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.     

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.     

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.     

A quantitative analysis on the energy dissipation mechanism of the non-obstructive particle damping technology

The non-obstructive particle damping (NOPD) technology has been recently developed from particle damping and impact damping technologies. In this paper, a quantitative analysis of the dissipation mechanism of NOPD based on a statistical theory is investigated for the first time to our knowledge. Under high-frequency vibrations, the dense granular motion of NOPD is very similar to turbulence. Thus, Kolmogorov's hypothesis in turbulence is adopted to describe the energy spectral density and velocity correlation function of the particles in the NOPD technology. It is shown that the NOPD's mean energy dissipation (per unit mass) increases with either the granular diameter or the volume ratio of the dense granular flow. The quantitative model for the NOPD technology presented in the paper should be useful in possible engineering applications of vibration reduction.     

Behavior of nonlinear fluid viscous dampers for control of shock vibrations

Fluid viscous dampers have been widely used for suppression of high velocity shocks. While linear fluid viscous dampers have been used for a long time, nonlinear fluid viscous dampers show considerable promise due to their superior energy dissipation characteristics and significant reduction in the damper force compared to a linear fluid viscous damper for the same peak displacement. This paper presents results from experimental study to characterize fluid viscous dampers when subjected to half-cycle sine shock excitation. The mathematical formulation and a numerical study to evaluate the relative performance of structures with fluid viscous dampers subjected to short-duration shock (impulse) loading are also discussed. The influence of damper nonlinearity (α) and the supplemental damping ratio (ξ_sd) on response has been investigated. The supplemental damping ratio of nonlinear fluid viscous dampers when subjected to shock excitation is found by equivalent linearization using the concept of equal energy dissipation. The paper also presents some design charts, which can be used for preliminary decisions on parameters of nonlinear dampers to be used in design.     

Dissipation,mass exchange and the microscopic time scale of heavy-ion collisions

The time scale provided by the nucleon exchange mechanism in heavy-ion reactions is employed to study kinetic energy damping. The experimental kinetic energy lost per nucleon exchanged in Kr- and Xe-induced reactions is observed to decrease linearly with the total kinetic energy loss. These results, which are consistent with energy dissipation and nucleon exchange occuring on a similar time scale, are compared with the predictions of a one-body dissipation mechanism and a diffusion model.     

Constrained layer damping with vitreous enamel

The concept of constrained layer damping with vitreous enamel has been experimentally evaluated. The constraining layer markedly broadens the free layer damping peak. The broadening has been explained on the basis of two simultaneous energy dissipation mechanisms and is related to the vitreous enamel's loss factor and viscosity.     

Boundary crisis and suppression of Fermi acceleration in a dissipative two-dimensional non-integrable time-dependent billiard

Some dynamical properties for a dissipative time-dependent oval-shaped billiard are studied. The system is described in terms of a four-dimensional nonlinear mapping. Dissipation is introduced via inelastic collisions of the particle with the boundary, thus implying that the particle has a fractional loss of energy upon collision. The dissipation causes profound modifications in the dynamics of the particle as well as in the phase space of the non-dissipative system. In particular, inelastic collisions can be assumed as an efficient mechanism to suppress Fermi acceleration of the particle. The dissipation also creates attractors in the system, including chaotic. We show that a slightly modification of the intensity of the damping coefficient yields a drastic and sudden destruction of the chaotic attractor, thus leading the system to experience a boundary crisis. We have characterized such a boundary crisis via a collision of the chaotic attractor with its own basin of attraction and confirmed that inelastic collisions do indeed suppress Fermi acceleration in two-dimensional time-dependent billiards.     

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.     

