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.

Influence of nonlinear stiffness on the dynamics of a slender elastic beam under torsional oscillations

This study focuses on analysing the effects of nonlinear torsional stiffness on the dynam-ics of a slender elastic beam under torsional oscillations, which can be subject to helical buckling.The helical buckling of an elastic beam confined in a cylinder is relevant to many applications. Someexamples include oil drilling, medical cateters and even the conformation and functioning of DNAmolecules. A recent study showed that the formation of the helical configuration is a result of onlythe torsional load, confirming that there is a different path to helical buckling which is not related tothe sinusoidal buckling, stressing the importance of the geometrical behaviour of the beam. A lowdimensional model of an elastic beam under torsional oscillations is used to analyse its dynamical be-haviour with different stiffness characteristics, which are present before and after the helical buckling.Hardening and softening characteristics are present, as the effects of torsion and bending are coupled.With the use of numerical algorithms applied to nonlinear dynamics, such as bifurcation diagramsand basins of attraction, it is shown that the nonlinear stiffness can shift the bifurcations and inducechanges in the stability of the desirable and undesirable solutions. Therefore, the proper modellingof these stiffness nonlinearities seems to be important for a better understanding of the dynamicalbehaviour of such beams.

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.

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

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

An experimental nonlinear low dynamic stiffness device for shock isolation

The problem of shock generated vibration is very common in practice and difficult to isolate due to the high levels of excitation involved and its transient nature. If not properly isolated it could lead to large transmitted forces and displacements. Typically, classical shock isolation relies on the use of passive stiffness elements to absorb energy by deformation and some damping mechanism to dissipate residual vibration. The approach of using nonlinear stiffness elements is explored in this paper, focusing in providing an isolation system with low dynamic stiffness. The possibilities of using such a configuration for a shock mount are studied experimentally following previous theoretical models. The model studied considers electromagnets and permanent magnets in order to obtain nonlinear stiffness forces using different voltage configurations. It is found that the stiffness nonlinearities could be advantageous in improving shock isolation in terms of absolute displacement and acceleration response when compared with linear elastic elements. Copyright (C) 2015 Elsevier Ltd. All rights reserved

Comments on nonlinear dynamics of a non-ideal Duffing-Rayleigh oscillator: Numerical and analytical approaches

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

Wave reflection at the end of a waveguide supported by a nonlinear spring

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

Modelo dinâmico da coluna lombar humana, com solicitação de esforço postero-anterior: análise com rigidez viscoelástica não linear

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Análise dinâmica de mecanismo articulado de suspensão com não-linearidade na rigidez devido à geometria e à excitação por desbalanceamento rotativo na condição não ideal

Pós-graduação em Engenharia Mecânica - FEB

Investigation and modelling of tremor reducer with the technology of targeted energy transfer

This thesis presents the study of a two-degree-of-freedom (2 DOF) nonlinear system consisting of two grounded linear oscillators coupled to two separate light weight nonlinear energy sinks of an essentially nonlinear stiffness. In this thesis, Targeted Energy Transfer (TET) and NES concept are introduced. Previous studies and research of Energy pumping and NES are presented. The characters in nonlinear energy pumping have been introduced at the start of the thesis. For the aim to design the application of a tremor reduction assessment device, the knowledge of tremor reduction has also been mentioned. Two main parties have been presented in the research: dynamical theoretic method of nonlinear energy pumping study and experiments of nonlinear vibration reduction model. In this thesis, nonlinear energy sink (NES) has been studied and used as a core attachment for the research. A new theoretic method of nonlinear vibration reduction which with two NESs has been attached to a primary system has been designed and tested with the technology of targeted energy transfer. Series connection and parallel connection structure systems have been designed to run the tests. Genetic algorithm has been used and presented in the thesis for searching the fit components. One more experiment has been tested with the final components. The results have been compared to find out most efficiency structure and components for the theoretic model. A tremor reduction experiment has been designed and presented in the thesis. The experiment is for designing an application for reducing human body tremor. By using the theoretic method earlier, the experiment has been designed and tested with a tremor reduction model. The experiment includes several tests, one single NES attached system and two NESs attached systems with different structures. The results of theoretic models and experiment models have been compared. The discussion has been made in the end. At the end of the thesis, some further work has been considered to designing the device of the tremor reduction.

The non-ideal problem behavior using a dynamic vibration absorber with nonlinear essential stiffness and timedependent damping properties

The purpose of this study is to develop a dynamic vibration absorber using viscoelastic material with nonlinear essential stiffness and time-dependent damping properties for a non-ideal vibrating system with Sommerfeld effect, resonance capture, and jump phenomenon. The absorber is a mass-bar subsystem that consists of a viscoelastic bar with memory attached to mass, in which the internal dissipative forces depend on current, deformations, and its operational frequency varies with limited temperature. The non-ideal vibrating system consists of a linear (nonlinear) oscillator (plane frame structure) under excitation, via spring connector, of a DC-motor with limited power supply. A viscoelastic dynamic absorber modeled with elastic stiffness essentially nonlinearities was developed to further reduce the Sommerfeld effect and the response of the structure. The numerical results show the performance of the absorber on the non-ideal system response through the resonance curves, time histories, and Poincarésections. Furthermore, the structure responses using the viscoelastic damper with and without memory were studied. © IMechE 2012.

