Dependent Damping Research Articles

Clamping effects on mechanical stability and energy dissipation in nanoresonators based on carbon nanotubes

With continuous downscaling of resonators, clamping is expected to significantly impact the mechanical stability as well as the energy dissipation mechanisms, especially at the nanoscale. To understand the clamping effects at the nanoscale, we here report on an experimental investigation of a same nanotube based resonator subjected to two different clamping configurations. We investigate clamping associated stability and damping mechanisms by pushing the resonator into the nonlinear regime. The nanotube was first dry-transferred and suspended between source-drain palladium electrodes resulting in a bottom clamped configuration. A selective top-metallization process by platinum atomic layer deposition applied later resulted in a top-bottom clamped configuration. Large nanotube motional amplitude leading to a nonlinear Duffing response initiated small slippage of the nanotube. This instability in clamping was seen in both clamping configurations and was measured as an irreversible resonance frequency downshift. For the measured resonator devices, a gate induced nanotube tension in the range of 58–71 pN was estimated to overcome clamping forces and initiate slipping. In terms of energy dissipation, the top-metallization process was accompanied by a reduction in amplitude dependent nonlinear damping and Q-factor enhancement. Subjecting the same nanotube to both clamping configurations allowed for a direct comparison of clamping and quantification of nonlinear damping. In the present case, nonlinear damping was observed at an estimated nanotube motional amplitude of 11 nm (and higher), being dominant in bottom clamped configuration, suggesting the origin of this nonlinear damping to partially stem from external mechanisms in addition to other possible internal dissipation paths reported such as viscoelastic effects.

Analyzing onset of nonlinearity of a colloidal gel at the critical point

In this work we study onset of nonlinear rheological behavior of a colloidal dispersion of a synthetic hectorite clay, Laponite, at the critical gel state while undergoing sol-gel transition. When subjected to step strain in the nonlinear regime, the relaxation modulus shifts vertically to the lower values such that the deviation from linearity can be accommodated using a strain dependent damping function. We also perform creep-recovery and start-up shear experiments on the studied colloidal dispersion at the critical gel state and monitor deviation in response as the flow becomes nonlinear. A quasi-linear integral model is developed with the time-strain separable relaxation modulus to account for the effect of nonlinear deformation. Remarkably, the proposed model predicts the deviation from linearity in the creep-recovery and start-up shear experiments very well leading to a simple formulation to analyze the onset of nonlinear rheological behavior in the critical gels. We also analyze the energy dissipation during the nonlinear deformation and validate the Bailey criterion using the developed viscoelastic framework.

Global well-posedness for the semilinear wave equation with time dependent damping in the overdamping case

We study the global existence of solutions to the Cauchy problem for the wave equation with time-dependent damping and a power nonlinearity in the overdamping case: { u t t − Δ u + b ( t ) u t = N ( u ) , a m p ; t ∈ [ 0 , T ) , x ∈ R d , u ( 0 ) = u 0 , u t ( 0 ) = u 1 , a m p ; x ∈ R d . \begin{align*}\left \{\begin {array}{ll} u_{tt} - \Delta u + b(t) u_t = N(u),&t\in [0,T),\ x\in \mathbb {R}^d,\\ u(0) = u_0,\ u_t(0) = u_1,&x\in \mathbb {R}^d. \end{array}\right . \end{align*} Here, b ( t ) b(t) is a positive C 1 C^1 -function on [ 0 , ∞ ) [0,\infty ) satisfying \[ b ( t ) − 1 ∈ L 1 ( 0 , ∞ ) , b(t)^{-1} \in L^1(0,\infty ), \] whose case is called overdamping. N ( u ) N(u) denotes the p p th order power nonlinearities. It is well known that the problem is locally well-posed in the energy space H 1 ( R d ) × L 2 ( R d ) H^1(\mathbb {R}^d)\times L^2(\mathbb {R}^d) in the energy-subcritical or energy-critical case 1 ≤ p ≤ p 1 1\le p\le p_1 , where p 1 := 1 + 4 d − 2 p_1:=1+\frac {4}{d-2} if d ≥ 3 d\ge 3 or p 1 = ∞ p_1=\infty if d = 1 , 2 d=1,2 . It is known that when N ( u ) := ± | u | p N(u):=\pm |u|^p , small data blow-up in L 1 L^1 -framework occurs in the case b ( t ) − 1 ∉ L 1 ( 0 , ∞ ) b(t)^{-1} \notin L^1(0,\infty ) and 1 > p > p c ( > p 1 ) 1>p>p_c(> p_1) , where p c p_c is a critical exponent, i.e., threshold exponent dividing the small data global existence and the small data blow-up. The main purpose in the present paper is to prove the global well-posedness to the problem for small data ( u 0 , u 1 ) ∈ H 1 ( R d ) × L 2 ( R d ) (u_0,u_1)\in H^1(\mathbb {R}^d)\times L^2(\mathbb {R}^d) in the whole energy-subcritical case, i.e., 1 ≤ p > p 1 1\le p>p_1 . This result implies that the small data blow-up does not occur in the overdamping case, different from the other case b ( t ) − 1 ∉ L 1 ( 0 , ∞ ) b(t)^{-1}\notin L^1(0,\infty ) , i.e., the effective or noneffective damping.

