Moderate Damping Research Articles

Damping and Interfacial Dzyaloshinskii-Moriya Interaction in Thulium Iron Garnet/Bismuth-Substituted Yttrium Iron Garnet Bilayers.

Thin films of ferrimagnetic iron garnets can exhibit useful magnetic properties, including perpendicular magnetic anisotropy (PMA) and high domain wall velocities. In particular, bismuth-substituted yttrium iron garnet (BiYIG) films grown on garnet substrates have a low Gilbert damping but zero Dzyaloshinskii-Moriya interaction (DMI), whereas thulium iron garnet (TmIG) films have higher damping but a nonzero DMI. We report the damping and DMI of thulium-substituted BiYIG (BiYTmIG) and TmIG|BiYIG bilayer thin films deposited on (111) substituted gadolinium gallium garnet and neodymium gallium garnet (NGG) substrates. The films are epitaxial and exhibit PMA. BiYIG|TmIG bilayers have a damping value that is an order of magnitude lower than that of TmIG, and BiYIG|TmIG|NGG have DMI of 0.0145 ± 0.0011 mJ/m2, similar to that of TmIG|NGG. The bilayer therefore provides a combination of DMI and moderate damping, useful for the development of high-speed spin orbit torque-driven devices.

The influence of steel reinforcements on static rigidity of epoxy granite spindle head for dynamic performance enhancement of machining center: Experiments and finite element simulation

Machine tool structures are subjected to continuous distortions and unwanted vibrations during machining. The structures should have excellent static and dynamic properties to minimize the adverse effects due to vibration. Cast iron is generally used as a structural material for machine tools owing to its higher structural rigidity and moderate damping properties. The lack of desired dynamic properties results in poor surface finish of the machined components. Epoxy granite is a resin mineral-based composite found to provide superior damping ability but it has lesser material stiffness. Steel reinforcements are more appropriate to enhance the static rigidity of epoxy granite structures. The cast iron spindle head of the vertical machining center is considered for the present study. Static structural analysis has been performed by finite element analysis and the results are considered as a benchmark for the design of epoxy granite spindle head. Multiple design configurations of steel reinforcements are evolved through topology optimization to achieve improved stiffness with a higher damping ratio. A model which exhibited higher stiffness with minimum steel has been proposed for fabrication. A 1:2 scaled model of the proposed configuration has been fabricated using epoxy granite. Experimental modal analysis and numerical static analyses have been carried out and the results are compared to those of cast iron spindle head. A significant reduction in mass and deformation of the epoxy granite spindle head by 22% and 57%, respectively, was observed compared to that of cast iron spindle head.

Effects of graphene, alumina, and their hybrid on dynamic mechanical behavior of epoxy-based nanocomposites

Graphene has excellent mechanical and thermal properties, while alumina has inexpensive and strong thermal stability, making it ideal for electronic packaging applications. The current work examines the effects of modest loadings of reduced graphene oxide (rGO), alumina (Ala), and their hybrids on the dynamic mechanical characteristics and thermal transitions of epoxy-based nanocomposites. The rGO was made using a modified Hummers’ method. Alumina nanoparticles were used as received. Various epoxy nanocomposite samples with 1 wt% of rGO, 1 wt% of Ala, and 0.5 wt% each of rGO and Ala were created. Then, Raman spectroscopy, XRD, FTIR, XPS, TEM, AFM, and SEM were used to analyze the fillers and their hybrid and epoxy-based nanocomposites. Dynamic mechanical analysis was used to examine the hybrid epoxy-based nanocomposites’ dynamic mechanical behavior. It has been demonstrated that different epoxy nanocomposites with 1 wt% Ala and 1 wt% rGO have higher elastic moduli than those with 0.5 wt% rGO and 0.5 wt% Ala. The rGO-Ala hybrid nanocomposites, on the other hand, exhibit moderate damping and glass transition temperatures. The reason for that may be because Ala filler increases the contact area between the rGO sheets and serves as a bridge between the two fillers, decreasing the resistance to deformation. This may enhance the possibility that these stress concentrations will weaken the composites.

Measurements of Phase Dynamics in Planar Josephson Junctions and SQUIDs.

