Local Damping Research Articles

Vibration damping of sandwich panels using the Acoustic Black Hole effect

Among the existing passive vibration control techniques, the use of the acoustic black hole (ABH) is a solution that has the advantage of not increasing the mass of the structure in which it is integrated. In this paper, the benefits of inserting an ABH into a three-layer sandwich panel (fibreglass skins and honeycomb core) are investigated. It is known that an ABH effect can be achieved in a panel by locally reducing its stiffness (using a reduction in plate thickness according to a power law profile) and increasing local damping (using a coating of viscoelastic material). A sandwich panel induces a shear effect that strongly affect the wave propagation and lead to specific properties to the ABH effect. The equations of motion of a thick, symmetrical sandwich panel with non-uniform characteristics are obtained within the framework of zig-zag theory by applying Hamilton's principle. These equations lead to a semi-analytical model of order 6, from which an effective bending stiffness, dependent on both frequency and space can be derived. Using this model, it is demonstrated that the sandwich effective bending stiffness favours the ABH effect. This interesting property is also validated by experimental tests on sandwich panels using laser vibrometry.

Stability of Laminated Timoshenko Beams with Local Viscoelastic Versus Frictional Damping

Stability of Laminated Timoshenko Beams with Local Viscoelastic Versus Frictional Damping

Numerical study of the linear and non-linear damping in an acoustically forced cold-flow test rig with coupled cavities

Quantifying the oscillation amplitude of thermoacoustic instabilities remains a critical and challenging issue, as it is a complex balance between driving and damping processes. The New Pressurized Coupled Cavities (NPCCs) setup designed for the study of acoustic damping is analyzed in this work. It is a cold-flow test rig mimicking the geometry of a liquid rocket engine and equipped with an acoustic forcing device. The chamber 1T mode triggers a strong non-linear harmonic response, while the 1T1L and 1T2L exhibit weak non-linearities. Disturbance energy budgets are used in large-eddy simulations to characterize the damping phenomena with the 1T2L and 1T1L forcing. The correct global damping of the system is retrieved, and local damping contributions are extracted. Then, a non-linear term representing the energy transfer to the harmonics is derived from non-linear acoustics theory. Combined with a linear model, this model correctly retrieves the limit-cycle of the 1T mode.

Magnonic φ Josephson junctions and synchronized precession

There has been a growing interest in non-Hermitian physics. One of its main goals is to engineer dissipation and to explore ensuing functionality. In magnonics, the effect of dissipation due to local damping on magnon transport has been explored. However, the effects of nonlocal damping on the magnonic analog of the Josephson effect remain missing, despite that nonlocal damping is inevitable and has been playing a central role in magnonics. Here, we uncover theoretically that a surprisingly rich dynamics can emerge in magnetic junctions due to intrinsic nonlocal damping, using analytical and numerical methods. In particular, under microwave pumping, we show that coherent spin precession in the right and left insulating ferromagnet (FM) of the junction becomes synchronized by nonlocal damping and thereby a magnonic analog of the φ Josephson junction emerges, where φ stands here for the relative precession phase of right and left FM in the stationary limit. Remarkably, φ decreases monotonically from π to π/2 as the magnon-magnon interaction, arising from spin anisotropies, increases. Moreover, we also find a magnonic diode effect giving rise to rectification of magnon currents. Our predictions are readily testable with current device and measurement technologies at room temperatures. Published by the American Physical Society 2024

DEM modelling of particle crushing of single carbonate sand using the improved bonded particle model

Carbonate sands have complex particle morphology and abundant intra-particle pores, influencing their mechanical beahviours. This paper presents a detailed modelling procedure for single-particle crushing of carbonate sands with different shapes. The particles were scanned, and their realistic profiles were simplified using a curvature-based simplification technique before being imported into the DEM program. An improved bonded particle model using coplanar Voronoi polyhedrons as cells was adopted, and the internal porosity of carbonate sands, which follows a Weibull distribution, was modelled by randomly removing internal cells. The effects of local damping and loading rate on crushing responses are discussed and their values are carefully determined. Four loading stages were observed during platen compression. Particles with different shapes experienced varying degrees of tension and shear failure in internal bonds and exhibited different probabilities of splitting, explosive, and chipping failures. The work presented lays the groundwork for subsequent simulations of carbonate assemblies.

