Damping Elements Research Articles

Modeling and application of MR dampers in semi-adaptive structures

The developing of technology has discovered new materials which have been applied to improve the performance of structures. The researchers have recently increased the attention in controllable fluids and its applications. Magnetorhelological (MR) dampers are devices that employ rheological fluids to modify their mechanical properties. Their mechanical simplicity, high dynamic range, lower power requirements, large force capacity, robustness and safe manner operation in case of fail have made them attractive devices to semi-active control in civil, aerospace and automotive applications. The characteristics of the MR damper change when the rheological fluid is exposed to a magnetic field changing its stiffness and damping coefficients. A non-linear new model based on the Bouc–Wen model, is employed to simulate the hysteresis behavior of the damper. The model considers the frequency, amplitude and current excitation as dependent variables. The finite element model (FEM) of the MR damper element has also been developed based on the proposed model. Subsequently finite element of the adaptive structure embedded with MR dampers has been established and the non-linear response of the whole structure is obtained. Experimental work was carried out to validate the simulations. For this study, a cantilever 3-D space truss structure with 4 bays exposed to different excitations has been considered in which one of the members has been substituted by the MR damper. A good agreement has been observed between the simulations and experimental data.

Equivalent force control method for generalized real‐time substructure testing with implicit integration

AbstractThis paper presents a new method, called the equivalent force control method, for solving the nonlinear equations of motion in a real‐time substructure test using an implicit time integration algorithm. The method replaces the numerical iteration in implicit integration with a force‐feedback control loop, while displacement control is retained to control the motion of an actuator. The method is formulated in such a way that it represents a unified approach that also encompasses the effective force test method. The accuracy and effectiveness of the method have been demonstrated with numerical simulations of real‐time substructure tests with physical substructures represented by spring and damper elements, respectively. The method has also been validated with actual tests in which a Magnetorheological damper was used as the physical substructure. Copyright © 2007 John Wiley & Sons, Ltd.

Nonlinear three-dimensional wagon–track model for the investigation of rail corrugation initiation on curved track

A nonlinear wagon–track model on curved track has been developed to characterize rail corrugation formation due to self-excitation of the wheel–rail stick–slip process. In this model, wagon movements were described using up to 78 degrees of freedom (DOFs) to model a three-piece freight bogie. Innovatively, the wheelset movements are described using nine DOFs, including torsional and bending modes about the longitudinal and vertical directions. The track modelling is considered as a one-layer structure (two rail beams on discrete spring and damper elements). The wheel sliding after creepage saturation is considered in the wheel–rail interface modelling. Simulation of a case study shows that the frequencies of the wheel stick–slip process are composed of the basic frequency, which might come from the combined effect of sleeper-passing frequency and one-third of the combined torsional and bending frequency of the wheelset, and the double and triple basic frequencies, which form the wavelengths of rail corrugation at different situations.

Mathematical modelling of a vehicle crash with emphasis on the dynamic response analysis of extendable cubic nonlinear dampers using the incremental harmonic balance method

A new direction of crashworthiness improvement using a smart extendable front-end structure is introduced in this paper to support the function of the existing vehicle structure. The smart front-end structure consists of two extendable, independently controlled hydraulic cylinders (dampers) integrated with the front-end longitudinal members. The main objectives of the smart front-end structure are to find solutions of the trade-off problem faced by the designer for offset collision events and to mitigate full frontal collisions. The work carried out in this paper includes developing and analysing mathematical models of different vehicle crash scenarios, including vehicle-to-vehicle frontal collision in both full and offset events. In these models, vehicle components are modelled by lumped masses and cubic non-linear springs. The hydraulic cylinders are represented by cubic non-linear damper elements. In this paper, the dynamic responses of the crash events are obtained with the aid of an analytical approach using the incremental harmonic balance method. The intrusion injury as the maximum deformation of the front-end structure and the occupant deceleration injury are used for interpreting the results. It is demonstrated from simulation results that significant improvements to both intrusion and deceleration injuries are obtained using the smart front-end structures.

Fluid isolator assembly and floating elastomeric damping element

An isolator apparatus is described to attenuate or isolate vibration. The isolator apparatus includes a fluid isolator assembly including a flexible diaphragm and a pressure chamber having a flow passage opened to the pressure chamber to provide a fluid spring. A floating isolator body including an elastomeric damping element is floatably interfaced with the flexible diaphragm of the fluid isolator assembly to isolate vibration.

