterior repositioning splints. Before and after treatment with occlusal splints both groups were analyzed using the SonoPAK Q/S recording system (BioResearch System, Inc.). The treatments with stabilizing bite splints were satisfactory, since they reduced the total amount of the sound energies (p<0.05), but the use of anterior repositioning splints for no more than 4 weeks produced significantly better results (p<0.01). The total amount of vibration energy involved in the vibrating movements of the TMJ showed significant improvement using anterior repositioning splints.

Effects of Variations in Nonlinear Damping Coefficients on the Parametric Vibration of a Cantilever Beam with a Lumped Mass

Uncertainties in damping estimates can significantly affect the dynamic response of a given flexible structure. A common practice in linear structural dynamics is to consider a linear viscous damping model as the major energy dissipation mechanism. However, it is well known that different forms of energy dissipation can affect the structure's dynamic response. The major goal of this paper is to address the effects of the turbulent frictional damping force, also known as drag force on the dynamic behavior of a typical flexible structure composed of a slender cantilever beam carrying a lumped-mass on the tip. First, the system's analytical equation is obtained and solved by employing a perturbation technique. The solution process considers variations of the drag force coefficient and its effects on the system's response. Then, experimental results are presented to demonstrate the effects of the nonlinear quadratic damping due to the turbulent frictional force on the system's dynamic response. In particular, the effects of the quadratic damping on the frequency-response and amplitude-response curves are investigated. Numerically simulated as well as experimental results indicate that variations on the drag force coefficient significantly alter the dynamics of the structure under investigation. Copyright (c) 2008 D. G. Silva and P. S. Varoto.

Vibration-induced extra torque during electrically-evoked contractions of the human calf muscles

Background: High-frequency trains of electrical stimulation applied over the lower limb muscles can generate forces higher than would be expected from a peripheral mechanism (i.e. by direct activation of motor axons). This phenomenon is presumably originated within the central nervous system by synaptic input from Ia afferents to motoneurons and is consistent with the development of plateau potentials. The first objective of this work was to investigate if vibration (sinusoidal or random) applied to the Achilles tendon is also able to generate large magnitude extra torques in the triceps surae muscle group. The second objective was to verify if the extra torques that were found were accompanied by increases in motoneuron excitability. Methods: Subjects (n = 6) were seated on a chair and the right foot was strapped to a pedal attached to a torque meter. The isometric ankle torque was measured in response to different patterns of coupled electrical (20-Hz, rectangular 1-ms pulses) and mechanical stimuli (either 100-Hz sinusoid or gaussian white noise) applied to the triceps surae muscle group. In an additional investigation, M(max) and F-waves were elicited at different times before or after the vibratory stimulation. Results: The vibratory bursts could generate substantial self-sustained extra torques, either with or without the background 20-Hz electrical stimulation applied simultaneously with the vibration. The extra torque generation was accompanied by increased motoneuron excitability, since an increase in the peak-to-peak amplitude of soleus F waves was observed. The delivery of electrical stimulation following the vibration was essential to keep the maintained extra torques and increased F-waves. Conclusions: These results show that vibratory stimuli applied with a background electrical stimulation generate considerable force levels (up to about 50% MVC) due to the spinal recruitment of motoneurons. The association of vibration and electrical stimulation could be beneficial for many therapeutic interventions and vibration-based exercise programs. The command for the vibration-induced extra torques presumably activates spinal motoneurons following the size principle, which is a desirable feature for stimulation paradigms.

Positioning of Deadeners for Vibration Reduction in Vehicle Roof Using Embedded Sensitivity

The noise, vibration and harshness (NVH) performance of passenger vehicles strongly depends on the fluid-structure interaction between the air in the vehicle cavity and the sheet metal structure of the vehicle. Most of the noise and vibration problems related to this interaction come from resonance peaks of the sheet metal, which are excited by external forces (road, engine, and wind). A reduction in these resonance peaks can be achieved by applying bitumen damping layers, also called deadeners, in the sheet metal. The problem is where these deadeners shall be fixed, which is usually done in a trial-and-error basis. In this work, one proposes the use of embedded sensitivity to locate the deadeners in the sheet metal of the vehicle, more specifically in the vehicle roof. Experimental frequency response functions (FRFs) of the roof are obtained and the data are processed by adopting the embedded sensitivity method, thus obtaining the sensitivity of the resonance peaks on the local increase in damping due to the deadeners. As a result, by examining the sensitivity functions, one can find the optimum location of the deadeners that maximize their effect in reducing the resonance peaks of interest. After locating the deadeners in the optimum positions, it was possible to verify a strong reduction in resonance peaks of the vehicle roof, thus showing the efficiency of the procedure. The main advantage of this procedure is that it only requires FRF measurements of the vehicle in its original state not needing any previous modification of the vehicle structure to find the sensitivity functions. [DOI: 10.1115/1.4000769]