Dynamics for wave equations connected in parallel with nonlinear localized damping

Abstract This study investigates the properties of solutions about one-dimensional wave equations connected in parallel under the effect of two nonlinear localized frictional damping mechanisms. First, under various growth conditions about the nonlinear dissipative effect, we try to establish the decay rate estimates by imposing minimal amount of support on the damping and provide some examples of exponential decay and polynomial decay. To achieve this, a proper observability inequality has been proposed and constructed based on some refined microlocal analysis. Then, the existence of a global attractor is proved when the damping terms are linearly bounded at infinity, a special weighting function has been used in this part, which eliminates undesirable terms of the higher order while contributing lower-order terms. Finally, we establish that the long-time behavior of solutions of the nonlinear system is completely determined by the dynamics of large finite number of functionals.

Stability for coupled thermoelastic systems with nonlinear localized damping and Wentzell boundary conditions

Stability for coupled thermoelastic systems with nonlinear localized damping and Wentzell boundary conditions

Modelling dynamic fracture and fragmentation of rocks under multiaxial coupled static and dynamic loads with a parallelised 3D FDEM

In this study, a three-dimensional (3D) combined finite-discrete element method (FDEM) based simulator, which enables the robust simulation of full-scale triaxial Hopkinson bar (Tri-HB) testing system, including the capture of fracture and fragmentation processes of rock specimens as well as the detection and analysis of generated rock fragments, is developed for investigating the dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads. An innovative two-step approach is proposed to first efficiently achieve the static stress state in the entire Tri-HB system and then apply dynamic loading to the system. The proposed approach with the schemes of mass scaling and local damping can significantly reduce the run time for static computation involving cohesive elements and complex contact mechanics in the framework of explicit time-integration. The developed program is well validated by achieving dynamic stress equilibrium in the Tri-HB system and comparing the simulated stress wave profiles with those from laboratory experiments. Then, the progressive dynamic fracture and fragmentation processes of rocks under different static stress conditions in a full-scale Tri-HB system are investigated, which vividly exhibit the confinement dependence of the dynamic behaviours of rocks in the testing system. It is found that, even with the same loading rate, separate input parameter sets for rock need to be established in FDEM for different confinement conditions to capture the actual rate dependent behaviour of rock. Further studies are also conducted to investigate the effect of interfacial friction on the fracture behaviour, and the results indicate that higher interfacial frictions significantly disturb the dynamic stress variations and the true rock behaviour in the system. Through high performance computing of 3D FDEM, this study is expected to contribute to the understanding of dynamic responses of rocks subjected to multiaxial coupled static and dynamic loads in deep underground engineering.

Fibre-Based Nonlinear Viscous Damping Model Defined for Dynamic Analysis Using Distributed Plasticity Elements

ABSTRACT This paper presents a new nonlinear viscous damping model implemented in the fibre where a constitutive rule is defined between the strain rates and the damping stresses. This model is developed for nonlinear dynamic analyses using distributed plasticity frame elements with fibre cross-sections. The model is proportional to the initial stiffness of the fibre material, but the maximum damping stress is limited to avoid local and global high damping forces and prevent them from decaying or taking negative values when the structure is in the inelastic range. The manuscript details the formulation used to find the fibre strain rates, the damping forces at each level of the structure and its implementation using the Newmark method. The predictions of the model are compared with the real response of a reinforced concrete structure tested on a seismic table under high demands. Additionally, a numerical case study addressing the inelastic response of a steel structure and sensitivity analyses are presented.