Incremental harmonic balance method for analysis of standard/smart vehicles-to-rigid barrier frontal collision

The aim of this paper is to investigate and to enhance crashworthiness of frontal barrier impact using a new idea of crash improvement. Two different types of smart front-end structure are proposed to support the function of the existing vehicle. The work described includes developing and analysing mathematical models of vehicle-to-rigid barrier full and offset frontal collision events for the two types of smart front-end structure. In these models, vehicle components are modelled by lumped masses and nonlinear springs. Moreover, the hydraulic cylinders are represented by non-linear damper elements. In this paper, the dynamic responses of the crash events are obtained with the aid of analytical approach using the Incremental Harmonic Balance Method (IHBM). In addition, the intrusion injury and occupant deceleration are used for interpreting the results. It is demonstrated from simulation results that significant improvements to both intrusion and deceleration injuries are obtained using the smart front-end structures.

Tuned mass damper with nonlinear viscous damping

This paper investigates the effect of tuned mass dampers with nonlinear viscous damping elements. The tuned mass damper is assumed to be attached to a single-degree-of-freedom system excited by white noise. Statistical linearization is used to analyze the system and the accuracy of this procedure is verified by stochastic simulation. The optimal linear tuned mass damper is defined in terms of minimizing the standard deviation of the structural displacement. The structural damping is shown to have little influence on the optimal parameter values for the linear tuned mass damper. The (approximate) optimal nonlinear tuned mass damper is defined as the system, which by statistical linearization identifies an optimal equivalent linear tuned mass damper. This is shown to lead to explicit expressions for the optimal parameter values of the nonlinear tuned mass damper. The fact that statistical linearization leads to very accurate results, implies that the optimal nonlinear tuned mass damper is practically as effective as a linear tuned mass damper. However, the nonlinear tuned mass damper must be tuned to a specific amplitude and excitation intensity, in contrast to a conventional linear tuned mass damper. The theory is demonstrated for a tuned mass damper with viscous power-law damping and for a tuned mass damper with Bingham-type damping. The probability distribution of the displacement of the structure seems to be a close approximation to a Gaussian distribution despite the nonlinearity. Furthermore, it is shown by stochastic simulation, that the approximate optimal nonlinear tuned mass damper (identified via statistical linearization) is in fact very close to the true optimum.

Nonlinear transient dynamic response of damped plates using a higher order shear deformation theory

Damped transient dynamic elasto-plastic analysis of plate is investigated. A finite element model based on a C0 higher order shear deformation theory has been developed. Nine noded Lagrangian elements with five degrees of freedom per node are used. Selective Gauss integration is used to evaluate energy terms so as to avoid shear locking and spurious mechanisms. Von Mises and Tresca yield criteria are incorporated along with associated flow rules. Explicit central difference time stepping scheme is employed to integrate temporal equations. The mass matrix is diagonalized by using the efficient proportional mass lumping scheme. A program is developed for damped transient dynamic finite element analysis of elasto-plastic plate. Several numerical examples are studied to unfold different facets of damping of elasto-plastic plates.

Tuned mass damper with fractional derivative damping

A tuned mass damper with a viscoelastic damping element applied to a single-degree-of-freedom system excited by white noise is considered. The viscoelastic damping is modelled as a force proportional to the fractional derivative of the relative displacement between the structure and the secondary mass. Optimal parameters for the tuned mass damper are obtained numerically by optimizing the effective damping ratio of the system. It is shown that the structural damping has very little influence on the optimal parameters. Furthermore, it is demonstrated that the effect of the damper is the same for different values of the fraction in the fractional derivative. This implies that this tuned mass damper with a fractional derivative damping element introduces the same reduction in the structural vibration as a conventional tuned mass damper if properly tuned. Simple approximate analytical expressions for optimal parameters are obtained by a frequency domain approach, in which the force acting between the structure and the secondary mass is assumed to be equal to the force of a conventional tuned mass damper at resonance.

