Classical Damping Research Articles

Classicalization of Quantum Mechanics: Classical Radiation Damping Without the Runaway Solution

In this paper, we review a new treatment of classical radiation damping, which resolves a known contradiction in the Abraham–Lorentz equation that has long been a concern. This radiation damping problem has already been solved in quantum mechanics by the method introduced by Friedrichs. Based on Friedrichs’ treatment, we solved this long-standing problem by classicalizing quantum mechanics by replacing the canonical commutation relation from quantum mechanics with the Poisson bracket relation in classical mechanics.

Protección sísmica de estructuras civiles mediante dispositivo INERTER en la provincia de Huancayo

This research work proposes the use of a Tuned-Mass-Damper-Inerter (TMDI), which combines a new configuration of passive vibration control using an “Inerter”. This two-terminal mechanical flywheel device, based on the well-known Tuned-Mass-Damper (TMD), generates resistance forces proportional to the relative acceleration of its terminals. TMDI takes advantage of the “mass amplification effect” of Inerter to improve performance compared to TMD. For harmonically excited primary linear systems, closed-form analytical software is modeled to obtain optimal design and tuning parameters of the TMDI, using established methods. It is observed that, with proper distribution of the dampers, the TMDI system is more effective in suppressing vibrations close to the natural frequency of the uncontrolled primary system and is more resistant to the effects of detuning and misdistribution. Furthermore, the results of the modeled structures show the effectiveness of the TMDI, modeled as a classical damper, in suppressing the fundamental mode of vibration for linear MDOF structures. The incorporation of the Inerter in the proposed TMDI configuration can replace part of the vibrating mass, achieving lightweight passive vibration control solutions or improving structural performance. The solution proposed and modeled with traditional dampers behaves linearly, in line with current performance trends for minimally damaged structures protected by passive control devices. Additionally, optimized TMDI is applied for vibration suppression and displacement control, offering optimal seismic protection.

Carbonyl stretching band in amides as Lorentz oscillator. Insights into anharmonicity and local environment in the liquid phase from NIR and MIR spectra of N-methylformamide and di-N,N-methylformamide

We investigated the anharmonicity and intermolecular interactions of N-methylformamide (NMF) and di-N,N-methylformamide (DMF) in the neat liquid phase with particular interest in the amide bands. The vibrational spectra, complex refractive index, and complex electric permittivity were determined in in the mid- (MIR) and near-infrared (NIR) regions (11,500–560 cm−1; 870–17857 nm). Dispersion analysis was based on the Classical Damped Harmonic Oscillator (CDHO) and simultaneous modelling of the real and imaginary components of the spectra. This data delivered insights into the vibrational energy dissipation and self-association in liquid amides. Identification of the MIR and NIR bands was based on anharmonic GVPT2//B3LYP/6-311++G(d,p) calculations. DMF and NMF follow distinct self-association, evidenced in the MIR fingerprint by the two components of the νCO, the analog of the Amide I band. These conclusions are supported by the structural information derived from the NIR spectra. Furthermore, the contribution of overtones and combination bands in the MIR spectra of amides was examined. The conclusions on molecular interactions and structural dynamics of NMF and DMF contribute to a deeper understanding of the effects of changes in the local environment of the amide group.

Enhanced Classical Radiation Damping of Electronic Cyclotron Motion in the Vicinity of the Van Hove Singularity in a Waveguide

Abstract We study the damping process of electron cyclotron motion and the resulting emission in a waveguide using the classical Friedrichs model without relying on perturbation analysis such as Fermi’s golden rule. A Van Hove singularity appears at the lower bound (or cutoff frequency) of the dispersion associated with each of the electromagnetic field modes in the waveguide. In the vicinity of the Van Hove singularity, we found that not only is the decay process associated with the resonance pole enhanced (amplification factor ∼104) but the branch-point effect is also comparably enhanced. As a result, the timescale on which most of the decay occurs is dramatically shortened. Further, this suggests that the non-Markovian branch-point effect should be experimentally observable in the vicinity of the Van Hove singularity. Our treatment yields a physically acceptable solution without the problematic runaway solution that is well known to appear in the traditional treatment of classical radiation damping based on the Abraham–Lorentz equation.

