Porous Damping Research Articles

Exponential stability of Lord Shulman thermoelastic system with porous damping and distributed delay term

In this paper, we consider a one-dimensional Lord–Shulman thermoelastic system [C. Cattaneo, On a form of heat equation which eliminates the paradox of instantaneous propagation, C. R. Acad. Sci. Paris 247 (1958) 431–433] with porous damping and distributed delay term acting on the porous equation. Under suitable assumptions on the weight of distributed delay, we establish the well posedness of the system by using semigroup theory and we show that the dissipations due to thermal effects with porous damping are strong enough to stabilise the system exponentially, independently of the wave speeds of the system.

Design and optimization of lightweight porous damping treatments

Here, it is shown that properly-designed limp porous materials such as fibrous layers can provide damping equivalent to conventional viscoelastic dampers while providing advantages such as light weight and effective sound absorption. This then allows porous layers to be used as multi-functional noise and vibration control solutions in automotive and aerospace applications. It has also been found that the addition of bulk elasticity to the solid phase of the porous medium is beneficial since it improves damping performance compared to equivalent limp treatments. In this study, porous media, such as fibers and foams, were designed to serve as treatments for various vibrating structures to examine their damping effectiveness. Both analytical modeling and numerical simulation based on finite element methods were involved depending on the complexity of the structure. Specifically, a Fourier transform-based computational method was introduced as the key step to realize the accurate prediction of a panel’s spatial response based on its wavenumber-frequency spectrum. Then, parametric studies were conducted on a porous layer to identify the optimal bulk properties that would allow the layer to provide the largest possible damping within the target frequency region. Finally, design concepts for achieving the maximum damping potential of porous layers are summarized.

Hydrodynamic behaviour of floating polygonal compound platforms with wide porous media

Presented herein are the formulation and semi-analytical solutions for the hydrodynamic characteristics and wave fields of floating polygonal compound platforms with wide porous media. The wetted porous medium is assumed to be homogeneous and fully saturated. Limiting cases of the semi-analytical solutions without the porous medium have been verified by the results obtained by using the commercial software ANSYS AQWA. The present semi-analytical solutions based on a matched eigenfunction expansion method are useful as benchmark results for analysts working on new numerical methods for the hydrodynamic analysis of floating platforms with porous media. Parametric studies were conducted to examine the effects of porous media on the wave exciting forces, RAOs, wave fields, porous damping and mooring loads. It is found that the wide porous medium with appropriate porosity and resistance coefficient contributes to reducing the wave exciting forces, RAOs, and overall level of wave fields in the long period region by attenuating the incident wave energy. Also, the porous medium helps to decrease the mooring loads, especially at resonance. Thus, a wide porous medium surrounding the compound platform is effective in both enhancing the motion performance of the floating platform and reducing the wave fields around it.

Research on vibration suppression of wind turbine blade with a multi-layer porous damping structure based on bamboo wall microstructure

As wind turbine blades are getting softer and thinner, the demand for their capability of vibration suppression is improving day by day. Drawing from bamboo’s quick recovery to its former position and mimicking the microstructure of bamboo wall, this paper puts forward a porous damping structure on the blade and sets up its mathematical model. The formula for its structural loss factor is deduced on the vibration theory. Then numerical simulation method is adopted to investigate its damping performance on one wind turbine blade by ABAQUS. The results indicate that the vibration damping property of the wind turbine blade with the porous damping structure is significantly increased. The porous damping structure dissipates more heat very quickly and its single material also displays advantages over composite material. This paper provides a reference for the design of highly efficient damping structures.