A hybrid finite element formulation for a beam-plate system

A new development in the area of the hybrid finite element analysis (hybrid FEA) is presented. The hybrid FEA method combines the conventional FEA method with energy FEA (EFEA) for analysis of systems that contain both flexible and stiff members. A formulation for analyzing flexible plates spot-welded to stiff beams when the excitation is applied on the stiff members is developed. Conventional FEA models are employed for modeling the behavior of the stiff members in a system. Appropriate damping elements are introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones. The component mode synthesis method is combined with analytical solutions for determining the driving point conductance at joints between stiff and flexible members and for defining the properties of the damping elements which represent the flexible members when analyzing the stiff components. Once the vibration of the stiff members and the amount of power dissipated at the damping elements has been identified, an EFEA analysis is performed in order to determine the amount of vibrational energy in the flexible members. The new developments are validated by comparing results of the hybrid FEA with results from very dense conventional finite element analyses for structures of increasing complexity.

Microplate cell-retaining methodology for high-content analysis of individual non-adherent unanchored cells in a population

A high throughput Microtiter plate Cell Retainer (MCR) has been developed to enable, for the first time, high-content, time-dependent analysis of the same single non-adherent and non-anchored cells in a large cell population, while bio-manipulating the cells. The identity of each cell in the investigated population is secured, even during bio-manipulation, by cell retention in a specially designed concave microlens, acting as a picoliter well (PW). The MCR technique combines micro-optical features and microtiter plate methodology. The array of PWs serves as the bottom of a microtiter plate, fitted with a unique flow damper element. The latter enables rapid fluid exchange without dislodging the cells from their original PWs, thus maintaining the cells' identity. Loading cell suspensions and reagents into the MCR is performed by simple pouring, followed by gravitational sedimentation and settling of cells into the PWs. Cell viability and cell division within the MCR were shown to be similar to those obtained under similar conditions in a standard microtiter plate. The efficiency of single cell occupancy in the MCR exceeded 90%. No cell dislodging was observed when comparing images before and after bio-manipulations (rinsing, staining, etc.). The MCR permits the performance of kinetic measurements on an individual cell basis. Data acquisition is governed by software, controlling microscope performance, stage position and image acquisition and analysis. The PW's unique micro-optical features enable rapid, simultaneous signal analysis of each individual cell, bypassing lengthy image analysis.

Application of a hybrid finite-element formulation for structure-borne vibration in an automotive vehicle structure

The hybrid FEA method combines the conventional FEA method with energy FEA (EFEA) for analyzing systems that contain both flexible and stiff members. Conventional FEA models are employed for modeling the behavior of the stiff members in a system. Appropriate damping elements are introduced in the connections between stiff and flexible members in order to capture the presence of the flexible members during the analyses of the stiff ones. The component mode synthesis method is combined with analytical solutions for determining the driving point conductance at joints between stiff and flexible members and for defining the properties of the damping elements which represent the flexible members when analyzing the stiff components. Once the vibration of the stiff members and the amount of power dissipated at the damping elements has been identified, an EFEA analysis is performed in order to determine the amount of vibrational energy in the flexible members. The new developments are validated by comparing results of the hybrid FEA with results from very dense conventional finite-element analyses for a typical body-in-white vehicle structure. [Work sponsored by the Automotive Research Center, supported by the U.S. Army NAC.]

A simple finite element model for vibration analyses induced by moving vehicles

This study developed a simple finite element method combining the moving wheel element, spring–damper element, lumped mass and rigid link effect to simulate complicated vehicles. The advantages of this vehicle model are (1) the dynamic matrix equation is symmetric, (2) the theory and formulations are very simple and can be added to a standard dynamic finite element codes easily and (3) very complicated vehicle models can be assembled using the proposed elements as simple as the traditional finite element method. The Fryba's solution of a simply supported beam subjected to a moving two-axle system was analysed to validate this finite element model. For a number of numerical simulations, the two solutions are almost identical, which means that the proposed finite element model of moving vehicles is considerably accurate. Field measurements were also used to validate this vehicle model through a very complicated finite element analysis, which indicates that the current moving vehicle model can be used to simulate complex problem with acceptable accuracy. Copyright © 2006 John Wiley & Sons, Ltd.