Dual-phase-lag thermoelastic damping analysis of a functionally graded sandwich micro-beam resonators incorporating double nonlocal effects

Functionally graded sandwich micro/nano-structures have attracted great attention due to the capability to resist high noise and thermal stress in a non-isothermal environment. Additionally, the design of high quality-factor micro/nano-resonators requires accurate estimation of their thermoelastic damping. However, the classical thermoelastic damping models fail at the micro/nano-scale due to the influences of the size-dependent effects related to heat transfer and elastic deformation. This work aims to investigate the influences of the size-dependent effects on the thermoelastic damping of functionally graded sandwich micro-beam resonators by combining the nonlocal dual-phase-lag heat conduction model and the nonlocal elasticity model. It is assumed that the functionally graded sandwich micro-beam resonators consist of a ceramic core and functionally graded surfaces. The energy equation and the transverse motion equation are derived. The analytical expression of thermoelastic damping is obtained by complex frequency method. Numerical results are analyzed for the effects of the thermal nonlocal parameter, the elastic nonlocal parameter, the power-law index, and the vibration modes on the thermoelastic damping of functionally graded sandwich micro-beam resonators. The results show that the thermoelastic damping of functionally graded sandwich micro-beam resonators can be adjusted by the suitably modified parameters, which strongly depends on the double nonlocal effects and the power-law index.

Bayesian modal identification of non-classically damped systems using time-domain data

In this work, we present a Bayesian time–domain method for identifying the complex modal parameters of a linear dynamic system from ambient vibration data. Complex modal parameter identification is valid for both classically and non-classically damped systems, in contrast to real modal parameter identification, which is exclusively applicable to classically damped systems. A Bayesian method is adopted here which makes it possible to determine the joint posterior Probability Density Function (PDF) of the modal parameters for given measured data and modeling assumptions. For sufficient data, it is seen that the modal parameters are globally identifiable, and the posterior PDF is approximated by a Gaussian distribution with mean at the optimal parameters that maximize the posterior PDF. The uncertainty in the identified modal parameters is given by the covariance matrix of the posterior PDF. Analytical expressions are derived for computing the gradient for efficient optimization and the Hessian for determining the covariance matrix. Further, it is shown that the assumption of classical damping during analysis results in poor prediction of damping ratios in the case of non-classically damped systems. The application of the proposed approach is illustrated by means of simulated examples and an experimental study.

On the zeros of three-DoF damped flexible systems

This paper presents an investigation of the non-minimum phase (NMP) zeros in the single input single output (SISO) transfer function of three-DoF (degrees of freedom) damped flexible linear time-invariant (LTI) systems under the assumption of classical damping. It is well-known that when all the modal residue signs of any multi-DoF damped flexible LTI system are the same, NMP zeros never occur in the system dynamics for any value of system parameters including modal residue, modal frequency and modal damping ratio. However, when all the modal residue signs are not the same, then additional conditions in terms of the system parameters are required to guarantee the elimination of NMP zeros. In this paper, the zero loci of a three-DoF damped flexible LTI system are developed to derive the sufficient and necessary conditions for the elimination of all NMP zeros. These conditions can be employed in the robust physical design of flexible systems, i.e., as long as these conditions are satisfied, the elimination of NMP zeros is guaranteed even when the system parameters undergo variations.

Identification methods of material‐based damping for cracked reinforced concrete beam models

AbstractSeismic performance evaluation in structural design requires the use of sophisticated numerical models. In particular, to accurately represent the non‐linear behaviour of reinforced concrete (RC) structures when subjected to dynamic loadings, the energy dissipation mechanisms must be accurately represented. However, the classical viscous damping models, which are still widely used, are not based on physical considerations at the material level and the choice of damping parameters is often arbitrary. This paper, thus, proposes a time‐domain damping identification method based on equivalent single‐degree‐of‐freedom (SDOF) systems. The methodology is developed using either an updated linear model or a non‐linear energy‐dissipating constitutive model. Energy dissipative phenomena are cracking, friction and unilateral effects upon crack closure. Both models allow the identification of different damping transient variations: (i) With the updated linear model, intrinsic damping ratios and frequencies are identified to define a simple generic damping model, and (ii) with the non‐linear constitutive model, the identified viscous damping ratios represent the dissipative phenomena not described by the material model. The aim is to propose simple models that can be used by anyone to complement their own models. Applying the method to experimental data allows evaluating effective damping ratio transient variations as functions of variables representative of non‐linear behaviour. It is shown that it is possible to accurately model the energy dissipation that is missing in the non‐linear dynamic constitutive models through effective viscous damping models based on dissipative phenomena internal variables.