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)

Finite Element Based Nonlinear Normalization of Human Lumbar Intervertebral Disc Stiffness to Account for Its Morphology

Disc degeneration, usually associated with low back pain and changes of intervertebral stiffness, represents a major health issue. As the intervertebral disc (IVD) morphology influences its stiffness, the link between mechanical properties and degenerative grade is partially lost without an efficient normalization of the stiffness with respect to the morphology. Moreover, although the behavior of soft tissues is highly nonlinear, only linear normalization protocols have been defined so far for the disc stiffness. Thus, the aim of this work is to propose a nonlinear normalization based on finite elements (FE) simulations and evaluate its impact on the stiffness of human anatomical specimens of lumbar IVD. First, a parameter study involving simulations of biomechanical tests (compression, flexion/extension, bilateral torsion and bending) on 20 FE models of IVDs with various dimensions was carried out to evaluate the effect of the disc's geometry on its compliance and establish stiffness/morphology relations necessary to the nonlinear normalization. The computed stiffness was then normalized by height (H), cross-sectional area (CSA), polar moment of inertia (J) or moments of inertia (Ixx, Iyy) to quantify the effect of both linear and nonlinear normalizations. In the second part of the study, T1-weighted MRI images were acquired to determine H, CSA, J, Ixx and Iyy of 14 human lumbar IVDs. Based on the measured morphology and pre-established relation with stiffness, linear and nonlinear normalization routines were then applied to the compliance of the specimens for each quasi-static biomechanical test. The variability of the stiffness prior to and after normalization was assessed via coefficient of variation (CV). The FE study confirmed that larger and thinner IVDs were stiffer while the normalization strongly attenuated the effect of the disc geometry on its stiffness. Yet, notwithstanding the results of the FE study, the experimental stiffness showed consistently higher CV after normalization. Assuming that geometry and material properties affect the mechanical response, they can also compensate for one another. Therefore, the larger CV after normalization can be interpreted as a strong variability of the material properties, previously hidden by the geometry's own influence. In conclusion, a new normalization protocol for the intervertebral disc stiffness in compression, flexion, extension, bilateral torsion and bending was proposed, with the possible use of MRI and FE to acquire the discs' anatomy and determine the nonlinear relations between stiffness and morphology. Such protocol may be useful to relate the disc's mechanical properties to its degree of degeneration.

An EFG method for the nonlinear analysis of plates undergoing arbitrarily large deformations

The applicability of a meshfree approximation method, namely the EFG method, on fully geometrically exact analysis of plates is investigated. Based on a unified nonlinear theory of plates, which allows for arbitrarily large rotations and displacements, a Galerkin approximation via MLS functions is settled. A hybrid method of analysis is proposed, where the solution is obtained by the independent approximation of the generalized internal displacement fields and the generalized boundary tractions. A consistent linearization procedure is performed, resulting in a semi-definite generalized tangent stiffness matrix which, for hyperelastic materials and conservative loadings, is always symmetric (even for configurations far from the generalized equilibrium trajectory). Besides the total Lagrangian formulation, an updated version is also presented, which enables the treatment of rotations beyond the parameterization limit. An extension of the arc-length method that includes the generalized domain displacement fields, the generalized boundary tractions and the load parameter in the constraint equation of the hyper-ellipsis is proposed to solve the resulting nonlinear problem. Extending the hybrid-displacement formulation, a multi-region decomposition is proposed to handle complex geometries. A criterium for the classification of the equilibrium`s stability, based on the Bordered-Hessian matrix analysis, is suggested. Several numerical examples are presented, illustrating the effectiveness of the method. Differently from the standard finite element methods (FEM), the resulting solutions are (arbitrary) smooth generalized displacement and stress fields. (c) 2007 Elsevier Ltd. All rights reserved.

Theoretical and experimental studies of unbraced tubular trusses allowing for torsional stiffness

This paper describes the buckling phenomenon of a tubular truss with unsupported length through a full-scale test and presents a practical computational method for the design of the trusses allowing for the contribution of torsional stiffness against buckling, of which the effect has never been considered previously by others. The current practice for the design of a planar truss has largely been based on the linear elastic approach which cannot allow for the contribution of torsional stiffness and tension members in a structural system against buckling. The over-simplified analytical technique is unable to provide a realistic and an economical design to a structure. In this paper the stability theory is applied to the second-order analysis and design of the structural form, with detailed allowance for the instability and second-order effects in compliance with design code requirements. Finally, the paper demonstrates the application of the proposed method to the stability design of a commonly adopted truss system used in support of glass panels in which lateral bracing members are highly undesirable for economical and aesthetic reasons.