Dependent Damping Research Articles

Time-domain impedance boundary conditions for acoustic reduced order finite element simulations

Transient responses impose additional restrictions concerning model order reduction of acoustic finite element systems. Time-stable model order reduction methods achieve model compaction while guaranteeing frequency domain models transform in a physically meaningful way. Efficiency and stability are of course of little consequence if the model is rendered inaccurate. Krylov subspaces inherently include system input and/or output behavior in the reduction basis making them ideal reduction bases for investigating system behavior outside of steady state. Realistic boundary conditions are demanded and must be preserved in the reduction basis. Frequency dependent impedance boundary conditions help in this regard but complicate both model reduction and time-integration strategies. Multiplications to enforce system damping in the frequency domain become time-domain convolutions. Recursively calculated minimal memory convolution formulations have long proven useful in lowering the associated computational burden. Complex frequency-dependent damping matrices create a challenge for Krylov subspace based model reduction due to the way the reduction basis is constructed. Arnoldi iterations implicitly match the moments of the system transfer function to span a Krylov subspace. This paper demonstrates how to maintain compatibility with such algorithms while including frequency dependent damping. This work proposes combining projection based model order reduction with an efficient time domain-impedance boundary condition formulation. An important benefit of working in the time domain is the ability to directly output binaural audio signals. To this end, discrepancies are discussed in the perceptual context of audibility. A reduction of system degrees of freedom from NDOF=13125 to RDOF=63 and the inclusion of time-domain impedance boundary conditions are shown to enable computational speedups by a factor of 11–36 without introducing audible differences.

A hysteretic loop phenomenon at strain amplitude dependent damping curves of pre-strained pure Mg during cyclic vibration

In this study, twins were introduced into pure Mg by pre-deformation, the strain amplitude dependent damping in pre-strained pure magnesium was investigated using cyclic vibration. The strain amplitude dependent damping curve exhibited a hysteretic loop as the strain amplitude was cycled. The damping value was greater during the high strain amplitude regime when the strain amplitude increased than when strain amplitude decreased. For the low strain amplitude regime, the opposite trend was observed. The results point to the damping behavior transitions between the two regimes occurring at a specific strain amplitude, increasing commensurately with increased pre-strain. This hysteretic loop phenomenon is attributed to the difference in mechanical energy consumed by the motion of the twin boundaries during cyclic vibration. The hysteretic loop indicates that twin dampening already exists. Therefore, the strain amplitude value of the intersection may be used as a reference parameter to detect twin damping.

Constant-roll inflation driven by q-de Sitter

We have studied constant-roll inflation using the q-de Sitter scale factor. Both the cold and warm inflation have been considered, and the scalar potential and inflaton field have been determined. Also tensor to scalar ratio and the spectral index are obtained. In the cold inflation case, the perturbations have been investigated using Mukhanov–Sasaki equation, and the results determined for the spectral index and tensor to scalar ration are consistent with observations. In the warm inflation two cases of constant damping ([Formula: see text]) and the field dependent damping ([Formula: see text]) have been studied. In both cases the power spectrum and the tensor to scalar ratio are determined as a function of the inflaton field. It has been shown that in both cases the spectral index is independent of the inflaton field. In the case of constant damping the obtained value for the spectral index is inconsistent with observations but for the case of field dependent damping the parameter [Formula: see text] can be chosen such that the value obtained for all the physical quantities including the spectral index be consistent with present cosmological observations.

Tuning of vessel parameters including sea state dependent roll damping

Online tuning of vessel models based on onboard measurement data can reduce the uncertainties of vessel motion prediction, and therefore potentially increase the safety and cost efficiency for marine operations. Among the uncertain vessel parameters, the roll damping coefficient is very important and highly nonlinear. In reality, roll damping depends on the sea state and vessel condition. This paper proposes two different procedures for tuning the sea state dependent roll damping coefficient together with other uncertain vessel parameters, i.e., 1-step tuning and 2-step tuning procedures. In addition, a roll damping prediction model based on Gaussian process regression is also proposed to predict the roll damping for future sea states based on historical data. The tuning procedure together with the proposed prediction model form an iterative closed loop of continuously improving the knowledge about the roll damping online, also estimating the model uncertainty based on prior knowledge, sampling uncertainties, and the applied kernel. Case studies are presented to demonstrate the procedures.