Dynamic analysis of masonry arches using Maxwell damping

Masonry arches are a fundamental component of historical structures. The assessment of the vulnerability of these heritage constructions to seismic loading requires reliable and efficient numerical models. Discrete element models are an alternative to finite element models, being particularly effective in modelling collapse mechanisms created by shearing and separation of the units along the joints. Discrete element codes typically rely on explicit methods of integration of the equations of motion for dynamic analysis, which may require large run times when the recommended stiffness-proportional component of Rayleigh damping is applied. A novel approach is proposed using an alternative damping model, Maxwell damping, which involves placing multiple spring-dashpot elements in the joints, in parallel with the standard stiffness springs. This damping model is tested in the dynamic analysis of masonry arches, under pulse and earthquake loading. The results obtained in this early investigation show a good performance in the simulation of collapse under dynamic loads, in general agreement with the analyses conducted with classical stiffness-proportional damping, but reducing significantly the computational effort.

A review of higher order Newton type methods and the effect of numerical damping for the solution of an advanced coupled Lemaitre damage model

In this paper, several Newton-type methods of convergence order 2 or higher were tested on various nonlinear systems of equations and on an advanced material law implemented in a finite-element code. The computational speed, numerical efficiency, and robustness of each method were evaluated for each studied case. The effect of numerical damping was also studied. The results were then compared to put in light the strengths and weaknesses of each method. The most efficient and robust method for the material law in the finite-element code was identified as the Newton method with a selective numerical damping. • Several Newton-type methods were evaluated for solving various numerical problems. • The methods were compared based on computational speed, efficiency, and robustness. • Classic numerical damping can improve the robustness of some, but not all, methods. • Newton method with selective numerical damping is the most efficient and robust.

Influence of the Experimental Setup on the Damping Properties of SLM Lattice Structures

BackgroundMetal lattice structures obtained through Selective Laser Melting may increase the strength-to-weight ratio of advanced 3D printed parts, as well as their damping properties. Recent experimental results showed that AlSi10Mg and AISI 316L lattices are characterized by higher Rayleigh damping coefficients with respect to the fully dense material. However, some unclear or contradictory results were found, depending on the experimental setup adopted for modal analysis.ObjectiveIn this work the influence of the experimental setup when performing modal analysis on different SLM AISI 316L lattice structures was deeply investigated. The study provides a critical comparison of various experimental modal analysis approaches, allowing to evaluate the influence of external damping sources and material internal damping phenomena.MethodsThe dynamic behaviour of SLM AISI 316L specimens incorporating lattice structures was estimated by means of pulse testing and sinusoidal excitation through an electromagnetic shaker. The validity of the viscous damping model was assessed by means of sinusoidal excitation with different levels of vibration velocity. Moreover, the influence of experimental setup on modal analysis results was critically evaluated, by considering different actuators, contact and non-contact sensors and boundary/clamping conditions.ResultsThe classical viscous damping model describes with good approximation the damping properties of SLM lattice structures. When exciting single specimens in free-free conditions, those embedding lattice structure and unmelted metal powder filler were characterized by superior internal damping properties with respect to the specimens incorporating the lattice structure without any filler, which was however more effective than the full density equivalent material. Most of the other experimental setups introduced additional external damping sources, that could alter this important outcome.ConclusionsSLM lattice structures embedded into 3D printed components provide superior damping properties against mechanical and acoustic vibrations and the metal powder filler does significantly enhance such damping capacity. A correct estimation of material internal damping was achieved by applying non-contact sensors and free-free boundary conditions, whereas other experimental setups were partly inadequate.

