Layer Damping Research Articles

Method to characterize the damping behavior of thin passively constrained layer laminates using dynamic mechanical analysis (DMA) in shear mode

In order to characterize the damping behavior of thin passively constrained layer damping (CLD) loudspeaker membranes, usually the whole loudspeaker has to be built. Therefore, a method was established to characterize the damping performance of these membranes with thicknesses below 50 μm at the film level using dynamic mechanical analysis (DMA).Since in the CLD design damping is provided via shear deformation of the middle damping layer, a test was set up to determine the mechanical loss factor tan δ (f,T) in DMA shear mode. Subsequently, results from 1-200 Hz were extrapolated to application-relevant frequencies of up to 1000 Hz via time-temperature superposition. Finally, the damping behavior was rated by the frequency dependent integrated average of the mechanical loss factor tA¯.Furthermore, in experiments with different constraining and damping layers, it was found that the damping performance was maintained as long as the adhesion between them was sufficiently strong.

Numerical analysis of the vibroacoustic properties of plates with embedded grids of acoustic black holes.

The concept of an Acoustic Black Hole (ABH) has been developed and exploited as an approach for passively attenuating structural vibration. The basic principle of the ABH relies on proper tailoring of the structure geometrical properties in order to produce a gradual reduction of the flexural wave speed, theoretically approaching zero. For practical systems the idealized "zero" wave speed condition cannot be achieved so the structural areas of low wave speed are treated with surface damping layers to allow the ABH to approach the idealized dissipation level. In this work, an investigation was conducted to assess the effects that distributions of ABHs embedded in plate-like structures have on both vibration and structure radiated sound, focusing on characterizing and improving low frequency performance. Finite Element and Boundary Element models were used to assess the vibration response and radiated sound power performance of several plate configurations, comparing baseline uniform plates with embedded periodic ABH designs. The computed modal loss factors showed the importance of the ABH unit cell low order modes in the overall vibration reduction effectiveness of the embedded ABH plates at low frequencies where the free plate bending wavelengths are longer than the scale of the ABH.

Analytical model of high-frequency energy flow response for a beam with free layer damping

Energy flow analysis (EFA) is developed to predict the vibrational energy density of beam structures with both full free layer damping (FFLD) and partial free layer damping (PFLD) treatments in the high frequency range. Both equivalent flexural stiffness and structural damping loss factor of a beam with free layer damping are obtained using the equivalent complex stiffness method. Then the energy density governing equation considering high damping effect is derived for a beam with FFLD treatment. Following obtainment of the energy transfer coefficients at both ends of free damping layer, the energy density within a beam with PFLD treatment is evaluated by solving the presented energy governing equation. To verify the proposed formulation, numerical simulations are performed for the pinned-pinned beams with FFLD and PFLD treatments. The EFA results are compared with the exact solutions from wave analysis at various frequencies, and good correlations are observed between the developed EFA results and the exact solutions.

A three-dimensional arbitrary Lagrangian–Eulerian Petrov–Galerkin finite element model for fully nonlinear free-surface waves

A three-dimensional numerical model based on the incompressible Navier–Stokes equations is developed to simulate fully nonlinear water wave propagation problems. The Navier–Stokes equations are solved using the Arbitrary Lagrangian–Eulerian scheme (ALE) and the Petrov–Galerkin Finite Element Method (PG-FEM). A fractional step method is used in the time discretization, where the convection and diffusion terms are separated from the pressure terms when solving the momentum equations. A damping layer is set in front of the outgoing boundary for absorbing the outgoing waves. The model is validated against a series of experimental data, including wave propagation over a submerged bar, wave propagation over a semicircular shoal and wave propagation over a submerged vertical breakwater. The good agreement between the numerical results and experimental data demonstrates the capacity and the accuracy of the model for simulating wave propagation over uneven seabed and wave interaction with submerged structures.

