External Damping Research Articles

Advancing the dynamic properties of a column with variable flexural stiffness in terms of structural mounting damping, external and internal damping

Advancing the dynamic properties of a column with variable flexural stiffness in terms of structural mounting damping, external and internal damping

Forced-Vibration Characteristics of Bowtie-Shaped Honeycomb Composite Sandwich Panel with Viscoelastic Damping Layer.

The incorporation of viscoelastic layers in laminates can markedly enhance the damped dynamic characteristics. This study focuses on integrating viscoelastic layers into the composite facesheet of the bowtie-shaped honeycomb core composite sandwich panel (BHC-CSP). The homogenization of the damped BHC-CSP is performed by employing the variational asymptotic method. Based on the generalized total energy equation, the energy functional of the representative unit cell of the damped BHC-CSP is asymptotically analyzed. The warping function, derived following the principle of minimum potential energy, provides a basis for obtaining the corresponding Euler-Lagrange equation to ascertain the equivalent elastic properties of the damped BHC-CSP. Utilizing the developed two-dimensional equivalent model, the free-vibration characteristics of the damped BHC-CSP are examined across diverse boundary conditions while delving into the impact of an external viscous damping layer on the natural frequency of the damped BHC-CSP. The results reveal that intensified boundary constraints effectively diminish the effective vibration region of the damped BHC-CSP, thereby enhancing its overall stability. The introduction of a PMI foam layer proves effective in adjusting the stiffness and mass distribution of the damped BHC-CSP. Resonance characteristics are explored through frequency and time-domain analyses, highlighting the pivotal roles of the excitation position and receiver point in influencing the displacement and velocity responses. Although the stiffness is improved by incorporating a PMI foam layer, its effect on the damping performance of the damped BHC-CSP is minimal when compared to the T-SW308 foam layer.

A damping method of grid strapdown inertial navigation system for polar region

Abstract The conventional north-pointing inertial navigation system (INS) always points to the geographic north. However, when the system crosses the pole in the polar region, the geographic north quickly changes with 180 degrees, and the rate of change of the geographic north direction will be infinite. Secondly, when the latitude approaches to 90 degrees, which will lead to singularities in math for the angular velocity caused by vehicle motion. With its special definition and mechanization, the grid coordinate system can solve the above problems. Nevertheless, the error analysis of the grid strapdown INS shows that there are Schuler periodic and Foucault periodic oscillations, which badly degrade the accuracy of the strap-down INS. To address the problem, the external horizontal damping technology is adopted in this paper, wherein the external velocity is provided by the Doppler velocity log (DVL). Finally, the feasibility and the effectiveness of the external damping technology were verified by simulation.

Forced vibration analysis of a beam-plate system coupled through multiple nonlinear single-freedom-degree systems

A beam-plate coupling system is widely used in the construction of different frameworks across industries according to engineering application requirements. In this paper, a nonlinear single-degree-of-freedom structure is introduced as a coupling element between the beam and the plate. Therefore, a coupling system connected through a plurality of the nonlinear single-degree-of-freedom structures is proposed with exposure of its operational mechanism and the dynamic behavior analysis as required. The nonlinear coupled governing equations of the beam-plate system with series nonlinear energy sinks are established according to the Hamilton principle and solvable by the Galerkin truncation method. Meanwhile, the nonlinear characteristics of transverse vibration of the coupling system are studied for discussing the effect of nonlinear stiffness on a low-frequency response of the beam-plate system. Further, the transverse vibration of the system may vary with changes in the nonlinear stiffness, the external viscous damping, and the motion mass of the nonlinear single-degree-of-freedom structures. Accordingly, the variations along with these factors are investigated. The results indicate that a reasonable nonlinear single-degree-of-freedom structure can have a significant influence on the transverse vibration characteristics of the beam-plate system.

