Studies of the performance of particle dampers under dynamic loads

This paper presents a systematic investigation of the performance of particle dampers (vertical and horizontal) attached to a primary system (single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF)) under different dynamic loads (free vibration, stationary random excitation as well as nonstationary random excitation, with single component or multi-component), and the optimum operating regions are all determined. The amount of dissipated energy due to impact and friction, and the concept of “Effective Momentum Exchange” are shown to be suitable “global” measures to interpret the physics involved in the behavior of particle dampers. Using the well-established discrete element method, the motion of vertical particle dampers can be analyzed and classified into three different regions, and the associated damping characteristics can be interpreted. The first mode of a MDOF primary system can be effectively controlled by a properly designed particle damper; however, the higher modes are more affected by other parameters. Consequently, extensive parametric studies are presented to evaluate the effects of various system parameters, such as: mass ratio, primary system damping, coefficient of restitution, container dimensions, excitation amplitude and components, input locations and damper locations.     

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.     

Analytical and experimental validation of a nondimensional Bingham model for mixed-mode magnetorheological dampers

In this paper an experimental validation of a nondimensional analysis for a mixed-mode magnetorheological (MR) damper is described. Based on the Bingham constitutive equation of an MR fluid, a nondimensional model describing damping capacity of the MR damper is formulated using nondimensional parameters including the Bingham number, nondimensional plug thickness, hydraulic amplification ratio, and equivalent viscous damping coefficient. The effects of the Bingham number and the hydraulic amplification ratio on the nondimensional plug thickness and equivalent viscous damping coefficient are analyzed. A mixed-mode MR damper is designed and fabricated to validate the relationships between nondimensional parameters. The damper is tested under various loading conditions and current (applied magnetic field intensity) levels. The nondimensional parameters and variables are measured experimentally, and the effectiveness of the nondimensional analysis model for mixed-mode MR dampers is demonstrated. In addition, comparisons between mixed and flow mode dampers are undertaken using this nondimensional analysis.     

H∞ optimization of fluid viscous dampers for reducing vibrations of high-speed railway bridges

This work deals with the optimization of fluid viscous damper systems (FVDs) to reduce the resonant dynamic structural response of high-speed railway bridges by algebraic and numerical approaches. The presented method chooses the objective function based on the _H∞$H_{\infty }$ norm over the frequency band of interest. This function allows taking into account structural damping properties and minimizing simultaneously the structural response associated with multiple modes. Especially, the proposed objective function may also be extended to nonlinear problems to determine optimal parameters of nonlinear fluid viscous dampers which may be an interesting solution in applications where high force levels are expected in the dampers. Finally, the proposed method is validated through numerical simulations. The simulation results show that the optimal FVD coefficients obtained by using the presented method are more exact than those by the previous method. Besides, the effectiveness of the method for solving the problems with the contribution of high modes and the consideration of nonlinear FVDs is also proved.     

Use of modal energy transfer as a new damping device with controllable bandwidth

This paper presents a new design of nonlinear dynamic absorber (NDA) using the phenomenon of modal energy transfer between the symmetric mode and the anti-symmetric mode of a curved beam. It can reduce the resonance vibration of a primary structure with a controllable operational frequency range. The energy transfer is initiated by an autoparametric vibration and the excitation force required is lowest when the ratio of the resonance frequencies of the first symmetric mode (ω₁) and first anti-symmetric mode (ω₂) is close to 2.The resonance frequency of the first anti-symmetric mode (ω₂) can be altered to control the operational frequency range. The autoparametric vibration response can be used to create an energy-dissipative region with a controllable bandwidth. It is also possible to create a non-dissipative region in between two dissipative regions. This is useful for providing damping for a conventional dynamic absorber without adding high damping material. The damping is due to the dissipation of energy to anti-symmetric mode. Numerical calculations indicate that the resonance vibration of a primary structure can be successfully reduced using this approach. The results are verified with experimental data.     

Energy dissipation of a friction damper

In this paper the energy dissipated through friction is analysed for a type of friction dampers used to reduce squeal noise from railway wheels. A one degree-of-freedom system is analytically studied. First the existence and stability of a periodic solution are demonstrated and then the energy dissipated per cycle is determined as a function of the system parameters. In this way the influence of the mass, natural frequency and internal damping of the friction damper on the energy dissipation is established. It is shown that increasing the mass and reducing the natural frequency and internal damping of the friction damper maximizes the dissipated energy.     