A shear beam finite element for the damping analysis of tubular laminated composite beams

The paper presents a three-dimensional beam element developed for predicting the damping of composite blades with hollow laminated cross-sections. The unified theoretical framework for synthesizing the equivalent damping properties of a tubular composite blade section is outlined. Building upon the damping mechanics, a damped three-dimensional shear beam finite element is developed, which explicitly provides damping, stiffness and mass matrices. A methodology for analyzing the damped free-vibration response of tubular beams is formulated, and modal frequencies and modal damping values are predicted. Application examples illustrate the ability of the beam element to predict the modal damping and modal frequencies of hollow blades of various uniform circular, elliptical and box sections. The results further quantify the ability of the element to capture the strong effect of skin laminations, as well as the contribution of shear to the modal damping of the beam.

412 ストッパーを用いたオートパラメトリック吸振器の改良

The auto-parametric vibration absorber, which is a kind of nonlinear absorber, suppresses the vibration of main system only at around the resonance point. However, because of the existence of another stable solution due to auto-parametric vibration absorber, the vibration of main system may increase when the excitation frequency is slightly apart from the resonance point. In this paper, the improvement of auto-parametric vibration absorber for the suppression of such another stable solution is investigated. A stopper consists of spring element and damper element is set to limit the absorber motion, and the effects of these elements are investigated and clarified.

The new “Air Damping System” in the BMW HP2 enduro

Having introduced innovative motorcycle wheel guidance systems serving to provide a superior anti-dive and antisquat effect, BMW Motorrad is now concentrating amongst other things on equally innovative spring and damper technology. Apart from the electrical adjustment of damper rates and spring pre-tension by the ESA (Electronic Suspension Adjustment) system, BMW is presenting a world-first achievement in the area of spring damper elements — the “Air Damping System” in BMW Motorrad’s sporting, large-displacement HP2 enduro, which, contrary to conventional air spring struts, uses air not only to provide spring action, but also as the damping medium, meaning that the entire system does completely without oil.

A fuzzy finite element procedure for the calculation of uncertain frequency response functions of damped structures: Part 2—Numerical case studies

This work introduces a numerical algorithm to calculate frequency response functions of damped finite element models with fuzzy uncertain parameters. Part 1 of this paper focusses on the numerical procedure for the solution of the underlying interval finite element problem, based on the undamped procedure and the principle of Rayleigh damping. Part 2 of this paper illustrates the applicability of the methodology through four case studies. The concepts of the interval and the fuzzy finite element frequency response function analysis are illustrated for different types of uncertainties. The obtained results are compared with the results of Monte Carlo simulations.

Implications of Modelling One-Dimensional Impact by Using a Spring and Damper Element

A spring and damper contact force element is often used for modelling impact in multi-body dynamics. The related condition for transition between contact and non-contact is, however, inconsistently implemented in the literature and commercial software. This comparative study aims to clarify the implications of four commonly used transition conditions. Principal differences are discussed and, by simulation of a typical system, it is shown that there are significant differences in the dynamics of the system depending on the different conditions. Two of them give unrealistic contact forces and should imply incorrect prediction of system dynamics in most applications. This suggests that it is important to review results obtained from using these conditions and to eliminate them from commercial software. A discussion of the two other conditions culminates in a recommendation.

A fuzzy finite element procedure for the calculation of uncertain frequency-response functions of damped structures: Part 1—Procedure

This work introduces a numerical algorithm to calculate frequency-response functions (FRFs) of damped finite element (FE) models with fuzzy uncertain parameters. Part one of this paper describes the numerical algorithm for the solution of the underlying interval finite element (IFE) problem. First, the IFE procedure for the calculation of undamped envelope FRFs is discussed. Starting from the undamped procedure, a strategy is developed to analyse damped structures based on the principle of Rayleigh damping. This is achieved by analysing the effect of the proportional damping coefficients on the subsequent steps of the undamped procedure. This finally results in a procedure for the calculation of fuzzy damped FRFs based on an analytical extension of the undamped algorithm. Part one of this paper introduces the numerical procedure. Part two of this paper illustrates the application of the methodology on four numerical case studies.

VIBRATION CHARACTERISTICS OF THE DAMPER ELEMENT COMPOSED OF ANNULAR MAGNETS AND MAGNETIC FLUID

This paper is concerned with the development of a damper with excellent characteristics. The vibration characteristics of the damper element composed of two annular permanent magnets and magnetic fluid are studied experimentally using a vibration testing system. The vibration amplitude of the upper magnet-magnetic fluid system is measured with an optical displacement detector system. It was found that the element of two annular permanent magnets adsorbed magnetic fluid is very effective over the wide frequency range.