Temperature Dependent Damping in Additively Manufactured Polymer Structures

Temperature effects are predominantly ignored when computing the dynamic response of structures. Yet, in applications where large changes in temperature occur, the dynamic response can drastically change. This is particularly true for polymers. While the temperature effects on modulus and loss factor are often available for most polymers, this change is not addressed or corrected for. Meanwhile, the recent research on additively manufactured polymer metastructures has yet to consider the effects of temperature change on their ability to suppress vibrations. In order to fill this gap, the study presented in this paper focuses on the effects of temperature change on additively manufactured structures.

Adapted gauge to small mass ratio binary black hole evolutions

We explore the benefits of adapted gauges to small mass ratio binary black hole evolutions in the moving puncture formulation. We find expressions that approximate the late time behavior of the lapse and shift, $({\ensuremath{\alpha}}_{0},{\ensuremath{\beta}}_{0})$, and use them as initial values for their evolutions. We also use a position and black hole mass dependent damping term, $\ensuremath{\eta}[{\stackrel{\ensuremath{\rightarrow}}{x}}_{1}(t),{\stackrel{\ensuremath{\rightarrow}}{x}}_{2}(t),{m}_{1},{m}_{2}]$, in the shift evolution, rather than a constant or conformal-factor dependent choice. We have found that this substantially reduces noise generation at the start of the numerical integration and keeps the numerical grid stable around both black holes, allowing for more accuracy with lower resolutions. We test our choices for this gauge in detail in a case study of a binary with a $7\ensuremath{\mathbin:}1$ mass ratio, and then use $15\ensuremath{\mathbin:}1$ and $32\ensuremath{\mathbin:}1$ binaries for a convergence study. Finally, we apply our new gauge to a $64\ensuremath{\mathbin:}1$ binary and a $128\ensuremath{\mathbin:}1$ binary to well cover the comparable and small mass ratio regimes.

Damped Oscillators within the General Theory of Casimir and van der Waals Forces

It is demonstrated that the general theory of Casimir and van der Waals forces describes the interaction-induced equilibrium thermodynamic potentials of the damped harmonic oscillator bilinearly coupled to the environment. An extended model for a damped oscillator is suggested along the lines of the general theory of Casimir and van der Waals forces, and the corresponding thermodynamic quantities obtained. While the original model involves a heat bath consisting of a large number of free oscillators having infinitesimal damping functions, the extended model allows any generally admissible frequency and temperature dependent dissipative susceptibilities of the heat bath constituents, influenced by the additional dissipative environmental channels that are not directly linked to the system oscillator. Consequently, the results obtained are applicable to the frequency and temperature dependent damping function of the system oscillator.

Temperature-Dependent Nonlinear Damping in Palladium Nanomechanical Resonators.

Advances in nanofabrication techniques have made it feasible to observe damping phenomena beyond the linear regime in nanomechanical systems. In this work, we report cubic nonlinear damping in palladium nanomechanical resonators. Nanoscale palladium beams exposed to a H2 atmosphere become softer and display enhanced Duffing nonlinearity as well as nonlinear damping at ultralow temperatures. The damping is highest at the lowest temperatures of ∼110 mK and decreases when warmed up to ∼1 K. We experimentally demonstrate for the first time temperature-dependent nonlinear damping in a nanomechanical system below 1 K. This is consistent with a predicted two-phonon-mediated nonlinear Akhiezer scenario with a ballistic phonon mean free path comparable to the beam thickness. This opens up new possibilities to engineer nonlinear phenomena at low temperatures.