Torsional friction damper optimization

A new approach for the analysis of friction dampers is presented in this work. The exact form of the steady-state solution for a friction damper implemented on a primary system is developed and numerical solutions are used to determine the optimum friction in a friction damper applied to a specific primary system. When compared to classical results presented by earlier authors, the new approach provides a more optimal solution. In addition, viscous damping in the primary system may be included with the new analysis approach. The ability to optimize a friction damper when viscous damping is included in the primary system is a significant improvement over earlier methods and shows potential for serving as a guide to realizing a more accurate estimate of the optimal damping for friction dampers.     

Numerical investigation of coexisting high and low amplitude responses and safe basin erosion for a coupled linear oscillator and nonlinear absorber system

Over the last half century, numerous nonlinear variants of the tuned mass damper have been developed in order to improve attenuation characteristics. In the present study, the performance of a linear oscillator and an absorber with a strongly nonlinear cubic stiffness is evaluated by using numerical methods. This configuration has been of recent interest due to its capability of wide-band energy absorption. However, high amplitude solutions, which would amplify the response of the system, have been shown to often coexist with the low amplitude solutions. The present research is focused on numerically determining the relative strength of the coexisting solutions. Erosion profiles are presented, quantifying the integrity of the system, i.e. the likelihood of converging to a safe, low amplitude response, and providing an indication of the structural safety of a practical absorber system. The results indicate that the high amplitude solutions not only exist but significantly influence the response of the system within the range of expected operating conditions, particularly at excitation frequencies lower than the natural frequency of the linear oscillator. The erosion profiles indicate a 20–40% increase in system integrity for the case of zero damping compared to a small amount of damping, no significant integrity change when adding a small linear stiffness component to the nonlinear absorber, and no significant change in integrity between the midpoint and extreme of the bi-stable range. Additional higher-period solutions are also discovered and evidence of a chaotic response is presented.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

The optimization of mechanical dampers to control self-excited galloping oscillations

The use of mechanical dampers for the control of the self-excited galloping of transmission lines is considered. Two particular dampers, an in-span damper and a resilient mounting, are studied, two mass representations being used. For both dampers it is possible to produce an optimum damper either by maximizing the negative damping excitation that the damped system can withstand, or by choosing the smaller logarithmic decrement of oscillation of the system to be as large as possible in the absence of excitation. These two procedures do not produce the same damper parameters. Simple analytical expressions are produced for the optimum parameters, and these are shown to agree well with numerically optimized parameters. For the in-span damper, either method of optimization gives a damper for a much wider range of ratios of the damper to conductor masses than is predicted by earlier work. For the resilient mounting the optimization based on damping gives very similar behaviour to that of the in-span damper. When aerodynamic excitation is considered for the resilient mounting, a clear optimum exists only for a small range of mass ratios. Results from a representation of the conductor by a stretched string are used to define the range of mass ratios over which the two-mass damper idealizations may be used to define damper properties.     

Torsional damper for maximum energy absorption with equilibrated polydimethylsiloxanes as damping fluids

Shear viscosity and effective shear modulus, quantities related to the complex viscosity, have been measured as functions of frequency for five polydimethylsiloxanes commonly used as damper fluids. Maximum energy dissipation is obtained by realizing a damper whose damping constant times the shear viscosity divided by the product of effective shear modulus and moment of inertia of the inertia member equals one. Experiments show that in this tuning the dissipated energy when polydimethylsiloxanes are used as damping fluids can be as much as a factor of two higher than the maximum dissipated energy when using Newtonian fluid.     

Analysis of energy dissipation in an elastic moving string with a viscous damper at one end

In this paper transverse vibration of an axially moving viscoelastic string with a viscous damper at one end is investigated analytically. The string is assumed to be travelling with constant velocity and the length of string is constant or time varying. The linear and nonlinear mathematical models are derived using the Lagrangian function and implemented using a finite element method. The method considers a time varying state space function applied to the linear model, the Newmark-Beta method is used to solve the response for the nonlinear problem numerically. The case of energy dissipated by a viscoelastic damper at one end of the string for different axial string velocities is considered. When a disturbance arrives at the boundary an exact value for the damper which provides maximum energy dissipation is investigated. Finally, numerical simulations are presented to establish the feasibility of the method.     

Mitigation of edgewise vibrations in wind turbine blades by means of roller dampers

Edgewise vibrations in wind turbine blades are lightly damped, and large amplitude vibrations induced by the turbulence may significantly shorten the fatigue life of the blade. This paper investigates the performance of roller dampers for mitigation of edgewise vibrations in rotating wind turbine blades. Normally, the centrifugal acceleration of the rotating blade can reach to a magnitude of 7–8g, which makes it possible to use this kind of damper with a relatively small mass ratio for suppressing edgewise vibrations effectively. The parameters of the damper to be optimized are the mass ratio, the frequency ratio, the coefficient of rolling friction and the position of the damper in the blade. The optimization of these parameters has been carried out on a reduced 2-DOF nonlinear model of the rotating wind turbine blade equipped with a roller damper in terms of a ball or a cylinder, ignoring the coupling with other degrees of freedom of the wind turbine. The edgewise modal loading on the blade has been calculated from a more sophisticated 13-DOF aeroelastic wind turbine model with due consideration to the indicated couplings, the turbulence and the aerodynamic damping. Various turbulence intensities and mean wind speeds have been considered to evaluate the effectiveness of the roller damper in reducing edgewise vibrations when the working conditions of the wind turbine are changed. Further, the optimized roller damper is incorporated into the 13-DOF wind turbine model to verify the application of the decoupled optimization. The results indicate that the proposed damper can effectively improve the structural response of wind turbine blades.     