Parameter Tuning and Positioning Strategy of VD and TMD Joint Control System for Multi-Modal Vibration of Stay Cables

Stay cables are becoming slender and their fundamental frequencies are becoming lower with the span of bridges increasing, thus leading to the occurrence of multi-modal vibration under various excitations. As a simple and effective strategy for cable vibration mitigation, the external damper is widely used in practice. However, one damper normally can target only fewer modes and poses limited effects on the control of multi-modal vibration. This paper proposed the use of a joint control system combining a viscous damper and a tuned mass damper for mitigating the multi-modal vibration of stay cables, followed by the optimization methodology of tuning and positioning. The control performance of the joint system was evaluated by numerical simulations. The feasibility of the joint control system was validated by analyzing the results of the comparative study, therefore providing a possible solution to multi-modal and high-modal vibration of stay cables.

Analysis and modeling of forced-damped vibrations and their applications in medicine

Forced-damped vibrations are pivotal in various medical applications, significantly contributing to the examination of tissue mechanical properties, development of medical devices, and understanding of biological systems’ complexities. These vibrations represent the dynamic behavior of systems subjected to external forces and damping, where an external force continues to act, and damping determines the rate of energy dissipation. Advanced exploration of damping properties has led to the creation of novel technologies and methods, enhancing our ability to probe and manipulate the complex mechanical dynamics of biological tissues.

Additively manufactured structures with powder inclusions for controllable dissipation: The critical influence of packing density

Particle dampers represent a simple yet effective means to reduce unwanted oscillations when attached to structural components. Powder bed fusion additive manufacturing of metals allows to integrate particle inclusions of arbitrary shape, size, and spatial distribution directly into bulk material, giving rise to novel metamaterials with controllable dissipation without the need for additional external damping devices. At present, however, it is not well understood how the degree of dissipation is influenced by the properties of the enclosed powder packing. In the present work, a two-way coupled discrete element - finite element model is proposed allowing for the first time to consistently describe the interaction between oscillating deformable structures and enclosed powder packings, while existing works have only considered rigid enclosures so far. As fundamental test case, the free oscillations of a hollow cantilever beam filled with various powder packings differing in packing density, particle size, and surface properties are considered to systematically study these factors of influence. Critically, it is found that the damping characteristics strongly depend on the packing density of the enclosed powder and that an optimal packing density exists at which the dissipation is maximized. Moreover, it is found that the influence of (absolute) particle size on dissipation is rather small. First-order analytical models for different deformation modes of such powder cavities are derived to shed light on this observation.

Effect of internal and external damping in the reduction of non-exhaust particulate matter emissions in a low metallic friction material formulation

Friction-induced vibrations in an automotive braking system are of serious concern, leading to different repercussions. Numerous conventional and unconventional methods have been proposed to curb these vibrations, which are also observed to be directly related to generating non-exhaust particulate matter emissions. In this study, an in-house formulated friction material, tested in the form of pins, was subjected to internal damping by adding rubber content from 0 to 3 wt% and external damping by wrapping the different pins in rubber tape. The DMTA showed a decrease in storage modulus and an increase in loss factor with the increase in rubber content. The pin density decreased with the increase in the rubber content. Dry sliding friction, wear, emissions, and vibrations tests were conducted on a pin on disc tribometer with relevant attachments to measure emissions and vibrations. A large drop in vibrations was observed with the rubber content, irrespective of external damping. On the other hand, a significant reduction in wear, emissions, and vibrations was observed with the sample containing the highest rubber addition and with the damping tape. This study showed the feasibility of employing the combination of internal and external damping, emphasizing the optimum rubber content in friction material formulations.

Investigating the Sommerfeld effect in the rotating shaft with internal and external damping using the Timoshenko beam theory

The Sommerfeld effect is a destructive phenomenon in rotating systems with a non-ideal electrical source, which causes instability in the system by applying a dynamic jump around critical speeds. In this article, the Sommerfeld effect has been investigated for the first time using the Timoshenko beam theory for an eccentric continuous shaft with internal and external damping. After deriving the governing equations and finding displacement functions using the semi-analytical method, the Sommerfeld effect near the critical speeds is detected using the instantaneous power balance method. As confirmation of the correctness of the derived relations, it has been shown that for thin shafts, there is a good consistency between the results obtained from the Euler–Bernoulli and Timoshenko theories in the early modes. However, it was observed that at higher critical speeds, the jump amplitude decreases, and the unstable speed range increases significantly, so the probability of entering the vicinity of the instability range in the next mode is not unexpected. Since no effect has been ignored in this study, the dynamic analysis of the Sommerfeld jump in thick shafts is also possible. Despite the common belief that Timoshenko beam theory is only considered suitable for studying thick shafts, it has been shown that the effects of shear deformation are significant in high-speed systems, even for non-thick shafts, and regardless of them in higher modes, it causes a calculation error in determining the point of occurrence of the Sommerfeld phenomenon.