A model order reduction technique for systems with nonlinear frequency dependent damping

Frequency domain solution of systems with frequency dependent damping is a computationally expensive endeavour especially when dealing with large order three-dimensional systems. A moment-matching based reduced order model is proposed in this work which is capable of handling nonlinear frequency dependent damping in second-order systems. In the proposed approach, local linear systems with frequency independent matrices are derived from the original system, and using the principles of the Rational Krylov approach, orthogonal basis vectors are computed from these local systems through the second-order Arnoldi procedure. The system is then projected on to the basis set to obtain a numerically efficient reduced order model, accurate in the entire frequency domain of interest. The proposed approach is also shown to be more accurate than the popular modal projection based multi-model approach of the same order. The proposed tool is applied to the problem of determining the frequency response of an idealised centrifugal compressor impeller with non-viscous (frequency dependent) damping.

Observations of variability and repeatability in jointed structures

Abstract The experimental study of joint mechanics has been limited in its effectiveness due to the high uncertainty associated with assemblies of sub-components. In particular, two categories of uncertainty are variability (the uncertainty in measurements of different, nominally identical parts) and repeatability (the uncertainty in measurements of the same set of parts). As a result, the uncertainty measured is often greater than the nonlinear characteristics being studied (such as amplitude dependent frequency and damping), which makes meaningful experimentation challenging. This paper analyzes the contributors to uncertainty in the form of variability and repeatability in order to make recommendations for methods to reduce the uncertainty and to redesign a joint to improve its dynamics. Experiments are summarized that investigate the role of experimental setup, interface roughness, settling versus wear, interface geometry (both meso-scale and macro-scale), and the structure surrounding the joint. From the results of these studies, recommendations for the measurement of nonlinearities in jointed structures are made.

Time-dependent damping effect for the dynamics of DNA transcription

DNA is an interesting macromolecule to study because it plays a role in the body of living beings. This paper modified the Peyrard-Bishop (PB) DNA model by involving time-dependent damping. Damping on this model is considered a time-dependent perturbation. The dynamics of DNA transcription with time dependent damping effect is described by the damped nonlinear Schrodinger (DNLS) equation. Solution of the equation is obtained by applying variational method. So obtained the required parameters and done analysis using matlab. The simulation for the solution is done for nucleotide mass 5.1 × 10−25 kg, distance between base neighbor 3.4 × 10−10 m, elastic coefficient 8 N/m, depth of morse potential 0.1 eV, and width of morse potential 2 × 1010 m−1. This research showed a wave of soliton type of breather and spatial soliton. This paper also showed time-dependent damping causes changes in the amplitude and width of the DNA soliton wave.

Choking Nonlocal Magnetic Damping in Exchange-Biased Ferromagnets

We investigated the temperature dependence of the magnetic damping in the exchange biased Pt/ Fe50Mn50 /Fe20Ni80 /SiOx multilayers. In samples having a strong exchange bias, we observed a drastic decrease of the magnetic damping of the FeNi with increasing temperature up to the blocking temperature. The results essentially indicate that the non-local enhancement of the magnetic damping can be choked by the adjacent antiferromagnet and its temperature dependent exchange bias. We also pointed out that such a strong temperature dependent damping may be very beneficial for spintronic applications.