Extending the dynamic range of an energy harvester using nonlinear damping

This paper introduces the use of nonlinear damping for extending the dynamic range of vibration energy harvesters. A cubic nonlinear damper is initially considered and the average harvested power and the throw are obtained for different sinusoidal base excitation amplitudes and frequencies, both numerically and analytically. It is demonstrated that when excited at resonance, at an amplitude below its maximum operational limit, the harvested power using a nonlinear damper can be significantly larger than that of a linear energy harvester, therefore expanding its dynamic range. A potential approach to implementing cubic nonlinearity using a shunted electromagnetic device is also presented.     

M-shaped asymmetric nonlinear oscillator for broadband vibration energy harvesting: Harmonic balance analysis and experimental validation

Over the past few years, nonlinear oscillators have been given growing attention due to their ability to enhance the performance of energy harvesting devices by increasing the frequency bandwidth. Duffing oscillators are a type of nonlinear oscillator characterized by a symmetric hardening or softening cubic restoring force. In order to realize the cubic nonlinearity in a cantilever at reasonable excitation levels, often an external magnetic field or mechanical load is imposed, since the inherent geometric nonlinearity would otherwise require impractically high excitation levels to be pronounced. As an alternative to magnetoelastic structures and other complex forms of symmetric Duffing oscillators, an M-shaped nonlinear bent beam with clamped end conditions is presented and investigated for bandwidth enhancement under base excitation. The proposed M-shaped oscillator made of spring steel is very easy to fabricate as it does not require extra discrete components to assemble, and furthermore, its asymmetric nonlinear behavior can be pronounced yielding broadband behavior under low excitation levels. For a prototype configuration, linear and nonlinear system parameters extracted from experiments are used to develop a lumped-parameter mathematical model. Quadratic damping is included in the model to account for nonlinear dissipative effects. A multi-term harmonic balance solution is obtained to study the effects of higher harmonics and a constant term. A single-term closed-form frequency response equation is also extracted and compared with the multi-term harmonic balance solution. It is observed that the single-term solution overestimates the frequency of upper saddle-node bifurcation point and underestimates the response magnitude in the large response branch. Multi-term solutions can be as accurate as time-domain solutions, with the advantage of significantly reduced computation time. Overall, substantial bandwidth enhancement with increasing base excitation is validated experimentally, analytically, and numerically. As compared to the 3 dB bandwidth of the corresponding linear system with the same linear damping ratio, the M-shaped oscillator offers 3200, 5600, and 8900 percent bandwidth enhancement at the root-mean-square base excitation levels of 0.03g, 0.05g, and 0.07g, respectively. The M-shaped configuration can easily be exploited in piezoelectric and electromagnetic energy harvesting as well as their hybrid combinations due to the existence of both large strain and kinetic energy regions. A demonstrative case study is given for electromagnetic energy harvesting, revealing the importance of higher harmonics and the need for multi-term harmonic balance analysis for predicting the electrical power output accurately.     

Nonlinear vibration control and energy harvesting of a beam using a nonlinear energy sink and a piezoelectric device

This paper presents an optimal design for a system comprising a nonlinear energy sink (NES) and a piezoelectric-based vibration energy harvester attached to a free–free beam under shock excitation. The energy harvester is used for scavenging vibration energy dissipated by the NES. Grounded and ungrounded configurations are examined and the systems parameters are optimized globally to both maximize the dissipated energy by the NES and increase the harvested energy by piezoelectric element. A satisfactory amount of energy has been harvested as electric power in both configurations. The realization of nonlinear vibration control through one-way irreversible nonlinear energy pumping and optimizing the system parameters result in acquiring up to 78 percent dissipation of the grounded system energy.     