Acoustic simulation of cavities with porous materials using an adaptive model order reduction technique

Porous materials are often used in the context of passive noise control applications due to their low cost and good sound absorption properties. As the most commonly used predictive tool, the finite element (FE) method is often applied in the design phase to obtain detailed information on the performance of complex vibro-acoustic systems with porous damping treatments. In this case, however, its use inevitably leads to very large, complex-valued and frequency-dependent numerical models, which makes original full-order model evaluation intractable due to time and memory limitations. In this paper, an adaptive model order reduction strategy is presented to reduce the number of degrees of freedom involved in the associated problems such that the required computational cost can be largely alleviated while a desired high accuracy can be achieved in a controllable way. This technique consists of making use of Taylor expansion to the multiple frequency-dependent scalar functions coming from the complex material behavior, and then performing the structure-preserving second-order Arnoldi algorithm based on a robust error indicator to solve the underlying FE model in the frequency domain. A further improvement in terms of the approximation accuracy of the constructed compact reduced-order model is also proposed to incorporate all available moment-matching information. Two widely used model types for porous materials are investigated, i.e. the equivalent fluid description and the Biot theory. Mono-physical poroelastic-poroelastic coupling and multi-physical acoustic-porous coupling are considered in order to demonstrate the simplicity, versatility and efficiency of the approach.

On the stabilization of linear porous elastic materials by microtemperature effect and porous damping

In this paper, we study the asymptotic behavior of solutions for the porous thermoelastic system with temperatures and microtemperatures effects. Our main result is to prove the exponential stability in case of zero thermal conductivity and without any condition on the coefficients of the system. This result is new and improve some recent results in the literature.

On the Decay Rates of Porous Elastic Systems

In this paper we analyze the porous elastic system. We show that viscoelasticity is not strong enough to make the solutions decay in an exponential way, independently of any relationship between the coefficients of wave propagation speed. However, it decays polynomially with optimal rate. When the porous damping is coupled with microtemperatures, we give an explicit characterization on the decay rate that can be exponential or polynomial type, depending on the relation between the coefficients of wave propagation speed. Numerical experiments using finite differences are given to confirm our analytical results. It is worth noting that the result obtained here is different from all existing in the literature for porous elastic materials, where the sum of the two slow decay processes determine a process that decay exponentially.

The mechanics of shape memory alloy metal rubber

This work presents a theoretical and experimental characterization of shape memory alloy metal rubber (SMA-MR) material. SMA-MR is a novel porous damping solid made of coil entangled nitinol wires. The constitutive model proposed in this work takes into account the geometry of the coils used, the manufacturing parameters of the SMA-MR material together with the thermo-mechanical behavior of the shape memory alloy wires. Metal rubber samples made with nitinol constitutive material are fabricated and tested under different quasi-static loading and temperature conditions. The special characteristics of SMA-MR such as hysteretic behavior, nonlinear stiffness, transverse isotropy, dry friction damping property and temperature dependency are predicted by the model, with the comparison between the theoretical and experimental results yielding discrepancies lower than 5% in the majority of the conditions considered.

감쇠판에 의한 원기둥의 상하운동 저감 모형시험

Motion reduction of an offshore structure at resonant frequency is essential for avoiding critical damage to the topside and mooring system. A damping plate has a distinct advantage in reducing the motion of a floating structure by increasing the added mass and the damping coefficient. In this study, the heave motion responses of a circular cylinder with an impermeable and a permeable damping plate attached at the bottom of the cylinder were investigated thru a model test. The viscous damping coefficients for various combinations of porosity were obtained from a free-decay test by determining the ratio between any pair of successive amplitudes. Maximum energy dissipation occurred at a porous plate with a porosity P = 0.1008. Experimental results for regular and irregular waves were compared with an analytical solution by Cho (2011). The measured heave RAO and spectrum reasonably followed the trends of the predicted values. A significant motion reduction at resonant frequency was pronounced and the heaving-motion energy calculated by the integration of the area under the heave motion spectrum was reduced by more than 75% by the damping plate. However, additional energy dissi pation by eddies of strong vorticity and flow separation inside a porous damping plate was not found in the present experiments.