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 design of an optimal viscous damper for a bridge stay cable using energy-based approach

An energy-based method is developed in the present paper to evaluate the damping property of a stay cable when transversely attached to a viscous damper. The overall increase of the cable damping offered by the external damper is determined by examining the time history of the kinetic energy in the damped cable. The concept of kinetic energy decay ratio is introduced as a key index to evaluate the effectiveness of a damper design in suppressing cable vibration. Compared to earlier studies, the proposed energy-based approach has no restrictions on the damper location. In addition, the flexural rigidity and sag extensibility of the cable are included in the formulation. Numerical simulation of free vibration of a damped stay cable is conducted using ABAQUS. To assist the design process, a set of damping estimation curves, which directly relate a damper design with the corresponding equivalent structural damping in a damped cable are developed for the practical parameter ranges of bridge stay cables. A number of numerical examples are presented. The validity and accuracy of the proposed method and damping estimation curves are verified by comparing with other studies. Results show that the energy-based approach developed in the present study is effective and efficient in determining the overall damping property of a cable-damper system, particularly in the preliminary stage of a damper design. In addition, the flexible applications of the developed damping estimation curves to damper design are demonstrated through these examples.     

In-flight and collisional dissipation as a mechanism to suppress Fermi acceleration in a breathing Lorentz gas

Some dynamical properties for a time dependent Lorentz gas considering both the dissipative and non dissipative dynamics are studied. The model is described by using a four-dimensional nonlinear mapping. For the conservative dynamics, scaling laws are obtained for the behavior of the average velocity for an ensemble of non interacting particles and the unlimited energy growth is confirmed. For the dissipative case, four different kinds of damping forces are considered namely: (i) restitution coefficient which makes the particle experiences a loss of energy upon collisions; and in-flight dissipation given by (ii) F=-ηV(2); (iii) F=-ηV(μ) with μ≠1 and μ≠2 and; (iv) F=-ηV, where η is the dissipation parameter. Extensive numerical simulations were made and our results confirm that the unlimited energy growth, observed for the conservative dynamics, is suppressed for the dissipative case. The behaviour of the average velocity is described using scaling arguments and classes of universalities are defined.     

Thermoelastic damping effect on in-extensional vibration of rotating thin ring

Sensitive devices such as resonant sensors and radio frequency micro-electro-mechanical system (RF-MEMS) filters etc., require high Quality factors (Q-factors) defined as the ratio of total system energy to dissipation that occurs due to various damping mechanisms. Also, thermoelastic damping is considered to be one of the most important factors to elicit energy dissipation due to the irreversible heat flow of oscillating structures in the micro scales. In this study, the Q-factor for thermoelastic damping is investigated in rotating thin rings with in-plane vibration. First, in order to obtain the temperature profile of the model, a heat conduction equation for the thermal flow across the radial direction is solved based on the bending approximation so-called in-extensional approximation of the ring. Using the temperature distribution coupled with a displacement, a governing equation of the ring model can then be derived. Eventually, an eigen-value analysis is performed to obtain the natural frequency of rotating thin rings, and the analytical and numerical values of Q-factors can then be determined by the definition. Furthermore, the effects of rotating speed, dimensions of the ring, mode numbers and ambient temperatures on the Q-factor are discussed in detail.     

Acoustic damping enhanced by gaps in baffled injectors in an acoustic chamber

Acoustic damping enhanced by gap width in baffled injectors is investigated numerically, which are installed to suppress pressure oscillations in a model acoustic chamber. The previous experimental works reported that baffled injectors show larger acoustic damping with gaps between adjoining injectors than baffled injectors without the gap or conventional baffles. Acoustic-damping behaviors of baffled injectors are simulated numerically and the damping mechanism is examined. Damping factors are calculated as a function of baffle gap and it is found that the maximum acoustic damping is observed at a gap of 0.1-0.2 mm. The enhanced damping by gaps is attributed to viscous dissipation on the surfaces of the injectors or baffle blades. The optimum gap for maximum damping depends on the viscosity of the medium in the chamber and it increases with the viscosity. As a quantitative parameter of viscous dissipation, the dissipation rate of kinetic energy is calculated as a function of baffle gap. The parameter shows its maximum value at a specific gap and especially, the viscous dissipation rate has the same profile as that of damping factor. It verifies that the enhanced damping by gaps is attributed to the viscous dissipation of acoustic energy increased by gaps in baffled injectors.     