Study on Vibration and Damping of Printed Circuit Boards Treated with Partial Constrained Damping Layer

Constrained damping layer (CDL) treatment has been an effective way to suppress vibration level of various structures. by introducing this method into the vibration control system of electronic equipments, this paper firstly discussed the dominant mechanism difference between free damping layer treatment and constrained damping layer treatment, Then base on the constrained layer damping layout optimization method in the vibration system of a rectangle thin board like PCB, a series of experimental investigations were presented on the vibration response of printed circuit boards treated with partial constrained damping layers. as a result, it proves the CDL treatment having good effect on vibration response control of PCBs.

Super-Grid Modeling of the Elastic Wave Equation in Semi-Bounded Domains

AbstractWe develop a super-grid modeling technique for solving the elastic wave equation in semi-bounded two- and three-dimensional spatial domains. In this method, waves are slowed down and dissipated in sponge layers near the far-field boundaries. Mathematically, this is equivalent to a coordinate mapping that transforms a very large physical domain to a significantly smaller computational domain, where the elastic wave equation is solved numerically on a regular grid. To damp out waves that become poorly resolved because of the coordinate mapping, a high order artificial dissipation operator is added in layers near the boundaries of the computational domain. We prove by energy estimates that the super-grid modeling leads to a stable numerical method with decreasing energy, which is valid for heterogeneous material properties and a free surface boundary condition on one side of the domain. Our spatial discretization is based on a fourth order accurate finite difference method, which satisfies the principle of summation by parts. We show that the discrete energy estimate holds also when a centered finite difference stencil is combined with homogeneous Dirichlet conditions at several ghost points outside of the far-field boundaries. Therefore, the coefficients in the finite difference stencils need only be boundary modified near the free surface. This allows for improved computational efficiency and significant simplifications of the implementation of the proposed method in multi-dimensional domains. Numerical experiments in three space dimensions show that the modeling error from truncating the domain can be made very small by choosing a sufficiently wide super-grid damping layer. The numerical accuracy is first evaluated against analytical solutions of Lamb’s problem, where fourth order accuracy is observed with a sixth order artificial dissipation. We then use successive grid refinements to study the numerical accuracy in the more complicated motion due to a point moment tensor source in a regularized layered material.

A novel viscoelastic damping treatment for honeycomb sandwich structures

Constrained layer dampers (CLD) are in widespread use for passive vibration damping, in applications including aerospace structures which are often lightweight. The location and dimensions of CLD devices on structures has been the target of several optimisation studies using a variety of techniques such as genetic algorithms, cellular automata, and gradient techniques. The recently developed double shear lap-joint (DSLJ) damper is an alternative method for vibration damping, and can be placed internally within structures. The performance of the DSLJ damper is compared in a parametric study with that of CLD dampers on beam and plate structures under both cantilever and simply supported boundary conditions, using finite element analysis. The objective was to determine which damper and in which configuration produced the highest modal loss factor and amplitude reduction for least added mass, as would be important for lightweight applications. The DSLJ tend to be more mass efficient in terms of loss factor and amplitude reduction for cantilevered beam and plate structure, and are competitive with CLD dampers in simply supported beam and plate structures. The DSLJ works well because it has the potential to magnify global flexural deformation into shear deformation in the viscoelastic more effectively than traditional CLD dampers.