Damped solitary waves on a superfluid vortex filament

We have investigated the evolution of bright solitary wave (solitons) on a thin vortex filament under the action of time dependent damping in a superfluid at the zero temperature limit by exactly solving the damped-nonlinear Schrodinger equation (dNLSE). It is found that the dissipation of the wave amplitude depends on the functional form of the time dependency of the damping force. The damping rate is not constant but varies significantly with time. Comparison has been made between the characteristics of amplitude decay due a constant damping and a particular form of time dependent damping factor, both qualitatively and quantitatively. Stability of the solitary wave has also been studied in presence of such dissipation.

Equilibrium of a Brownian particle with coordinate dependent diffusivity and damping: Generalized Boltzmann distribution

Fick’s law for coordinate dependent diffusivity is derived. Corresponding diffusion current in the presence of coordinate dependent diffusivity is consistent with the form as given by Kramers–Moyal expansion. We have obtained the equilibrium solution of the corresponding Smoluchowski equation. The equilibrium distribution is a generalization of the Boltzmann distribution. This generalized Boltzmann distribution involves an effective potential which is a function of coordinate dependent diffusivity. We discuss various implications of the existence of this generalized Boltzmann distribution for equilibrium of systems with coordinate dependent diffusivity and damping.

Deformation dependent equivalent modal damping ratios for the performance-based seismic design of plane R/C structures

A performance-based seismic design method is proposed for three types of plane R/C structures, i.e., moment resisting frames, infilled moment resisting frames and wall-frame dual systems. It is a force-based design method using the concept of the equivalent viscous damping ratio ξ to account for inelastic energy dissipation instead of that of the behavior (or strength reduction) factor q (or R). More specifically, it uses equivalent modal damping ratios ξk defined for the equivalent linear multi-degree-of-freedom system to the original non-linear multi-degree-of-freedom system. This equivalent system has the same mass and the elastic stiffness of the non-linear one. Furthermore, these equivalent modal damping ratios ξk are constructed as functions of the periods of the structure, the target non-structural and structural deformation (both expressed in terms of inter-storey drift ratio and member plastic rotation) and soil type. Thus, the proposed method is more rational and leads to more accurate results in one step (only strength checking) than code-based design methods requiring two steps (strength and deformation checkings). In addition, it can be used as a performance-based seismic design method with two or more performance levels. Explicit expressions of these ξk for the first few significant modes are proposed. These expressions have been obtained through extensive parametric studies involving non-linear dynamic analysis of 76 frames under 100 far-fault ground motions (corresponding to four soil types of EC8) for different deformation targets. These ξk can be used for seismic design through linear analysis in conjunction with an elastic acceleration design spectrum modified for high amounts of damping. The proposed method is illustrated and validated by numerical examples which demonstrate its advantages over the Eurocode 8 seismic design method.

Wavelet transform based estimation of modal parameters of rotors during operation

Modal analysis of non-rotating structures using wavelet transforms is well established area of research. However, advantages offered by wavelet transforms have not been explored to identify modal parameters of rotating structures. In this study the wavelet based method for estimating speed dependent damping and natural frequencies of a Multi Degree of Freedom (MDOF) rotor bearing systems is presented. Hilbert transform based method to estimate the modal properties is used to validate the wavelet based analysis. The filtering property of wavelet transform is explored to identify the modal parameters corresponding to individual modes of the rotor. A finite element model based simulated results have been presented along with experimental results on a test rotor to illustrate the proposed method. It is observed that for the rotor on fluid film bearings the damping ratio decreased with respect to the excitation frequency. And, for the rotor on rolling element bearings the damping remained nearly constant.

Passive direction displacement dependent damping (D3) device

Viscous fluid damping has been used worldwide to provide energy dissipation to structures during earthquakes. Semi-active dissipation devices have also shown significant potential to re-shape structural hysteresis behaviour and thus provide significant response and damage reduction. However, semi-active devices are far more complex and costly than passive devices, and thus potentially less robust over time. Ideally, a passive device design would provide the unique response behaviour of a semi-active device, but in a far more robust and low-cost device. This study presents the design, development and characterization of a passive Direction and Displacement Dependent viscous damping (D3) device. It can provide viscous damping in any single quadrant of the force-displacement hysteresis loop and any two in combination. Previously, this behaviour could only be obtained with a semi-active device. The D3 device is developed from a typical viscous damper, which is tested to evaluate the baseline of orifice sizing, force levels and velocity dependence. This prototype viscous damper is then modified in clear steps to produce a device with the desired single quadrant hysteresis loop. The overall results provide the design approach, device characterization and validation for this novel device design.