We experimentally investigate the stochastic phase dynamics of planar Josephson junctions (JJs) and superconducting quantum interference devices (SQUIDs) defined in epitaxial InAs/Al heterostructures, and characterized by a large ratio of Josephson energy to charging energy. We observe a crossover from a regime of macroscopic quantum tunneling to one of phase diffusion as a function of temperature, where the transition temperature T^{*} is gate-tunable. The switching probability distributions are shown to be consistent with a small shunt capacitance and moderate damping, resulting in a switching current which is a small fraction of the critical current. Phase locking between two JJs leads to a difference in switching current between that of a JJ measured in isolation and that of the same JJ measured in an asymmetric SQUID loop. In the case of the loop, T^{*} is also tuned by a magnetic flux.

The Optimum Inertial Amplifier Tuned Mass Dampers for Nonlinear Dynamic Systems

The optimum inertial amplifier tuned mass dampers (IATMD) for vibration reduction of linear and nonlinear dynamic systems are introduced in this paper. [Formula: see text] and [Formula: see text] optimization methods are applied to derive the exact closed-form expressions for optimal design parameters such as frequency and viscous damping ratios in simplified form mathematically for IATMD. From the parametric study, using these optimal closed-form solutions, a higher damper mass ratio, a higher amplifier mass ratio, and a lower inertial angle are recommended to design optimum IATMD to achieve robust dynamic response reduction capacity having moderate viscous damping and lower frequency ratios at an affordable range. The optimum IATMD systems are installed on top of linear and nonlinear single-degree-of-freedom systems to mitigate their dynamic responses of them. The linear dynamic responses are determined through transfer matrix formations, and nonlinear dynamic responses are derived using the harmonic balance (HB) method. [Formula: see text] optimized IATMD is significantly [Formula: see text] and [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper one (CTMD1) and conventional tuned mass damper two (CTMD2). Furthermore, [Formula: see text] optimized IATMD is significantly [Formula: see text] superior to the [Formula: see text] optimized conventional tuned mass damper (CTMD). According to the nonlinear dynamic analysis, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. Furthermore, [Formula: see text] optimized IATMD systems are significantly [Formula: see text], [Formula: see text], and [Formula: see text] superior to the [Formula: see text] optimized CTMD. The results of this study are mathematically accurate and feasible for practical applications.

Quantum metrology with a non-linear kicked Mach–Zehnder interferometer

We study the sensitivity of a Mach–Zehnder interferometer that contains in addition to the phase shifter a non-linear element. By including both elements in a cavity or a loop that the light transverses many times, a non-linear kicked version of the interferometer arises. We study its sensitivity as function of the phase shift, the kicking strength, the maximally reached average number of photons, and damping due to photon loss for an initial coherent state. We find that for vanishing damping Heisenberg-limited scaling of the sensitivity arises if squeezing dominates the total photon number. For small to moderate damping rates the non-linear kicks can considerably increase the sensitivity as measured by the quantum Fisher information per unit time.

All-round responses and boundaries of a shaft and dry friction damper assembly

A helicopter tailrotor driveline is equipped with dampers to suppress the resonance of transmission shafts. A dry friction damper and a slender shaft form an assembly The comprehensive understanding of different responses of the assembly provides the basis for a more reasonable parameter configuration of the damper. To this end, the assembly is modeled as a dynamic system with rub impact between a rotor with continuous parameter distribution and a suspended elastic stator. Boundaries of rub impact and condition of Hopf bifurcation are derived. Pinned natural frequencies and backward whirl frequencies are solved by analytical deduction. The critical speed for triggering a backward whirl with consideration of eccentric excitation is obtained by the multiple scale perturbation method. Then, all-round responses and boundaries are solved by both analytical and numerical approaches based on the parameters of a helicopter. The effects of friction coefficient, internal damping, suspension stiffness, variable impact stiffness, etc. on the boundaries are presented in detail with the discussion of relationships between physical reasons and analytical conditions. Results show that smaller impact stiffness difference and friction coefficient, a greater mass damping ring, moderate suspension stiffness, greater internal and external damping are the key factors for the damper design. This study has reference significance not only for the assembly in a helicopter but also for similar mechanical systems.

Dissipation-Dependent Thermal Escape from a Potential Well.

Langevin simulations are conducted to investigate the Josephson escape statistics over a large set of parameter values for damping and temperature. The results are compared to both Kramers and Büttiker–Harris–Landauer (BHL) models, and good agreement is found with the Kramers model for high to moderate damping, while the BHL model provides further good agreement down to lower damping values. However, for extremely low damping, even the BHL model fails to reproduce the progression of the escape statistics. In order to explain this discrepancy, we develop a new model which shows that the bias sweep effectively cools the system below the thermodynamic value as the potential well broadens due to the increasing bias. A simple expression for the temperature is derived, and the model is validated against direct Langevin simulations for extremely low damping values.