Refined sandwich model for the vibration of beams with embedded shear piezoelectric actuators and sensors

This work extends a previously presented refined sandwich beam finite element (FE) model to vibration analysis, including dynamic piezoelectric actuation and sensing. The mechanical model is a refinement of the classical sandwich theory (CST), for which the core is modelled with a third-order shear deformation theory (TSDT). The FE model is developed considering, through the beam length, electrically: constant voltage for piezoelectric layers and quadratic third-order variable of the electric potential in the core, while meclianically: linear axial displacement, quadratic bending rotation of the core and cubic transverse displacement of the sandwich beam. Despite the refinement of mechanical and electric behaviours of the piezoelectric core, the model leads to the same number of degrees of freedom as the previous CST one due to a two-step static condensation of the internal dof (bending rotation and core electric potential third-order variable). The results obtained with the proposed FE model are compared to available numerical, analytical and experimental ones. Results confirm that the TSDT and the induced cubic electric potential yield an extra stiffness to the sandwich beam. (C) 2007 Elsevier Ltd. All rights reserved.

Experimental analysis of active-passive vibration control using viscoelastic materials and extension and shear piezoelectric actuators

Hybrid active-passive damping treatments combine the reliability, low cost and robustness of viscoelastic damping treatments and the high-performance, modal selective and adaptive piezoelectric active control. Numerous hybrid damping treatments have been reported in the literature. They differ mainly by the relative positions of viscoelastic treatments, sensors and piezoelectric actuators. In this work we present an experimental analysis of three active-passive damping design configurations applied to a cantilever beam. In particular, two design configurations based on the extension mode of piezoelectric actuators combined with viscoelastic constrained layer damping treatments and one design configuration with shear piezoelectric actuators embedded in a sandwich beam with viscoelastic core are analyzed. For comparison purposes, a purely active design configuration with an extension piezoelectric actuator bonded to an elastic beam is also analyzed. The active-passive damping performance of the four design configurations is compared. Results show that active-passive design configurations provide more reliable and wider-range damping performance than the purely active configuration.

Multimodal passive vibration control of sandwich beams with shunted shear piezoelectric materials

This work presents a performance analysis of multimodal passive vibration control of a sandwich beam using shear piezoelectric materials, embedded in a sandwich beam core, connected to independent resistive shunt circuits. Shear piezoelectric actuators were recently shown to be more interesting for higher frequencies and stiffer structures. In particular, for shunted damping, it was shown that equivalent material loss factors of up to 31% can be achieved by optimizing the shunt circuit. In the present work, special attention is given to the design of multimodal vibration control through independent shunted shear piezoelectric sensors. In particular, a parametric analysis is performed to evaluate optimal configurations for a set of modes to be damped. Then, a methodology to evaluate the modal damping resulting from each shunted piezoelectric sensor is presented using the modal strain energy method. Results show that modal damping factors of 1%-2% can be obtained for three selected vibration modes.

On the wake-induced vibration of tandem circular cylinders: the vortex interaction excitation mechanism

The mechanism of wake-induced vibrations (WIV) of a pair of cylinders in a tandem arrangement is investigated by experiments. A typical WIV response is characterized by a build-up of amplitude persisting to high reduced velocities; this is different from a typical vortex-induced vibration (VIV) response, which occurs in a limited resonance range. We suggest that WIV of the downstream cylinder is excited by the unsteady vortex-structure interactions between the body and the upstream wake. Coherent vortices interfering with the downstream cylinder induce fluctuations in the fluid force that are not synchronized with the motion. A favourable phase lag between the displacement and the fluid force guarantees that a positive energy transfer from the flow to the structure sustains the oscillations. If the unsteady vortices are removed from the wake of the upstream body then WIV will not be excited. An experiment performed in a steady shear flow turned out to be central to the understanding of the origin of the fluid forces acting on the downstream cylinder.

3D CFD Simulation of Vortex-induced Vibration of Cylinder

The 3D flow around a circular cylinder free to oscillate transversely to the free stream was simulated using Computational Fluid Dynamics (CFD) and the Spalart-Allmaras Detached Eddy Simulation (DES) turbulence model for a Reynolds number Re = 10(4). Simulations were carried out for a small mass-damping parameter m*zeta = 0.00858, where m* = 3.3 and zeta = 0.0026. We found good agreement between the numerical results and experimental data. The simulations predicted the high observed amplitudes of the upper branch of vortex-induced vibrations for low mass-damping parameters.