Parametric study of damping characteristics of rotating laminated composite cylindrical shells using Haar wavelets

In this paper, the damping characteristics of rotating laminated composite cylindrical shells considering the frequency dependent damping of composite materials are studied. Based on the Love thin shell theory, Hamilton principle is used to obtain the governing equations of the composite cylindrical shell, which are converted into ordinal differential equations by the separation of variables. The dynamical equations and corresponding boundary conditions are discretized by Haar wavelet method and then the standard eigenvalue equation is obtained. The damping with frequency dependence of composite materials is taken into account by the complex modulus method. The eigenvalue equation is solved by iterative calculation to obtain the modal frequency and damping characteristics of rotating composite cylindrical shells. The correctness of present analysis is validated by comparing the predicted results with those given in the literature. The effects of frequency, rotation speed, lamination and geometric parameters on damping properties of the composite shell under four typical boundary conditions are further analyzed. Numerical results show that it is important to consider the frequency dependence of damping of composite materials, especially for the analysis of lower order modes. There are forward and backward damping respectively corresponding to the forward travelling wave and backward travelling wave modes, and the forward wave motion is more stable. The rotating composite cylindrical shell may lose its stability under certain geometric parameters due to the influences of rotation and the inherent material damping.

Role of hot electron scattering in epsilon-near-zero optical nonlinearity

Abstract The physical origin of epsilon-near-zero (ENZ) optical nonlinearity lies in the hot-electron dynamics, in which electron scattering plays an important role. With the damping factor defined by hot electron scattering time, the Drude model could be extended to modeling ENZ optical nonlinearity completely. We proposed a statistical electron scattering model that takes into account the effect of electron distribution in a nonparabolic band and conducted the investigation on indium tin oxide (ITO) with femtosecond-pump continuum-probe experiment. We found that ionized impurity scattering and acoustic phonon scattering are the two major scattering mechanisms, of which the latter had been neglected before. They dominate at low-energy and high-energy electrons, respectively, and are weakened or boosted for high electron temperature, respectively. The electron energy–dependent scattering time contributed from multiple scattering mechanisms shows the electron density–dependent damping factor. The comprehensive understanding of electron scattering in ITO will help to develop a complete model of ENZ optical nonlinearity.

A direct displacement-based seismic design method using a MDOF equivalent system: application to R/C framed structures

An improved version of the direct displacement-based design (DDBD) method for the seismic design of plane moment resisting frames in the framework of performance-based design approach is presented. The method employs a multi-degree-of-freedom equivalent system instead of the single-degree-of-freedom equivalent system used by the conventional DDBD method. Thus, the proposed method can take more rationally and with higher accuracy into account the higher mode and P-Δ effects than the conventional one. This is accomplished with the aid of the concept of deformation dependent equivalent modal damping ratios previously developed by the present authors for other purposes and the concept of the design modal displacements developed herein. These design modal displacements are determined on the basis of target inter-storey drift ratios for every performance level and the first few modes significantly contributing to the structural response. Thus, one can determine from the displacement spectrum with high amounts of viscous damping the required modal periods for known values of the design modal displacements. From those modal periods, the corresponding required modal stiffness and hence the modal base shear forces can be obtained. The final required design base shear can be obtained by a combination rule, like the SRSS rule. Numerical examples involving the seismic design of two moment resisting reinforced concrete plane frames are presented in detail for illustrating the proposed approach and demonstrating its merits over the conventional DDBD method and the force-based design method of Eurocode 8.

Strauss exponent for semilinear wave equations with scattering space dependent damping

It has been asserted that the semilinear wave equation with scattering damping admits the same Strauss critical exponent as the classical semilinear wave equation. In this paper, we devote to showing that this assertion holds for the space dependent damping wave equation when the decay rate of the space dependent variable coefficients of the damping is greater than 2. In particular, we derive the lifespan upperbound estimates for both sub-critical and critical exponents. Moreover, when the nonlinear term is of derivative type, we also obtain the same Glassey exponent and the same upper bound lifespan as that of the corresponding problem for wave equation without damping. Both results show the “hyperbolicity” of the equation from the blow-up aspect.