Exploring energy harvesting and vibration mitigation in tall buildings accounting for wind and seismic loads

With the changing climate and the limited supply of fossil fuels available for global energy use, much research has been done to develop innovative methods of producing clean and renewable energy. Out of the various energy sources, wind forces can cause tall buildings to undergo significant vibrations presenting a potential source of clean and renewable energy for buildings and the power grid. To mitigate wind-induced vibrations in tall buildings, viscous dampers have been widely utilized, which, unlike tuned-mass dampers, are also effective in mitigating earthquake-induced vibrations. Contrary to conventional designs, this research explores the use of energy harvesting transducers, in place of viscous dampers, as a means of not only mitigating vibrations under extreme loading conditions (e.g. earthquakes), but also harvesting energy from wind induced vibrations during service conditions and converting it to electricity. This research demonstrates the often conflicting requirements for supplemental damping related to energy harvesting (EH) from wind loads under service conditions vs. vibration mitigation (VM) under extreme events (e.g., earthquakes). Specifically, this research shows that large damping is usually required for VM, whereas small or moderate damping is often required to maximize EH. In doing so, this research develops, and validates using test data, a nonlinear model for an electromagnetic EH transducer, quantifies the EH potential of a selected tall building as a function of the supplemental damping and wind speed showing that EH power generation can reach kWs (as opposed to W), and assesses the seismic performance of the same building as a function of the supplemental damping for two seismic hazard levels. The findings of this research will support future studies pursuing the concept of energy harvesting in structural design.

Surmounting potential barriers: Hydrodynamic memory hedges against thermal fluctuations in particle transport.

Recently, trapped-particle experiments have probed the instantaneous velocity of Brownian motion revealing that, at early times, hydrodynamic history forces dominate Stokes damping. In these experiments, nonuniform particle motion is well described by the Basset-Boussinesq-Oseen (BBO) equation, which captures the unsteady Basset history force at a low Reynolds number. Building off of these results, earlier we showed that, at low temperature, BBO particles could exploit fluid inertia in order to overcome potential barriers (generically modeled as a tilted washboard), while its Langevin counter-part could not. Here, we explore the behavior of neutrally buoyant BBO particles at finite temperature for moderate Stokes damping. Remarkably, we find that the transport of particles injected into a bumpy potential with sufficiently high barriers can be completely quenched at intermediate temperatures, whereas itinerancy may be possible above and below that temperature window. This effect is present for both Langevin and BBO dynamics, though these occur over drastically different temperature ranges. Furthermore, hydrodynamic memory mitigates these effects by sustaining initial particle momentum, even in the difficult intermediate temperature regime.

Use of scrap tire pads in vibration control system for seismic response reduction of buildings

This study evaluated the use of scrap tire pads (STPs) made of used tires in a vibration control system for earthquake protection of building structures. Concepts and advantages of the seismic mass damper system using STPs, experimental investigation of a STP unit specimen, and numerical assessment of the control effects by the proposed system are presented. Dynamic loading tests under constant vertical pressures as well as vertical loading tests on the STP specimen were conducted to obtain the basic mechanical characteristics of the STP. The test results demonstrated that the STP specimen exhibited stable hysteresis loops against lateral cyclic loadings and showed a moderate damping capacity without any additional energy dissipation devices. Also, dependencies of the lateral equivalent stiffness and viscous damping factor on displacement magnitude, vertical pressure, loading frequency, and cycle number were obtained from the test results. Moreover, an earthquake response analysis was carried out to evaluate the response reduction effects if the proposed mass damper system was installed in a building. The results showed the effectiveness of the proposed system under various seismic input motions.

Effect of inter-layer spin diffusion on skyrmion motion in magnetic multilayers

It is well known that skyrmions can be driven using spin-orbit torques due to the spin-Hall effect. Here we show an additional contribution in multilayered stacks arises from vertical spin currents due to inter-layer diffusion of a spin accumulation generated at a skyrmion. This additional interfacial spin torque is similar in form to the in-plane spin transfer torque, but is significantly enhanced in ultra-thin films and acts in the opposite direction to the electron flow. The combination of this diffusive spin torque and the spin-orbit torque results in skyrmion motion which helps to explain the observation of small skyrmion Hall angles even with moderate magnetisation damping values. Further, the effect of material imperfections on threshold currents and skyrmion Hall angle is also investigated. Topographical surface roughness, as small as a single monolayer variation, is shown to be an important contributing factor in ultra-thin films, resulting in good agreement with experimental observations.

