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.

On the Performance of a Two-Stage Vibration Isolation System Which has Geometrically Nonlinear Stiffness

Linear single-stage vibration isolation systems have a limitation on their performance, which can be overcome passively by using linear two-stage isolations systems. It has been demonstrated by several researchers that linear single-stage isolation systems can be improved upon by using nonlinear stiffness elements, especially for low-frequency vibrations. In this paper, an investigation is conducted into whether the same improvements can be made to a linear two-stage isolation system using the same methodology for both force and base excitation. The benefits of incorporating geometric stiffness nonlinearity in both upper and lower stages are studied. It is found that there are beneficial effects of using nonlinearity in the stiffness in both stages for both types of excitation. Further, it is found that this nonlinearity causes the transmissibility at the lower resonance frequency to bend to the right, but the transmissibility at the higher resonance frequency is not affected in the same way. Generally, it is found that a nonlinear two-stage system has superior isolation performance compared to that of a linear two-stage isolator.

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.

The characteristics of a nonlinear vibration neutralizer

This paper concerns an investigation into the use of cubic nonlinearity in a vibration neutralizer to improve its effectiveness. It is assumed that the frequency of the harmonic excitation is well above the resonance frequency of the machine to which the neutralizer is attached, and that the machine acts as a simple mass. It is also assumed that the response of the system is predominantly at the harmonic excitation frequency of the machine. The harmonic balance method is used to analyze the system. It is shown how the nonlinearity has the effect of shifting the resonant peak to a higher frequency away from the tuned frequency of the neutralizer so that the device is robust to mistune. In a linear neutralizer this can only be achieved by adding mass to the neutralizer, so the nonlinearity has a similar effect to that of adding mass. Some characteristic features are highlighted, and the effects of the system parameters on the performance are discussed. It is shown that, for a particular combination of the system parameters, the effect of the nonlinearity is also to increase the bandwidth of the device compared to the linear neutralizer with similar mass and damping. Some approximate expressions are derived, which facilitate insight into the parameters which influence the dynamics of the system. The results are validated by some experimental work. (c) 2012 Elsevier Ltd. All rights reserved.

On numerical simulations of a nonlinear self-excited system with two non-ideal sources

In this work, the dynamic behavior of self-synchronization and synchronization through mechanical interactions between the nonlinear self-excited oscillating system and two non-ideal sources are examined by numerical simulations. The physical model of the system vibrating consists of a non-linear spring of Duffing type and a nonlinear damping described by Rayleigh's term. This system is additional forced by two unbalanced identical direct current motors with limited power (non-ideal excitations). The present work mathematically implements the parametric excitation described by two periodically changing stiffness of Mathieu type that are switched on/off. Copyright © 2005 by ASME.

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.

Comparison between the performances of a linear isolator and an isolator with a geometrically nonlinear damper

Pós-graduação em Engenharia Mecânica - FEIS

On the shock performance of a nonlinear vibration isolator with high-static-low-dynamic-stiffness

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the contact stiffness and nonlinear vibration of an elastic body with a rough surface in contact with a rigid flat surface

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

Prediction and measurement of forced response of a composite blade undergoing nonlinear vibration

The main objective of this project is to experimentally demonstrate geometrical nonlinear phenomena due to large displacements during resonant vibration of composite materials and to explain the problem associated with fatigue prediction at resonant conditions. Three different composite blades to be tested were designed and manufactured, being their difference in the composite layup (i.e. unidirectional, cross-ply, and angle-ply layups). Manual envelope bagging technique is explained as applied to the actual manufacturing of the components; problems encountered and their solutions are detailed. Forced response tests of the first flexural, first torsional, and second flexural modes were performed by means of a uniquely contactless excitation system which induced vibration by using a pulsed airflow. Vibration intensity was acquired by means of Polytec LDV system. The first flexural mode is found to be completely linear irrespective of the vibration amplitude. The first torsional mode exhibits a general nonlinear softening behaviour which is interestingly coupled with a hardening behaviour for the unidirectional layup. The second flexural mode has a hardening nonlinear behaviour for either the unidirectional and angle-ply blade, whereas it is slightly softening for the cross-ply layup. By using the same equipment as that used for forced response analyses, free decay tests were performed at different airflow intensities. Discrete Fourier Trasform over the entire decay and Sliding DFT were computed so as to visualise the presence of nonlinear superharmonics in the decay signal and when they were damped out from the vibration over the decay time. Linear modes exhibit an exponential decay, while nonlinearities are associated with a dry-friction damping phenomenon which tends to increase with increasing amplitude. Damping ratio is derived from logarithmic decrement for the exponential branch of the decay.