The damping of gypsum plaster board wooden stud cavity walls

Published test reports on the sound insulation of gypsum plaster board cavity stud walls with viscoelastic glue sandwiched between two layers of gypsum plaster board working as a constrained layer damper show large increases in sound insulation compared to the sound insulation of the same wall without the viscoelastic material. An increase in the sound insulation would be expected above the critical frequency of the gypsum plaster board panels and in the vicinity of the mass–air–mass resonant frequency due to the increased damping. However the test results show significant increases at other frequencies as well. A critical examination of the theory shows that the sound transmission via the air in the wall cavity is not expected to be greatly affected by the damping at these other frequencies. On the other hand, the sound transmission via the studs is affected at all frequencies by the damping. Hence it is not surprising that the published results are all for cavity stud walls. The sound insulation of two 16mm thick gypsum plaster board sheets was measured. The sheets were mounted touching each other in three different configurations. These were without glue in between, bonded together with viscoelastic glue and spot bonded together with standard commercial glue. Surprisingly the elastic material compound gave better results even below the critical frequency, although the improvement became smaller and then disappeared as the frequency was decreased. A cavity stud wall with the second and third of the above configurations on each side of the studs was also tested. Again the viscoelastic glue performed better than the standard commercial glue, but the viscoelastic results were less than the original published results. Further published results were found which were in between the original published results and the experimental results obtained by the authors of this paper.

Research on the Interior Noise Reduction of an Elastic Cavity by the Multipoint Panel Acoustic Contribution Method Based on Moore–Glasberg Loudness Model

More and more attention has been paid to reduce the low frequency interior noise of the elastic cavity, such as automobiles, ships, airplanes, and railway vehicles, to provide the more comfortable riding environment for passengers. Identification of the interior acoustical sources in the low frequency range is vitally important for the sound quality design inside the elastic cavity. By transformation of the sound pressure level into the specific loudness, a multipoint panel acoustic contribution method based on Moore–Glasberg loudness model is proposed to identify the acoustic contribution of local structural panels of an elastic cavity. The finite element (FE) equation of vibro-acoustic coupling structure with the visco-elastic damping is formulated to evaluate the acoustic panel contribution. Two parameters of acoustic contribution sum and total sound field contribution are derived to measure the acoustic contribution of each panel at the important peak frequencies for the multiple evaluation points. A carriage of high-speed train is modeled as the elastic cavity to demonstrate the application of the developed algorithm. The bottom panel of the carriage is identified to make the most significant contribution to the loudness of evaluation points. The reduction effect of the various design parameters of visco-elastic damping layer on the bottom panel is investigated. The proposed method can efficiently arrange the visco-elastic damping layer on the bottom panel to reduce the interior loudness.

Vibration and damping characteristics of sandwich plates with viscoelastic core

As an effective approach to suppress vibrations and noise, passive constrained layer damping (PCLD) treatments are widely used in engineering practice. However most of the studies concentrate on the one-dimensional beams with active/passive constrained damping layer, the analysis on the two-dimensional plates are relatively small. This research proposes an efficient sandwich modeling technique to deal with the vibration and damping characteristics of the PLCD plate structure. A type of three-layer four-node rectangular element with seven degrees of freedom on every node is used to simulate the PLCD plate structure. The displacement relationships of each layer are obtained based on the first-order shear deformation theory. The finite element equations of motions are derived by the Hamilton principle in variation form. The natural frequency and loss factor are discussed based on the eigenvalue problems. Numerical examples are provided to verify the accuracy and efficiency of the present finite element method. Finally, the influences of the layer thickness, the loss factors of the viscoelastic cores on the natural frequencies and loss factors of the PLCD plate structure are discussed as well.

Vibration and Damping Analysis of Carbon Fiber Wind Turbine Blade with Viscoelastic Damping Treatment

The paper have described the vibration and damping analysis of carbon fiber wind turbine blade with viscoelastic damping treatment using commercial ANSYS program. The wind turbine system including a carbon fiber layer and a viscoelastic damping layer was attached on inside of carbon layer. Firstly, the natural frequencies and mode shape of pure carbon fiber turbine blade were compared with viscoelastic damping treated turbine blade using modal analysis. There were 1mm, 2mm, 3mm thickness damping layer finite element model to be constructed. The results show the little changes in lower first mode but getting smaller with higher modes. Finally, the frequency response functions of damped and undamped turbine blade were calculated for investigating the damping effect of viscoelastic damping layer. As shown in the results, the viscoelastic damping layer has good damping effect for vibration control of carbon fiber wind turbine blade.