Mechanics and finite elements for the damped dynamic characteristics of curvilinear laminates and composite shell structures

Integrated mechanics and a finite element method are presented for predicting the damping of doubly curved laminates and laminated shell composite structures. Damping mechanics are formulated in curvilinear co-ordinates from ply to structural level and the structural modal loss factors are calculated using the energy dissipation method. The modelling of damping at the laminate level is based on first order shear shell theory. An eight-node shell damping finite element is developed. Comparisons of the present model with classical and discrete layer laminate damping theory predictions are shown. Modal damping and natural frequencies of composite plates and open cylindrical shells were measured and correlated with predicted results. Parametric studies illustrate the effect of curvature and lamination on modal damping and natural frequency.     

Soft hollow particle damping identification in honeycomb structures

The aim of this study is to provide a structural damping solution for space applications to enhance mission performance of honeycomb structures. Classical particle dampers are enclosures partially filled with small metallic or glass spheres, attached to a vibrating structure. The induced damping mechanism is mainly due to frictional losses and collision effects. This paper deals with replacing classical hard particles with soft hollow ones. This study is oriented toward experimental investigations and theoretical validation in order to distinguish dissipation phenomena. The experimental approach first relies on identifying the damping in small honeycomb samples filled with particles. Instead of dissipation by friction and impact, the elliptical shape of the measured hysteresis loops highlights that visco-elastic behavior is dominant with these specific soft particle dampers. Then, experimental and numerical validations are performed on aluminum honeycomb cantilever beams filled with particles. To take into account the effect of the particles, equivalent oscillators, based on the previous experimental damping identification, are added to a finite element model. These kinds of particle dampers are highly nonlinear as a function of excitation frequency and amplitude. It is shown that good damping efficiency is achieved across a large frequency range with low impact on structure stiffness. This paper suggests a convenient method to model the structural damping induced by soft hollow particles.     

Efficient prediction of the quality factors of micromechanical resonators

A high quality factor (Q-factor) is one of the major requirements of high-performance resonators. An understanding of the dissipation mechanism is crucial for maximizing the quality factor by reducing the energy loss. Thermoelastic damping has been well-known as the important intrinsic dissipation that affects the quality factor of micro-resonators. In this study, a finite element formulation based on the weak form of fully coupled thermoelastic problems is suggested. The coupled thermoelastic equation usually leads to a large-size complex eigenvalue problem, which is very massive and time-consuming to solve. Therefore, we also applied the model order reduction (MOR) scheme to this coupled multiphysical problem in order to achieve computational efficiency. The present approach is validated by comparing the numerical results and analytical solutions.     

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.     

Discrete element method model and damping performance of bean bag dampers

Bean bag dampers (BBDs) have been widely applied in engineering to attenuate the vibration of a structural system, but the theoretical analysis on BBDs has been scarcely reported because of their nonlinear damping performance and complex mechanism. In this work, a three-dimensional model of a BBD was established based on the discrete element method (DEM); its flexible boundary was discretized. The model was verified by comparing simulation with test data. Based on the model, the selection of proper particle diameter on the flexible boundary of the BBD was discussed first, and then the effects of internal particle size of the BBD, the BBD?s tightness and the gap between BBD and the inner wall of its enclosure on the energy dissipation capacity were studied. Moreover, the filling ratio of BBD (total internal particles? volume/the flexible boundary?s capacity) was defined to quantitatively describe the tightness of BBD, and the effects of the internal particle size, the natural frequency of primary system and the enclosure size on the optimum tightness of the BBD were also considered. The results can be used as a guide in the design of BBDs.