Microstructure and damping capacity of AA6061/graphite surface composites produced through friction stir processing

The present study is to improve the damping properties of AA6061-T6 alloy by incorporating graphite (Gr) flakes through friction stir processing (FSP). The amount of graphite varied from 5 to 15 vol%. The distribution of graphite particles and the microstructure refinement were analysed using optical and electron microscopy. The grains were indistinguishable in the stirred zone. The hardness of the surface composites decreased with an increase of graphite fraction. The dynamic mechanical analyzer was used to analyze the damping capacity of specimens extracted from the stir zone. The frequency dependent and temperature dependent damping capacity of FSP-ed AA6061 and the surface composites were observed to be better than the base metal. Significantly, the damping capacity of composite with 15 vol% graphite was 3.5 times of base-metal's damping at 250 °C.

Hardening vs. softening dichotomy of a hinged-simply supported beam with one end axial linear spring: Experimental and numerical studies

The aim of this paper is to validate experimentally a nonlinear model of a kinematically excited hinged-simply supported beam with a spring subjected to one end. An experimental setup configuration enables to test different variants of axial boundary conditions: first a typical simply supported beam (no spring), and next two different spring systems. The prototype is kinematically excited with different amplitudes of excitation and then full frequency response curves are drawn wherein hardening/softening dichotomy is recognized. A set of mechanical properties of the system is identified and then used to reproduce tests with finite element simulations. Consequently numerical vs. experiment results are compared. The analysis demonstrates amplitude dependent damping as well as that the natural frequency depends on environmental conditions, and thus may change over experiments.

Model reduction and dynamic matrices extraction from state-space representation applied to rotating machines

Model reduction is a relevant subject within the field of rotordynamics since low order models are fundamental for control strategies design and implementation, health monitoring, behavior prediction, Fault Detection and Identification (FDI) and stochastic analyses. In this context, this article proposes a complete review of three widely used reduction methods: static or Guyan technique, the System Equivalent Reduction Expansion Process (SEREP) and the modified SEREP. Regarding SEREP, a new approach is presented in which right and left eigenvectors from the undamped original system (with mass and stiffness matrices not symmetric) are used to transform all original system dynamic matrices. To modified SEREP (that contemplates all original system characteristics, including frequency dependent damping and gyroscopic effect) an extraction from the reduced state-space representation is achieved to build rotor and bearings reduced dynamic matrices with physical interpretability. A set of practical recommendations is presented, highlighting key aspects to increase reduction success chances. The methods are applied to two different rotors and results show satisfactory agreement between reduced and complete model responses when analyzing Frequency Response Functions (FRFs) and Campbell diagrams. The computational costs of processing each reduced model and running common rotordynamic analyses with reduced and complete models are compared.

Generalization of Stokes–Einstein relation to coordinate dependent damping and diffusivity: an apparent conflict

Brownian motion with coordinate dependent damping and diffusivity is ubiquitous. Understanding equilibrium of a Brownian particle with coordinate dependent diffusion and damping is a contentious area. In this paper, we present an alternative approach to this problem based on already established methods. We solve for the equilibrium distribution of the over-damped dynamics using Kramers–Moyal expansion. We compare this with the over-damped limit of the generalized/modified Maxwell–Boltzmann distribution. We investigate two distinct possibilities of the Stokes–Einstein relation not holding locally and holding locally everywhere. In the former case we get a local proportional relation between the coordinate dependent diffusivity and damping which is consistent with other requirements of equilibrium. The latter case requires restrictions on the upper limit of the local velocity of the Brownian particle to make the modified Maxwell–Boltzmann relation obtain the correct over-damped limit.

Experimental and Numerical Characterization of High Damping Martensitic CuAlMn Sheets.