The level-crossing problem of a weakly damped particle in quadratic potential well under harmonic excitation

Escape and level-crossing are fundamental and closely related problems in transient dynamics. Often, when a particle reaches a critical displacement, its escape becomes inevitable. Therefore, escape models based on truncated potentials are often used, resulting in similar problems to level-crossing formulations. Two different types of dynamics can be identified, leading to different kinds of level-crossing depending on the relationship between the damping and the excitation level. The first one (“fast escape”) is mainly governed by the initial energy of the system, which is determined through the initial conditions. The second one (“slow escape”) is governed by the beatings determined through the relationship between external excitation and damping. An analytic approach for estimating the size and location of the safe basins (SBs) in the plane of the initial conditions (ICs) of a 1-DOF externally excited oscillator is suggested. It enables the identification of the set of ICs where the particle never reaches a certain threshold under the given excitation. The SBs depend on the damping coefficient and the excitation’s amplitude, frequency, and phase. Nonetheless, one can describe the essential properties of an SBs in the case of the almost resonant excitation using only two parameters: the forced response amplitude and the damping coefficient ratio to the difference between the natural and the excitation frequencies. Although the analysis is performed for a linear oscillator, it provides insight into the rush erosion process of the SBs (“Dover cliff” phenomenon), described previously only for nonlinear systems. The analysis reveals that the “Dover cliff” phenomenon is related to the decay rate of the transient motion and that it can occur even in linear systems too. From the engineering point of view, the rush erosion of the SBs is critical in noisy environments where devices operating in regions close to the “Dover cliff” are unsafe. Due to its simplicity, the proposed mechanical model might be generic for further analysis of the escape and level-crossing problems considering various nonlinearities (e.g., Coulomb friction, small polynomial-type nonlinearities of the restoring force, or constant restoring force). Possible applications include but are not limited to avoiding collisions for systems with clearances and durability analysis of brittle materials subjected to noisy loads.

Vibration and bifurcation analysis of rotor systems with air ring bearings including ring tilting

Air ring bearings may be considered as a further development of classical air bearings. A drawback of classical rigid air bearings is their reduced damping behavior, which usually prevents a secure operation above the linear threshold speed of instability. Considering air ring bearings, the ring-shaped bearing bushing is visco-elastically mounted in the housing so that external damping is provided. Alternatively, the bushing ring may also be mounted in the housing by a foil structure (beam or bump foil design) so that dissipation is generated by dry friction. Due to the external damping/friction provided by the ring mounting, rotor systems with air ring bearings can be operated above the threshold speed of instability so that stable self-excited vibrations with moderate amplitudes are observed. For certain system parameters, however, the rotor system can bifurcate into a rather dangerous vibration mode, where bearing ring modes are excited by the whirl/whip frequency of the air films. To accurately predict the bifurcation into the problematic ring modes, ring tilting has to be taken into account.Here, a detailed analysis for rotor systems with air ring bearings is presented, which fully incorporates ring tilting effects. The influence of ring tilting on the stability and bifurcation behavior is discussed in detail with the help of nonlinear rotor/bearing models. In connection with the bifurcation into the dangerous ring mode, an interesting nonlinear mode coupling effect (1:2 mode synchronization) is detected. A detailed analysis and a clear physical explanation of this mode coupling phenomenon is given.