Integration Method for Response History Analysis of Single-Degree-of-Freedom Systems with Negative Stiffness

The present article deals with the mathematical investigation of a negative-stiffness ideal system that can be used in seismic isolation of civil engineering structures. Negative-stiffness systems can be used in the seismic isolation of structures, because in the case of a strong earthquake, they do not easily allow vibrations to develop. These negative-stiffness systems can be significantly more efficient than the usual seismic isolation systems, as they drastically reduce the vibrational amplitudes of structures, as well as eliminate the inertial seismic structure loadings. The mathematical investigation of a negative-stiffness ideal system provides documented answers about the effect of negative-stiffness systems in the seismic behavior of structures. First, the differential equation of motion of a single-degree-of-freedom oscillator (SDoF) is formulated, without classical damping, but with negative stiffness. Furthermore, the mathematical solution of the equation of motion is given, where it is proven that this solution does not describe a structure vibration. Furthermore, the seismic structure motion follows an exponential increase when the seismic ground excitation is purely sinusoidal. Finally, to calculate the real response of the negative-stiffness system, a suitable modification of the Newmark iterative numerical method is proposed.

State-space Bloch mode synthesis for fast band-structure calculations of non-classically damped phononic materials

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig–Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey–O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced-order model and demonstrate the underlying accuracy–efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties.

Efficient band-structure calculations of non-classically damped phononic materials by Bloch mode synthesis in state space

Bloch mode synthesis (BMS) techniques enable efficient band-structure calculations of periodic media by forming reduced-order models of the unit cell. Rooted in the framework of the Craig-Bampton component mode synthesis methodology, these techniques decompose the unit cell into interior and boundary degrees-of-freedom that are nominally described, respectively, by sets of normal modes and constraint modes. In this paper, we generalize the BMS approach by state-space transformation to extend its applicability to generally damped periodic materials that violate the Caughey-O’Kelly condition for classical damping. In non-classically damped periodic models, the fixed-interface eigenvalue problem may, in general, produce a mixture of underdamped and overdamped modes. We examine two mode-selection schemes for the reduced order model and demonstrate the underlying accuracy-efficiency trade-offs when qualitatively distinct mixtures of underdamped and overdamped modes are incorporated. The proposed approach provides a highly effective computational tool for analysis of large models of phononic crystals and acoustic/elastic metamaterials with complex damping properties. This investigation does not only extend the applicability of BMS techniques to the most generally damped models of periodic media, it also advances our understanding of the nature of damping modes and the non-trivial manner by which they contribute to the wave propagation properties.

Study on Identification Method of Motion States at Interface for Soil-Structure Interaction Damping System

The damping system characterizes the spatial distribution of structural energy dissipation. Identifying a damping system is the premise for determining the dynamic analysis method. Concepts of nonlinear processes and non-classical damping systems are often confused without theoretical primary and experimental verification. This paper proposes an identification method of damping systems based on motion states at the interface by analyzing the correlation between the damping system and dynamic characteristics. The relationship between the change of damping system type and relative motion states at the interface is studied by investigating multiple material properties through shaking table model tests of a large-scale soil-structure interaction (SSI) system. The results show that a nonlinear system can demonstrate the characteristics of the classical damping system as soon as there is no mutation of motion states at the interface of the system. The identification method of damping system based on motion states at the interface can reflect the change of dynamical characteristics of the system under linear and nonlinear processes.

A universal rate-dependent damping model for arbitrary damping-frequency distribution

Damping is fundamental to structural dynamics. Reasonable damping models facilitate accurate and reliable dynamic analyses of damped structures. Existing experiments indicate that damping is dependent but not proportional to the frequency. Hence, it may be challenging for viscous and rate-independent damping models to accurately simulate the frequency characteristics. This study proposes a universal rate-dependent damping model and its implementation in an open-source finite-element analysis software, OpenSees. A comparison with experimental results verify that the proposed damping model can accurately and flexibly simulate the distribution of damping energy dissipation in various frequency domains wherein the relative error of the damping is significantly smaller than that of the widely used classical damping models.