This paper deals with the experimental and numerical characterization of a high damping CuAlMn sheet with a martensitic micro-structure at ambient temperature. A Cu-Al-Mn shape memory alloy containing 11.65 wt.% of Al and 3 wt.% of Mn, was cast and hot rolled to the thickness of 0.4–0.3 mm. Transformation temperatures, micro-structure and mechanical properties were studied. Effects of the heat treatment on damping were investigated, identifying the proper heat treatment to obtain a higher damping. Having to model the amplitude dependent damping of the material investigated, a material model was developed based of cyclic behavior under traction-compression load. The model was validated with experiments on the non-linear damping of the material.

Mathematical modeling and parametric study of magnetic negative stiffness dampers

This article presents mathematical modeling and parametric study of a type of magnetic negative stiffness dampers. A magnetic negative stiffness damper uses the interaction forces and movement of magnets inside a conductive pipe to achieve inverse force–deformation response and create frequency dependent damping. One advantage of magnetic negative stiffness dampers over other conventional dampers is that they do not add stiffness to the system and hence will not increase the force in the structural members to which the magnetic negative stiffness damper is attached. Using nonlinear regression analysis, simple formulas to describe the magnetic force and electromagnetic damping of a specific type of magnetic negative stiffness dampers are derived. A parametric study is then performed to show that maximum negative stiffness is obtained when the height-to-diameter (aspect) ratio of the magnets is in the range of 0.3–0.4, and for design applications upper bound values for the clear spacing-to-radius ratio and aspect ratio of the magnets are determined to be 3 and 2, respectively. The highest value of damping coefficient is found to correspond to a magnet aspect ratio of 1.6, and for design purpose the pipe wall thickness should be set equal to the height of the magnet. Based on a pushover analysis of three frames modeled as single-degree-of-freedom systems, it is found that the frame with the magnetic negative stiffness damper experiences lower base shear at the expense of a slightly higher residual drift. The effect of base shear reduction is more pronounced when the target displacement is small.

Examination of polarization coupling in a plucked musical instrument string via experiments and simulations

In this article, the transient motion of a realistically plucked guitar string is studied experimentally and numerically in both transversal polarizations. The frequency dependent damping and suitable initial conditions are identified in the experiment and used in a simulation. For this reason an experimental set-up consisting of a string, an excitation mechanism and two laser Doppler vibrometers is developed. The excitation mechanism performs a realistic and reproducible plucking motion with a plectrum. Two laser Doppler vibrometers are used to measure the string oscillation transversally in two polarizations. The experimental set-up makes it possible to measure the string’s motion under reproducible conditions and, hence, at different positions for the same oscillation. This capability renders the identification of suitable initial conditions, i.e., initial displacement and velocity as well as the pre-tension, for a string model possible. Furthermore, a finite element model for the string is developed that takes into account the oscillation in both transversal planes of polarization and the coupling between them. Finally, the model results are in good agreement with the measurements. With help of the numerical model it can be vividly shown that the coupling between the polarizations of the oscillation is due to a torsional movement of the string on the saddle.

Dislocation Damping and Defect Friction Damping in Magnesium: Molecular Dynamics Study

In this study, the molecular dynamics method was used to study the damping mechanism in Mg alloys at the atomic scale. The energy dissipated by the nucleation and motion of dislocations and by defects friction, and the effect of defects, such as vacancies, cracks, and grain boundaries, on them were studied. The study shows that different kinds of defect have different effects on the dislocation damping and defect friction damping. And then, the effect of strain amplitude and temperature on damping capacity of Mg was studied. The result shows that the amplitude independent damping is caused by defect friction and the amplitude dependent damping is mainly caused by the nucleation and motion of dislocation; the damping of Mg increased exponentially with the temperature, and the damping peck appeared at 440 K is attributed to the appearance of dislocations at the grain boundaries which may be caused by boundaries self-diffusion.