Drill-string stability and stress localization: Influence of complex delay effects and dry friction

With the aim of enhancing the understanding of the complex dynamics of deep drilling, an integrated model with complex time delays and Stribeck friction is presented for studies on the axial-torsional dynamics of a drill string. Various aspects of the drill string are considered, including spatial distribution, structural and external damping, dry friction-induced damping, boundary conditions, and complex bit-rock interactions. The drill-string structure is spatially discretized by using the finite element method. With the resulting discretized complex delay system, stability analysis is conducted following the semi-discretization procedure. Through parametric studies, the effects of drilling parameters, dry friction, boundary conditions, and rock-strength properties on the drilling stability are obtained. Subsequently, an optimally tuned boundary condition with compliance is deployed at the top drive to expand the stable region and mitigate self-excited vibrations in the operational parameter space of drilling. To find the distribution of stress along the drill string, numerical simulations are conducted. The dynamical stress caused by self-excited vibrations is illustrated in the spatial–temporal plane. Strain and stress analysis reveal wave propagation along the drill string, including traveling and standing waves. The dynamic effective stress along the drill string is studied, and the von Mises effective stress is determined by combining the axial stress and torsional stress. On the basis of this information, the locations of the vulnerable points along the drill string are found in terms of structural strength. Finally, the tuned boundary condition at the top is deployed in the numerical simulations to show vibration control effectiveness. The results point to two possible vibration-cancellation approaches that can benefit from a tuned top boundary. The findings of this work can serve as a basis for identifying the locations of vulnerable points and alleviating the levels of axial-torsional vibrations in drilling applications.

High-order composite implicit time integration schemes based on rational approximations for elastodynamics

A new approach for developing implicit composite time integration schemes is established starting with rational approximations of the matrix exponential in the solution of the equations of motion. The rational approximations are designed to have the same effective stiffness matrix in all sub-steps. An efficient algorithm is devised so that the implicit equation for a sub-step is in the same form as that of the trapezoidal method. The proposed M-schemes are Mth order accurate using M sub-steps. The amount of numerical dissipation is controlled by a user-specified parameter ρ∞. The (M+1)-schemes that are (M+1)th order accurate using M sub-steps can also be constructed, but the amount of numerical dissipation is built in the schemes and not adjustable. The order of accuracy of all the schemes is not affected by external forces and physical damping. Numerical examples demonstrate that the proposed high-order composite schemes are effective for introducing numerical dissipation and allow the use of large time step sizes in wave propagation problems. The source code written in MATLAB is available for download at: https://github.com/ChongminSong/CompsiteTimeIntegration.

Spatial Variation of the Coefficient of Restitution for Frictionless Impacts on Circular Beams

Abstract The spatial variation of the coefficient of restitution for frictionless impacts along the length of a circular beam is investigated using a continuous impact model. The equations of motion are obtained using the finite element method, and direct time integration is used to simulate the collision on a fast time scale. For collision of a pinned beam with a fixed cylinder, the spatial variation of the coefficient of restitution, impulse magnitude, duration of collision, energetics, and the role of damping are investigated. In the absence of significant external damping, the kinematic and kinetic definitions of the coefficient of restitution provide identical results. Experiments validate the results from simulation which indicate that the coefficient of restitution is sensitive to the location of impact.

Parametric analysis of the effectiveness of external damping and strengthening on reducing the dynamic response of the footbridge over the Vistula River in Warsaw

Parametric analysis of the effectiveness of external damping and strengthening on reducing the dynamic response of the footbridge over the Vistula River in Warsaw

Fractional-Order Models of Damping Phenomena in a Flexible Sensing Antenna Used for Haptic Robot Navigation

In this paper, two types of fractional-order damping are proposed for a single flexible link: internal and external friction, related to the material of the link and the environment, respectively. Considering these dampings, the Laplace transform is used to obtain the exact model of a slewing flexible link by means of the Euler–Bernoulli beam theory. The model obtained is used in a sensing antenna with the aim of accurately describing its dynamic behavior, thanks to the incorporation of the mentioned damping models. Therefore, experimental data are used to identify the damping phenomena of this system in the frequency domain. Welch’s method is employed to estimate the experimental frequency responses. To determine the best damping model for the sensing antenna, a cost function with two weighting forms is minimized for different model structures (i.e., with internal and/or external dampings of integer- and/or fractional-order), and their robustness and fitting performance are analyzed.