Finite element code-based modeling of a multi-feature isolation system and passive alleviation of possible inner pounding

The existing seismic isolation systems are based on well-known and accepted physical principles, but they are still having some functional drawbacks. As an attempt of improvement, the Roll-N-Cage (RNC) isolator has been recently proposed. It is designed to achieve a balance in controlling isolator displacement demands and structural accelerations. It provides in a single unit all the necessary functions of vertical rigid support, horizontal flexibility with enhanced stability, resistance to low service loads and minor vibration, and hysteretic energy dissipation characteristics. It is characterized by two unique features that are a self-braking (buffer) and a self-recentering mechanism. This paper presents an advanced representation of the main and unique features of the RNC isolator using an available finite element code called SAP2000. The validity of the obtained SAP2000 model is then checked using experimental, numerical and analytical results. Then, the paper investigates the merits and demerits of activating the built-in buffer mechanism on both structural pounding mitigation and isolation efficiency. The paper addresses the problem of passive alleviation of possible inner pounding within the RNC isolator, which may arise due to the activation of its self-braking mechanism under sever excitations such as near-fault earthquakes. The results show that the obtained finite element code-based model can closely match and accurately predict the overall behavior of the RNC isolator with effectively small errors. Moreover, the inherent buffer mechanism of the RNC isolator could mitigate or even eliminate direct structure-tostructure pounding under severe excitation considering limited septation gaps between adjacent structures. In addition, the increase of inherent hysteretic damping of the RNC isolator can efficiently limit its peak displacement together with the severity of the possibly developed inner pounding and, therefore, alleviate or even eliminate the possibly arising negative effects of the buffer mechanism on the overall RNC-isolated structural responses.

A 3D printed electromagnetic nonlinear vibration energy harvester

A 3D printed electromagnetic vibration energy harvester is presented. The motion of the device is in-plane with the excitation vibrations, and this is enabled through the exploitation of a leaf isosceles trapezoidal flexural pivot topology. This topology is ideally suited for systems requiring restricted out-of-plane motion and benefits from being fabricated monolithically. This is achieved by 3D printing the topology with materials having a low flexural modulus. The presented system has a nonlinear softening spring response, as a result of designed magnetic force interactions. A discussion of fatigue performance is presented and it is suggested that whilst fabricating, the raster of the suspension element is printed perpendicular to the flexural direction and that the experienced stress is as low as possible during operation, to ensure longevity. A demonstrated power of ~25 μW at 0.1 g is achieved and 2.9 mW is demonstrated at 1 g. The corresponding bandwidths reach up-to 4.5 Hz. The system's corresponding power density of ~0.48 mW cm−3 and normalised power integral density of 11.9 kg m−3 (at 1 g) are comparable to other in-plane systems found in the literature.

Influence of ideal and non-ideal excitation sources on the dynamics of a nonlinear vibro-impact system

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

Two-dimensional numerical approach for the vibration isolation analysis on thin walled wave barriers in poroelastic soils.

[EN]This paper is concerned with the vibration isolation efficiency analysis of total or partially buried thin walled wave barriers in poroelastic soils. A two-dimensional time harmonic model that treats soils and structures in a direct way by combining appropriately the conventional Boundary Element Method (BEM), the Dual BEM (DBEM) and the Finite Element Method es developed to this aim.

NONLINEAR TIME SERIES/SYSTEM ANALYSIS (STATE-SPACE, DYNAMICS, INTERVENTION, RESILIENCE, KALMAN)

A discussion of nonlinear dynamics, demonstrated by the familiar automobile, is followed by the development of a systematic method of analysis of a possibly nonlinear time series using difference equations in the general state-space format. This format allows recursive state-dependent parameter estimation after each observation thereby revealing the dynamics inherent in the system in combination with random external perturbations.^ The one-step ahead prediction errors at each time period, transformed to have constant variance, and the estimated parametric sequences provide the information to (1) formally test whether time series observations y(,t) are some linear function of random errors (ELEM)(,s), for some t and s, or whether the series would more appropriately be described by a nonlinear model such as bilinear, exponential, threshold, etc., (2) formally test whether a statistically significant change has occurred in structure/level either historically or as it occurs, (3) forecast nonlinear system with a new and innovative (but very old numerical) technique utilizing rational functions to extrapolate individual parameters as smooth functions of time which are then combined to obtain the forecast of y and (4) suggest a measure of resilience, i.e. how much perturbation a structure/level can tolerate, whether internal or external to the system, and remain statistically unchanged. Although similar to one-step control, this provides a less rigid way to think about changes affecting social systems.^ Applications consisting of the analysis of some familiar and some simulated series demonstrate the procedure. Empirical results suggest that this state-space or modified augmented Kalman filter may provide interesting ways to identify particular kinds of nonlinearities as they occur in structural change via the state trajectory.^ A computational flow-chart detailing computations and software input and output is provided in the body of the text. IBM Advanced BASIC program listings to accomplish most of the analysis are provided in the appendix. ^