Analysis of the exponential stability of a beam-string-beam transmission problem with local damping on the string

We consider a beam-string-beam problem, where two undamped beams are coupled to a locally damped string (first by a damping of frictional type and then by one of Kelvin–Voigt (K–V) type) by transmission conditions. We show that for this structure, the dissipation produced by the frictional part is strong enough to produce an exponential decay of the solution no matter how small is its size, but the semigroup associated with the system is not exponentially stable when we apply a some localized K–V damping on the string, given by a suitable discontinuous function and certain condition under the length of the parts of the structure. However, when we impose hinged conditions on the beams on the interface points, the dissipation produced by a some localized K–V damping, given by a suitable continuous function, is strong enough to produce an exponential decay of the system solution. For the proof of these three results we use a frequency-domain method of semigroup theory, where in the proofs of exponential stability we also use a contradiction argument.

Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping

Exponential stability of extensible beams equation with Balakrishnan–Taylor, strong and localized nonlinear damping

Stabilization of string–beam–string transmission systems with localized frictional damping and delay

In this paper, we consider two string–beam–string boundary transmission problems with localized frictional damping and delay. The first transmission problem is that the frictional damping and delay are in the left string equation and the right string equation is thermoelastic. The second transmission problem is that the damping and the delay are both only acting on the middle beam equation. Using the semigroup theory, we get the existence and the uniqueness of solution under suitable assumptions on the weight of the damping and the weight of the delay. Furthermore, we prove that the first transmission problem is exponentially stable and the second transmission problem is polynomially stable using the frequency domain method and the multiplier techniques.

Uniform stability of a semilinear coupled Timoshenko beam and an elastodynamic system in an inhomogeneous medium

In this paper, we consider a semilinear coupled Timoshenko beam and an elastodynamic system posed in an inhomogeneous one-dimensional medium subject to localized damping mechanisms acting in the three equations. We show uniform decay rates for the energy of the solutions of such a problem without assuming any restrictions on the non-constant coefficients. To establish these results, refined arguments of the Microlocal Analysis Theory are applied.

Energy decay for wave equations with a potential and a localized damping

Energy decay for wave equations with a potential and a localized damping

Suppression method of ultralow-frequency oscillation under ambient excitation in hydro-dominant power systems

Ultralow-frequency oscillations (ULFOs) have frequently occurred in hydro-dominant power systems in recent years. These phenomena seriously threaten the safe and stable operation of power systems. Therefore, measures that can effectively suppress ULFO need to be taken. Currently, the hydropower unit governor can enhance the dynamic stability and dampening oscillations of a system through adjusting the proportional–integral–derivative parameters. However, modifying these parameters can affect the primary frequency regulation performance, which compromises the assurance of grid frequency quality. This study proposes a switching type of hydro generator governor based on the local damping contribution rate to address the aforementioned problems. The approach incorporates the energy structure into the classical governor model, calculates the local damping contribution rate, and enables automatic switching of the hydro generator governor parameters based on positive and negative local damping contributions. This way allows for segmented control with different parameter settings, which enables the system to effectively consider the damping characteristics of ULFO while maintaining primary frequency regulation performance. It can also accurately and efficiently suppress the ULFO. The proposed method is verified through arithmetic analysis conducted on a 16-machine 5-zone system and an actual grid system. Simulation results demonstrate the effectiveness of the method.

Stability result of the Kawahara equation with localized damping and time-varying delay

Stability result of the Kawahara equation with localized damping and time-varying delay

Stability of degenerate wave equations with a singular potential and local damping

Stability of degenerate wave equations with a singular potential and local damping

Gevrey regularity of the semigroup corresponding to an Euler-Bernoulli plate equation with localized structural damping

Gevrey regularity of the semigroup corresponding to an Euler-Bernoulli plate equation with localized structural damping

Stability for variable-coefficient wave equation with local frictional damping and memory type dynamic boundary conditions

Stability for variable-coefficient wave equation with local frictional damping and memory type dynamic boundary conditions

Global attractor of the Euler-Bernoulli equations with a localized nonlinear damping

Global attractor of the Euler-Bernoulli equations with a localized nonlinear damping