Energy dissipation prediction of particle dampers

This paper presents initial work on developing models for predicting particle dampers (PDs) behaviour using the Discrete Element Method (DEM). In the DEM approach, individual particles are typically represented as elements with mass and rotational inertia. Contacts between particles and with walls are represented using springs, dampers and sliding friction interfaces. In order to use DEM to predict damper behaviour adequately, it is important to identify representative models of the contact conditions. It is particularly important to get the appropriate trade-off between accuracy and computational efficiency as PDs have so many individual elements. In order to understand appropriate models, experimental work was carried out to understand interactions between the typically small (～1.5–3 mm diameter) particles used. Measurements were made of coefficient of restitution and interface friction. These were used to give an indication of the level of uncertainty that the simplest (linear) models might assume. These data were used to predict energy dissipation in a PD via a DEM simulation. The results were compared with that of an experiment.     

Novel schemes for inserting seismic dampers in shear-type systems based upon the mass proportional component of the Rayleigh damping matrix

This paper presents the results of an extensive study carried out to investigate the applicability of a novel scheme for inserting added viscous dampers in shear-type systems. The findings, even though developed with specific reference to civil building structures, provide useful insight also for the effective addition of viscous dampers in mechanical dynamic systems (of similar characteristics) when excited at the base.The novel scheme proposed (referred to as the MPD system) is based upon the mass proportional component of the Rayleigh damping matrix (MPD matrix) and is characterised by a peculiar damper placement which sees the dampers placed so that they connect each mass to a fixed point.Firstly, the paper briefly recalls (a) the physical principles and (b) selected results of numerical investigations which show that the MPD system is characterised by superior dissipative properties.Secondly, the paper investigates the implementation of the MPD system in civil building structures. Two solutions are envisaged herein: direct implementation (through the use of long buckling-resistant dampers which connect each storey to the ground) and indirect implementation (by placing common dampers between the structure and a very stiff lateral-resisting element adjacent or internal to the structure). The first solution leads to the implementation in the structure of an exact MPD matrix, if damper sizing is chosen appropriately. The second solution (simpler than the first one to implement in building structures) leads to an exact MPD matrix, if, in addition to appropriate damper sizing, the lateral-resisting element is infinitely stiff. As far as the direct implementation is concerned, this paper shows how long buckling-resistant braces are available for structural systems up to three storey high. As far as the indirect implementation is concerned, this paper shows (through extensive numerical parametric investigations) how this solution is capable of providing damping effects which are similar to those offered by the direct implementation, even for lateral-resisting elements characterised by finite lateral stiffness. The results obtained also provide insight for the optimal insertion of viscous dampers in coupled mechanical dynamic systems.     

Damping performance of two simple oscillators coupled by a visco-elastic connection

A simple dynamic system composed of two linear oscillators is employed to analyze the passive control performance that can be achieved through a visco-elastic damper connecting two adjacent free-standing structures. By extension, the model may also describe the energy dissipation which can be obtained by an internal coupling between two quasi-independent sub-systems composing a single complex structure. Two alternatives are evaluated for the linear coupling by considering either the serial or the parallel spring–dashpot arrangement known as the Kelvin–Voigt and the Maxwell damper model, which may synthetically reproduce the constitutive behavior of different industrial devices. The complex eigenvalues of the coupled system are parametrically analyzed to determine the potential benefits realized by different combinations of the coupling stiffness and damping coefficient. A design strategy to assess these parameters is outlined, driven by the relevant observation that a perfect tuning of the natural frequencies always corresponds, in the parameter space, to the maximum modal damping for one of the resonant modes, independent of the damper model. The effectiveness of the proposed strategy is discussed for different classes of the controlled system, depending on the mass and stiffness ratio of the component oscillators. As a major result, different design parameter charts for the two damper models are carried out and compared to each other. Performance indexes are introduced to quantitatively evaluate the passive control performance with respect to the mitigation of the system forced response under harmonic and seismic ground excitation. The analyses confirm the validity of the design strategy for a well-balanced mitigation of the displacement and acceleration response in both the oscillators.     

Quasi-active suspension design using magnetorheological dampers

Quasi-active damping is a method of coupled mechanical and control system design using multiple semi-active dampers. By designing the systems such that the desired control force may always be achieved using a combination of the dampers, quasi-active damping seeks to approach levels of vibration isolation achievable through active damping, whilst retaining the desirable attributes of semi-active systems. In this article a design is proposed for a quasi-active, base-isolating suspension system.Control laws are firstly defined in a generalised form, where semi-active dampers are considered as idealised variable viscous dampers. This system is used to demonstrate in detail the principles of quasi-active damping, in particular the necessary interaction between mechanical and control systems. It is shown how such a system can produce a tunable, quasi-active region in the frequency response of very low displacement transmissibility.Quasi-active control laws are then proposed which are specific for use with magnetorheological dampers. These are validated in simulation using a realistic model of the damper dynamics, again producing a quasi-active region in the frequency response. Finally, the robustness of the magnetorheological, quasi-active suspension system is demonstrated.