Nonlinear multi-element interactions in an elastically coupled microcantilever array subject to electrodynamic excitation

In this work, we formulate and investigate a nonlinear initial boundary-value problem for an array of N elastically coupled hybrid microcantilever beams that are subject to electrodynamic excitation. The equations of motion for the individual viscoelastic element consist of two fields: the base component which is common to all cantilevers and the unrestrained component which is excited electrodynamically. The coupling of the elements is obtained via an equivalent linear stiffness that is estimated from experimental measurements of a 5-element array. We employ a Galerkin ansatz to obtain a modal dynamical system that consistently incorporates a quintic nonlinearity due to the combined effects of cubic viscoelasticity and quadratic electrodynamics. We validate the periodic response of a 5-element array with moderate damping and construct numerically a comprehensive bifurcation structure for a 25-element array. The analysis reveals an intricate structure for small damping that includes both quasiperiodic and nonstationary chaotic-like energy transfer between the elements of the array. It is noteworthy that an array with a larger coupling stiffness, corresponding to a smaller distance between adjacent elements, yields a chaotic bifurcation structure for a larger value of viscoelastic damping.

An accurate two‐stage explicit time integration scheme for structural dynamics and various dynamic problems

SummaryIn this article, a two‐stage explicit time integration method is presented for the numerical analysis of various dynamic problems described by second‐order ordinary differential equations in time. The newly proposed method have negligible damping and period errors in the important low‐frequency range and can introduce moderate numerical damping into the spurious high‐frequency range. The computational effort per step required in the new method is the same as the effort needed in the existing two‐stage explicit methods. The proposed method can provide fourth‐order accurate solutions for velocity independent problems and second‐order accurate solutions for velocity dependent problems, which is not possible in the existing methods. The proposed new method is expected to be an excellent tool for numerical analyses of various dynamic problems including structural dynamics.

Synchronisation vs. resonance: Isolated resonances in damped nonlinear oscillators

We describe differences between synchronisation and resonance, and analyse different types of nonlinear resonances in a weakly damped Duffing oscillator using bifurcation theory techniques. In addition to previously reported (i) odd subharmonic resonances found on the primary branch of symmetric periodic solutions with the forcing frequency and (ii) even subharmonic resonances due to symmetry-broken periodic solutions that bifurcate off the primary branch and also oscillate at the forcing frequency, we uncover (iii) novel resonance type due to isolas of periodic solutions that are not connected to the primary branch. These occur between odd and even resonances, oscillate at a fraction of the forcing frequency, and give rise to a complicated resonance ‘curve’ with disconnected elements and high degree of multistability.We use bifurcation continuation to compute resonance tongues in the plane of the forcing frequency vs. the forcing amplitude for different but fixed values of the damping rate. Our analysis shows that identified here isolated resonances explain the intriguing “intermingled tongues” that were observed for weak damping and misinterpreted as (synchronisation) Arnold tongues in Paar and Pavin (1998). What is more, isolated resonances link “intermingled tongues” to a seemingly unrelated phenomenon of “bifurcation superstructure” described for moderate damping in Parlitz and Lauterborn (1985).

Nonlinear evolutions of large amplitude oblique whistler waves

This paper investigates nonlinear evolutions of large amplitude oblique whistler waves (LOWWs) and the interaction with electrons using one-dimensional electromagnetic kinetic simulations. The present research is motivated by recent studies about the nonlinear phenomena of LOWWs. When the propagation angle is not close to the resonance cone angle, the trapping of electrons in the electric potential of LOWWs leads to a moderate damping and a mild acceleration of the electrons via the O'Neil-type damping. In contrast, when the propagation angle of LOWWs is close to the resonance cone angle, the LOWWs undergo a heavy damping accompanied by the stochastic thermalization of the electrons, especially in the perpendicular direction. It is found that the stochastic parameter S, defined by S=16k∥2(eme)Φ0 |J0(k⊥ρ)|ωce2, is a crucial factor determining the damping process. This result demonstrates the importance of self-consistent electron kinetic effects, which are not included in the previous single-particle or fluid approach. The implications of the present findings are discussed.