Flexible epoxy‐silicone rubber laminates for high voltage insulations with enhanced delamination resistance

In this work, functionalized damping layers consisting of crosslinked silicone rubber are incorporated into brittle epoxy‐based composites to improve the delamination resistance of high voltage insulations. Selected functional organosilanes are attached onto the elastomer surface by a two‐step modification to ensure a covalent bonding between the thermosetting resin and the damping layer. Functional model insulations and stator bar prototypes are then prepared with a vacuum pressure impregnation process. The influence of the damping layer on the thermo‐mechanical and electrical properties as well as the delamination resistance is characterized. The results give evidence that the flexibility of the new composite materials can be increased significantly whereas the electrical properties are not affected by the elastomer layer. By evaluating the performance of the stator bar prototypes it can be clearly shown that both delamination resistance as well as high voltage endurance can be enhanced considerably by the application of flexible damping layers. POLYM. COMPOS., 36:2238–2247, 2015. © 2014 Society of Plastics Engineers

Geomechanical validation of the parameters and technique for damping layer in the vicinity of underground excavation for overburden pressure relief

The data on stress-strain state around an underground excavation in an unstable rock mass are reported. For overburden pressure relief, it is proved necessary to create a damping layer, and the related drilling-and-blasting parameters are determined. Zones of probable fracture of rock mass under camouflet blasting are identified.

Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The aerodynamic version amounts to a minor modification of a synthetic turbulence generator developed by the authors previously, but the acoustically adapted version is new and includes an internal damping layer, where the pressure field is computed by “weighting” of the instantaneous pressure fields from LES and RANS. This is motivated by the need to avoid creating spurious noise as part of the turbulence generation. In terms of pure aerodynamics, the validation includes canonical shear flows (developed channel flow, zero pressure gradient boundary layer, and plane mixing layer), as well as a more complex flow over the wall-mounted hump with non-fixed separation and reattachment, with emphasis on a rapid conversion from modeled to resolved Reynolds stresses. The aeroacoustic applications include the flow past a trailing edge and over a two-element airfoil configuration. In all cases the methodology ensures a very acceptable accuracy for the mean flow, turbulent statistics and, also, the near- and far-field noise.

Analysis of natural frequency of free damping composite cylindrical shell submerged in viscous fluids

The effect of fluid viscosity and material parameters of the damping layer on the natural frequency characteristics of a circular cylindrical shell covered with free damping layer immersed in a viscous acoustic medium is studied in the present paper. An equivalent method is applied to the damping layer coated on the surface of the cylindrical shell. Then, the wave equation for viscous flow field derived from the linear equations of continuity, Navier–Stokes and state, the Flügge’s thin shell theory for the isotropic, elastic, thin cylindrical shell and the appropriate wave harmonic field expansions in association with the pertinent boundary conditions are employed to get the equations of motion and the characteristic equation in the coupled system. Subsequently, numerical analysis is applied to solve the characteristic equation for the coupled system at various material parameters and viscosity coefficients, the influence of which can be illustrated by the calculation results.

A wave-resolving model for nearshore suspended sediment transport

This paper presents a wave-resolving sediment transport model, which is capable of simulating sediment suspension in the field-scale surf zone. The surf zone hydrodynamics is modeled by the non-hydrostatic model NHWAVE (Ma et al., 2012). The turbulent flow and suspended sediment are simulated in a coupled manner. Three effects of suspended sediment on turbulent flow field are considered: (1) baroclinic forcing effect; (2) turbulence damping effect and (3) bottom boundary layer effect. Through the validation with the laboratory measurements of suspended sediment under nonbreaking skewed waves and surfzone breaking waves, we demonstrate that the model can reasonably predict wave-averaged sediment profiles. The model is then utilized to simulate a rip current field experiment (RCEX) and nearshore suspended sediment transport. The offshore sediment transport by rip currents is captured by the model. The effects of suspended sediment on self-suspension are also investigated. The turbulence damping and bottom boundary layer effects are significant on sediment suspension. The suspended sediment creates a stably stratified water column, damping fluid turbulence and reducing turbulent diffusivity. The suspension of sediment also produces a stably stratified bottom boundary layer. Thus, the drag coefficient and bottom shear stress are reduced, causing less sediment pickup from the bottom. The cross-shore suspended sediment flux is analyzed as well. The mean Eulerian suspended sediment flux is shoreward outside the surf zone, while it is seaward in the surf zone.