A novel reduced-order dynamic-stiffness formulation for locally resonant metamaterial plates

A novel dynamic-stiffness formulation is presented to study the dynamics of locally resonant metamaterial plates. Focusing on an assembly of plates coupled by periodic arrays of resonators, the formulation hinges on a reduced-order dynamic-stiffness model obtained by exact dynamic condensation of the degrees of freedom within the resonators. Two are the main results. First, a reduced-order global dynamic-stiffness matrix is constructed, to calculate natural frequencies and undamped modes by the Wittrick–Williams algorithm. Second, two specific orthogonality conditions are derived for the modes of the plates only, which lead to closed analytical forms for the modal response under arbitrary loading, in time and frequency domains, under the assumption of classical damping. Remarkably, the modal response is obtained for the whole set of response variables, including those within the resonators. The comparison with finite-element results obtained in ABAQUS substantiates accuracy and effectiveness of the proposed reduced-order dynamic-stiffness formulation.

Dissipative joints under impact loadings

AbstractUnforeseen and unpredictable exceptional events can lead to abnormal loading distribution in the structures; however, in such situation, structures have to withstand additional loadings to avoid disproportionate damage and progressive collapse. Impact loadings are among the exceptional events that a structure can experience during its lifetime. In order to give a contribution to the research on impulsive loading on structural joints, this work focuses on the behavior of slide hinge joints (SHJ) with a Symmetric Friction Damper (SFD) under drop weight impact tests. Six drop weight impact tests on a double‐sided beam‐to‐column joints were performed and a 3D finite element model was created and validated in ABAQUS/CAE Explicit. The model includes the calibration of material damage, correlating the equivalent plastic strain to the stress triaxiality, damping of the system, calibrated on elastic impact tests using Rayleigh's classical damping and strain rate sensitivity through the Johnson Cook model. Furthermore, a parametric analysis was performed in order to investigate the influence of three parameters on the joint behavior: the impact velocity, the impact mass and the impact energy. The energy is used to estimate the dissipation rate of the joint, which can be considered as a reliable parameter to quantify the joint behavior under drop weight impact.

Analysis of the Vibration Suppression of Double-Beam System via Nonlinear Switching Piezoelectric Network

In this paper, a method to suppress the vibration of a double-beam system with nonlinear synchronized switch damping on the inductor via a network (SSDI-net) is proposed. Unlike the classical linear piezoelectric shunt damping, SSDI-net is a nonlinear piezoelectric damping. A double-beam system with SSDI-net was simplified to a lumped parameter electromechanical coupling model and analyzed by using the multi-harmonic balance method, at first with alternating frequency–time techniques (MHBM/AFT). Then, a new lower-power autonomous switching control circuit board was designed, based on SSD technique, and vibration control experiments using a double-beam system with an SSDI network are conducted, to verify the validity of the proposed analysis method and its calculation results. The nonlinear switching piezoelectric network proposed in this article can increase the voltage inversion factor. Furthermore, future applications of this switching piezoelectric network technology in the vibration suppression of bladed-disk structures in aero engines can reduce the number of switches by at least half and obtain almost the same damping effect.

Kinetic instability in inductively oscillatory plasma equilibrium.

A uniform in space, oscillatory in time plasma equilibrium sustained by a time-dependent current density is analytically and numerically studied resorting to particle-in-cell simulations. The dispersion relation is derived from the Vlasov equation for oscillating equilibrium distribution functions, and used to demonstrate that the plasma has an infinite number of unstable kinetic modes. This instability represents a kinetic mechanism for the decay of the initial mode of infinite wavelength (or equivalently null wave number), for which no classical wave breaking or Landau damping exists. The relativistic generalization of the instability is discussed. In this regime, the growth rate of the fastest growing unstable modes scales with γ_{T}^{-1/2}, where γ_{T} is the largest Lorentz factor of the plasma distribution. This result hints that this instability is not as severely suppressed for large Lorentz factor flows as purely streaming instabilities. The relevance of this instability in inductive electric field oscillations driven in pulsar magnetospheres is discussed.