Tunability of Free Volume and Viscoelastic Damping of Thiol–Ene Networks Deep in the Glassy State

Model thiol-click glassy networks with low shrinkage and sharp glass transition temperatures are studied down to cryogenic temperatures to relate viscoelastic damping to changes in microscopic hole volume. Networks synthesized by polymerization of divinyl sulfone with pentaerythritol tetrakis(3-mercaptopropionate) (PETMP), trimethylolpropane tris(3-mercaptopropionate) (TMPTMP), and pentaerythritol tetrakis(2-mercaptoacetate) (PETT) were studied to ∼50 K using positron annihilation and thermal analysis methods. Across the glass transition temperature, overall volume expansivity is dominated by expansion of microscopic holes. Beneath Tg, holes contract upon cooling and then become static with negligible expansivity at temperatures well above 0 K. A trade-off between complete rigidity of static free volume and viscoelastic damping ability below Tg is discussed. All samples show moderate damping (tan δ > 0.05), and one sample exhibits a prominent β-transition in its viscoelastic loss spectra. These results in...

Biparametric investigation of the general standard map: multistability and global bifurcations

We investigate multistability and global bifurcations in the general standard map, a biparametric two-dimensional map. Departing from the conservative case of the map, we describe the evolution of periodic solutions and their basins of attraction as dissipation builds up, paying special attention on how the biparametric variation affects multistability. We examine general and specific phenomena and behavior for three distinct dynamical regimes, namely small, moderate, and large damping and different forcing amplitudes. Also, we report numerically the mechanism of global bifurcations associated to small chaotic attractors in the multistable system. Several global bifurcations are investigated as dissipation increases. Specifically, through the characterization of an interior, a merging and a boundary crisis, we study the crucial role played by fundamental hyperbolic invariant structures, such as unstable periodic orbits and their stable and unstable invariant manifolds, in the mechanisms by which the phase space is globally transformed.

Breaking mean-motion resonances during Type I planet migration

AbstractWe present 2D hydrodynamical simulations of pairs of planets migrating simultaneously in the Type I regime in a protoplanetary disc. Convergent migration naturally leads to the trapping of these planets in mean-motion resonances. Once in resonance the planets’ eccentricity grows rapidly, and disc-planet torques cause the planets to escape resonance on a time-scale of a few hundred orbits. The effect is more pronounced in highly viscous discs, but operates efficiently even in inviscid discs. We attribute this resonance-breaking to overstable librations driven by moderate eccentricity damping, but find that this mechanism operates differently in hydrodynamic simulations than in previous analytic calculations. Planets escaping resonance in this manner can potentially explain the observed paucity of resonances in Kepler multitransiting systems, and we suggest that simultaneous disc-driven migration remains the most plausible means of assembling tightly packed planetary systems.

CORRELATIONS BETWEEN COMPOSITIONS AND ORBITS ESTABLISHED BY THE GIANT IMPACT ERA OF PLANET FORMATION

ABSTRACT The giant impact phase of terrestrial planet formation establishes connections between super-Earths’ orbital properties (semimajor axis spacings, eccentricities, mutual inclinations) and interior compositions (the presence or absence of gaseous envelopes). Using N-body simulations and analytic arguments, we show that spacings derive not only from eccentricities, but also from inclinations. Flatter systems attain tighter spacings, a consequence of an eccentricity equilibrium between gravitational scatterings, which increase eccentricities, and mergers, which damp them. Dynamical friction by residual disk gas plays a critical role in regulating mergers and in damping inclinations and eccentricities. Systems with moderate gas damping and high solid surface density spawn gas-enveloped super-Earths with tight spacings, small eccentricities, and small inclinations. Systems in which super-Earths coagulate without as much ambient gas, in disks with low solid surface density, produce rocky planets with wider spacings, larger eccentricities, and larger mutual inclinations. A combination of both populations can reproduce the observed distributions of spacings, period ratios, transiting planet multiplicities, and transit duration ratios exhibited by Kepler super-Earths. The two populations, both formed in situ, also help to explain observed trends of eccentricity versus planet size, and bulk density versus method of mass measurement (radial velocities versus transit timing variations). Simplifications made in this study—including the limited time span of the simulations, and the approximate treatments of gas dynamical friction and gas depletion history—should be improved on in future work to enable a detailed quantitative comparison to the observations.