Damping-induced dispersion in simple waveguides

The goal is to gain a non-dimensional formulation of the complex wavenumber knowing the onedimensional partial differential equation for wave propagation and the harmonic wave approach. This can be disassembled into its components, namely the imaginary part, showing the decay of a wave, and the real part, showing its spatial propagation. Having an eye on damping in waveguides including internal and external damping, we discuss the resulting consequences, which are frequency-dependent phase and group velocities (dispersion), as well as the energy transport and dissipation. This bears relevance for many domains of physics such as seismic and electromagnetic waves.

Nanomechanics with plasmonic nanoantennas: ultrafast and local exchange between electromagnetic and mechanical energy

Converted into mechanical nanoresonators after optical pulsed excitation and electron decay into coherent acoustic phonons, plasmonic nanoantennas produce a periodic modulation of their optical properties, allowing, in turn, an optical reading of these extremely small movements. In this work, we review the physics of these nanoresonators and their acoustic vibrations, whose frequencies are in the range of a few to tens of GHz. The accurate determination of their oscillation frequencies allows them to act as mechanical nanoprobes, measure local mechanical moduli of the environment, and perform high-resolution imaging using phononic reconstruction. Furthermore, the internal and external damping mechanisms that affect the quality factor of the nanoresonator and, in particular, the role of the substrate when the nanoantennas are integrated into platforms and probed individually are also reviewed. Finally, we discuss the all-optical generation of hypersonic surface acoustic waves with nanoantennas and the importance of their manipulation for potential acousto-plasmonic devices operating in the GHz range and at nanoscale.

Integrability, breather, lump and quasi-periodic waves of non-autonomous Kadomtsev–Petviashvili equation based on Bell-polynomial approach

This article describes the infinite conservation law, quasi-periodic wave, breather, lump, and characteristic of integrability via bilinear Bäcklund and lax pairs of the non-autonomous Kadomtsev–Petviashvili (NKP) equation (in the presence of an external force and damping). Bell-polynomial is deduced from Bäcklund transformation from which infinite conservation law for NKP equation is derived. Obtaining well-known quasi-periodic solutions is an important aspect of this investigation. A limiting procedure is used for analyzing the asymptotic behavior of multi-periodic waves. This method proves rigorously that periodic waves tend toward soliton solutions under a small amplitude limit, which results in a relationship between periodic waves and soliton solutions. For the first time, the effect of external force in a quasi-periodic wave is demonstrated explicitly from the numerical understanding. Further, some complicated solution structures of the NKP equation such as lump and breather-type solitons are explored from the bilinear form of the said equation with the appropriate choice of polynomial functions. Important characteristics of lump and breather waves in different forcing backgrounds are graphically described. Finally, the lump wave of the NKP equation is explored from the breather wave in the limiting stage. It is also confirmed from the analytical results of the relevant motions that the velocity, maximum altitude, and interacting natures of the wave quantities are all influenced by the damping and forcing terms.

Stochastic Data‐Driven Parameterization of Unresolved Eddy Effects in a Baroclinic Quasi‐Geostrophic Model

AbstractIn this work, a stochastic representation based on a physical transport principle is proposed to account for mesoscale eddy effects on the large‐scale oceanic circulation. This stochastic framework arises from a decomposition of the Lagrangian velocity into a smooth‐in‐time component and a highly oscillating noise term. One important characteristic of this random model, without any external forcing and damping, is that it conserves the total energy of the resolved flow for any realization. The proposed stochastic formulation is successfully implemented in a well established multi‐layered quasi‐geostrophic dynamical core. The empirical spatial correlation of the unresolved noise is calibrated from the eddy‐resolving simulation data. In particular, a stationary correction drift can be introduced in the noise through Girsanov transformation. This non‐intuitive term appears to be important in reproducing on a coarse mesh the eastward jet of the wind‐driven double‐gyre circulation. In addition, a projection method has been proposed to constrain the noise to act along the iso‐surfaces of the vertical stratification. The resulting noise enables us to improve the intrinsic low‐frequency variability of the large‐scale current.