Topology Optimization for Constrained Layer Damping Plates Using Evolutionary Structural Optimization Method

The evolutionary structural optimization (ESO) is used to optimize constrained damping layer structure. Considering the vibration and energy dissipation mode of the plate with constrained layer damping treatment, the elements of constrained damping layers and modal loss factor are considered as design variable and objective function, while damping material consumption is considered as a constraint. The sensitivity of modal loss factor to design variable is further derived using modal strain energy analysis method. Numerical example is used to demonstrate the effectiveness of the proposed topology optimization approach. The results show that vibration energy dissipation of the plates can be enhanced by the optimal constrained layer damping layout.

Excellent Performance of Earth Dams under Resonance Motion Using Isolator Damping Layer

The effect of blanket layer using isolator damping layer (IDL) between river sand foundation and short embankment to remove damage under severe earthquake was investigated in the present study. In case of numerical analysis by ANSYS program, dominant frequency (DF) was computed by free vibration analysis. Soil mechanic tests for thirteen samples to design IDL formula were carried out. In terms of critical condition for earthquake effect such as resonance, five physical small models were tested using vibrator table under the dominant frequency with scale parameter 1/100. As a result, dam was significantly damaged without blanket layer IDL. In order to reduce damage, the best performance was observed using blanket layer (IDL) when this layer was expanded below the reservoir region. The reinforced thickness layer size is one-fourth of dam height. This method is a novel suggestion for earth dam design in seismic zone.

Constrained Layer Damper Modelling and Performance Evaluation for Eliminating Squeal Noise in Trams

This paper presents the modelling and design of a constrained layer damper to eliminate squeal noise in a particular tram. Even though resilient wheels are installed in every bogie, squeal noise is generated at the frequency of 780–800 Hz due to the small radius curves that the tram has to draw. Tuned constrained layer dampers provide a solution to this particular problem. Butyl rubber is chosen as the viscoelastic material for the damper, and conventional steel is used for the metallic sheets. The modelling approach and the final design of the damper are presented, together with evaluation of its performance in a real application. Experimental measurements on track have demonstrated that the constrained layer damper is properly tuned to the squealing frequency and that there is a significant reduction in noise when the proposed damper is attached to the wheels.

Vibration Power Flow Analysis of a Submerged Constrained Layer Damping Cylindrical Shell

The vibration power flow in a submerged infinite constrained layer damping (CLD) cylindrical shell is studied in the present paper using the wave propagation approach. Dynamic equations of the shell are derived with the Hamilton principle in conjunction with the Donnell shell assumptions. Besides, the pressure field in the fluid is described by the Helmholtz equation and the damping characteristics are considered with the complex modulus method. Then, the shell-fluid coupling dynamic equations are obtained by using the coupling between the shell and the fluid. Vibration power flows inputted to the coupled system and transmitted along the shell axial direction are both studied. Results show that input power flow varies with driving frequency and circumferential mode order, and the constrained damping layer will restrict the exciting force inputting power flow into the shell, especially for a thicker viscoelastic layer, a thicker or stiffer constraining layer (CL), and a higher circumferential mode order. Cut-off frequencies do not exist in the CLD cylindrical shell, so that the exciting force can input power flow into the shell at any frequency and for any circumferential mode order. The power flow transmitted in the CLD cylindrical shell exhibits an exponential decay form along its axial direction, which indicates that the constrained damping layer has a good damping effect, especially at middle or high frequencies.