Calculating the transport properties of magnetic materials from first principles including thermal and alloy disorder, noncollinearity, and spin-orbit coupling

A density functional theory based two-terminal scattering formalism that includes spin-orbit coupling and spin non-collinearity is described. An implementation using tight-binding muffin-tin orbitals combined with extensive use of sparse matrix techniques allows a wide variety of inhomogeneous structures to be flexibly modelled with various types of disorder including temperature induced lattice and spin disorder. The methodology is illustrated with calculations of the temperature dependent resistivity and magnetization damping for the important substitutional disordered magnetic alloy Permalloy (Py), Ni$_{80}$Fe$_{20}$. Comparison of calculated results with recent experimental measurements of the damping (including its temperature dependence) indicates that the scattering approach captures the most important contributions to this important property.

Flow rate influencing effects of micropumps

Current micropump technology features bubble tolerance and self-priming ability, achieved with high pressure ability at shallow pump chambers for low dead volume and high compression ratio. Though, the pump dynamics are strongly affected by a pump chamber height dependent viscous squeeze film damping. Therefore, we investigated all major flow influencing effects for micro diaphragm pumps, being liquid resistive damping, cavitation based gaseous capacitive damping and reactive valve volumes. Analytical models were developed that are able to describe and predict the transient actuator displacement, derive the frequency dependent displacement and estimate the valve loss effect in order to determine the flow rate performance of micropumps. In addition, a new oscillator model is able to simulate the inception of cavitation and the time course of both actuator and liquid. The individual effect models were combined into a single-cycle based, frequency dependent, flow rate model, validated for frequencies of up to 100 Hz. Compared to the maximum achievable flow rate, the liquid resistive damping reduces dynamic stroke volume and is responsible for a reduction of 23–57 % at 100 Hz. Valve induced flow losses reduce the effectively redirected volume towards the outlet. The effect is enhanced by the strong damping, but also feeds back on the actuator by reducing initial damping significantly. Reactive valve volumes amount for 6.2–12.4% flow rate reduction at 100 Hz. Full cavitation, generated at the supply mode and affecting the pump mode, can cause gas bubble generation and lead to a drop of flow rate down to 65% at 80 Hz. By placing an in-line degasser the flow stability was improved to ±2.2% over 10 h. After reducing the frequency to 20 Hz, cavitation only affected the supply mode and in combination with a degasser a flow stability of ±0.15% over 2 h was achieved. By reducing voltage levels, cavitation was avoided completely, featuring a stability of ±0.08%. The understanding of the flow rate limiting effects enables the application specific design to meet all performance and reliability requirements for micropump based liquid dosing systems.

Damping properties of non-conductive composite materials for applications in power transmission pylons

This study aims to characterize the fibre direction dependent damping properties of non-conductive composite materials to be used in newly designed electrical power transmission pylons, on which the conducting cables will be directly connected. Thus, the composite structure can be designed both to insulate and to act as a damper to avoid for example conductor line galloping. In order to predict the damping of the composite materials, a comprehensive analysis on a representative unidirectional laminate was carried out. The fibre direction dependent damping analysis of glass and aramid reinforced epoxy and vinylester, partly reinforced with nanoclay or fibre-hybridized, was investigated using a Dynamic Mechanical Thermal Analysis and a Vibrating Beam Testing procedure for five different fibre orientations (0°, 30°, 45°, 60° and 90°). The focus was on damping behaviour evaluation at low temperatures (−20°C and 0°C) and low vibration frequencies (0.5 Hz, 1 Hz and 2 Hz), in order to represent the environmental conditions of vibrating conductor lines during. The prediction of the damping behaviour for coupon-level-specimens with three balanced laminates was successfully carried out with a maximal deviation of maximal 12.1%.

A generic signature of a fluctuating magnetic field: An additional turnover prior to the Kramers’ one

In this paper we have presented the dynamics of a Brownian particle which is coupled to a thermal bath in the presence of a fluctuating magnetic field (FMF). By virtue of the FMF the Brownian particle experiences a time dependent damping strength for the x−direction motion even in the presence of a stationary Markovian thermal bath. There is a transition state along this direction. The time dependent damping strength leads to appear a bi-turnover phenomenon in the variation of the barrier crossing rate as a function of the thermal bath induced damping strength. It is a generic signature of the fluctuating magnetic field.

Design optimization of a viscoelastic dynamic vibration absorber using a modified fixed-points theory.

A viscoelastic dynamic vibration absorber (VDVA) is proposed for suppressing infrasonic vibrations of heavy structures because the traditional dynamic vibration absorber equipped with a viscous damper is not effective in suppressing low frequency vibrations. The proposed VDVA has an elastic spring and a viscoelastic damper with frequency dependent modulus and damping properties. The standard fixed-points theory cannot be applied to derive the optimum design parameters of the VDVA because both its stiffness and damping are frequency dependent. A modified fixed-points theory is therefore proposed to solve this problem. H∞ design optimization of the proposed VDVA have been derived for the minimization of resonant vibration amplitude of a single degree-of-freedom system excited by harmonic forces or due to ground motions. The stiffness and damping of the proposed VDVA can be decoupled such that both of these two properties of the absorber can be tuned independently to their optimal values by following a specified procedure. The proposed VDVA with optimized design is tested numerically using two real commercial viscoelastic damping materials. It is found that the proposed viscoelastic absorber can provide much stronger vibration reduction effect than the conventional VDVA without the elastic spring.

A State Space Viscoelastic Shaft Finite Element for Stability and Response Analysis of Rotors with Structural and Frequency Dependent Damping

The present work proposes a new Euler–Bernoulli shaft element for structurally damped and viscoelastic rotors in a spinning frame. The Maxwell–Wiechert linear viscoelastic material model, having one elastic branch and several parallel Maxwell branches, is used. This model introduces additional internal displacement variables between elastic and viscous elements in the Maxwell branches. Here, the stress depends not only on the elastic strain and elastic strain rate but also on additional fictitious strains and their rates. In the present work, it is assumed that these additional strains can be derived from continuous fictitious displacement variables in the same way as the elastic strains are derived from the actual displacement variables. These continuous fictitious displacements in turn are interpolated from their nodal values using the conventional beam shape functions. Therefore, in addition to the standard degrees of freedom, extra degrees of freedom are defined at the nodes. The viscoelastic shaft element is then used in time-domain analysis of rotors with structural damping or frequency-dependent damping. Parameters of the Maxwell–Wiechert model are so selected that they appropriately represent structural damping of a mild steel rotor and frequency-dependent storage modulus and loss coefficient of a typical viscoelastic rotor. Both stability and time response analyses are performed. The results obtained through dynamic analysis of two different rotor models using both structurally damped mild steel and a typical viscoelastic material PPC as shaft material are similar to those available in the literature and justify the methods applied.

Singularity formation for the 1D compressible Euler equations with variable damping coefficient

In this paper, we consider some blow-up problems for the 1D Euler equations with time and space dependent damping. We investigate sufficient conditions on initial data and the rate of spatial or time-like decay of the coefficient of damping for the occurrence of the finite time blow-up. In particular, our sufficient conditions ensure that the derivative blow-up occurs in finite time with the solution itself and the pressure bounded. Our method is based on simple estimates with Riemann invariant. Furthermore, we give sharp lower and upper estimates of the lifespan of solutions, when initial data are small perturbations of constant states.

Performance improvement of passive suspension of vehicles using position dependent damping

This paper presents the analysis of position dependent damping (PDD) and a methodology for estimation of its parameters for passive suspension of vehicles. The time domain simulation of a quarter-car model with non-linear PDD is performed over the generated random road profile for different forward speeds of vehicle. The time domain response is transformed to frequency domain power spectral density (PSD) and root mean square (RMS) response is determined. Also, the time domain simulation with half sine bump is performed to obtain the bump response spectrum to evaluate the performance of vehicle suspension to transient road excitation. The performance of passive suspension with PDD is compared with that of linear damping in terms of ride comfort, suspension travel and road holding ability. It is shown that the concept of PDD has potential to improve the performance of vehicle suspension by minimising the well-known ride-handling conflict associated with passive suspensions.