Breaking solitary wave evolution over a porous underwater step

Solitary wave evolution over a shelf including porous damping is investigated using Volume-Averaged Reynolds Averaged Navier–Stokes equations. Porous media induced damping is determined based on empirical formulations for relevant parameters, and numerical results are compared with experimental information available in the literature. The aim of this work is to investigate the effect of wave damping on soliton disintegration and evolution along the step for both breaking and non-breaking solitary waves. The influence of several parameters such as geometrical configuration (step height and still water level), porous media properties (porosity and nominal diameter) or solitary wave characteristics (wave height) is analyzed. Numerical simulations show the porous bed induced wave damping is able to modify wave evolution along the step. Step height is observed as a relevant parameter to influence wave evolution. Depth ratio upstream and downstream of the edge appears to be the more relevant parameter in the transmission and reflection coefficients than porosity or the ratio of wave height–water depth. Porous step also modifies the fission and the solitary wave disintegration process although the number of solitons is observed to be the same in both porous and impermeable steps. In the absence of breaking, porous bed triggers a faster fission of the incident wave into a second and a third soliton, and the leading and the second soliton reduces their amplitude while propagating. This decrement is observed to increase with porosity. Moreover, the second soliton is released before on an impermeable step. Breaking process is observed to dominate over the wave dissipation at the porous bottom. Fission is first produced on a porous bed revealing a clear influence of the bottom characteristics on the soliton generation. The amplitude of the second and third solitons is very similar in both impermeable and porous steps but they evolved differently due to the effect of bed damping.

Fundamental Properties of Boussinesq-Type Equations for Wave Motion Over a Permeable Bed

This paper presents analyses of the fundamental properties of the fully nonlinear Boussinesq-type equations for waves and currents over a permeable seabed introduced by Chen [2005]. These properties are the wave celerity and the spatial porous damping rate for wave propagation on permeable beds. The governing equations for horizontally two-dimensional wave and current motions are first summarized, citing its methods of derivation, applicability and accuracy, and with emphasis on the inclusion of higher-order dispersive damping terms in the permeable-layer momentum equation. Then the fundamental properties are analyzed by extracting the complex linear dispersion relation embedded in the model equations using a Stokes-type approach and accounting for the coupling of the real and imaginary wavenumbers. Plots of the fundamental properties reveal that the inclusion of higher-order dispersive damping terms in the porous-layer momentum equation improves its agreement with the exact solution from shallow to deep water. Inclusion of these terms is also indispensable in obtaining accurate fundamental properties for high values of the permeable-layer thickness ratio. Determination of the model parameter values based on optimization is discussed. Finally, rational expansion of the dispersion equations is used to elucidate the observed behavior of the model's fundamental properties.

On the time decay of solutions in one-dimensional theories of porous materials

In this paper we investigate the temporal asymptotic behavior of the solutions of the one-dimensional porous-elasticity problem when several damping effects are present. We show that viscoelasticity and temperature produce slow decay in time, and the same result is obtained when the porous viscosity is combined with microtemperatures. However, when the viscoelasticity is coupled with porous damping or with microtemperatures the decay is controlled by a negative exponential.

Exponential decay in one-dimensional porous-thermo-elasticity

This paper concerns the one-dimensional problem of the porous-thermo-elasticity. Two kinds of dissipation process are considered: the viscosity type in the porous structure and the thermal dissipation. It is known that when only thermal damping is considered or when only porous damping is considered we have the slow decay of the solutions. Here we prove that when both kinds of dissipation terms are taken into account in the evolution equations the solutions are exponentially stable.

Boussinesq equations for wave transformation on porous beds

A set of time-dependent vertically-integrated equations is derived to model the horizontally two-dimensional transformation of waves on a porous bed. The basic equations, called the Boussinesq equations for porous beds, contain the leading orders of nonlinearity and dispersivity. A general resistance equation has been used for the porous medium. The applicability bounds of the basic equations, limited by weak dispersivity and underestimated porous damping rates in deeper waters, have been extended by adding dispersion terms to the momentum equations and calibrating the resulting dispersion relation with a linear theory for porous beds. A numerical method based on finite differences is employed to solve the equations for two dimensions. The extended equations are verified for damped wave propagation on a horizontal bed, wave transformation on uniform porous slopes and combined refraction, diffraction, shoaling and damping around a submerged porous breakwater with an opening.

The damping of panels by thick layers of elastic porous media

In this paper a technique is presented for calculating the response of a panel to a line force input when loaded by both a finite-depth layer of elastic porous material and a heavy fluid. Damping theories normally require that an attached damping layer be thin compared to the flexural wavelength in the base panel. Here this requirement is avoided by allowing explicitly for wave propagation within the damping layer. Specifically, the porous damping layer is modeled using a theory derived by Biot that allows for the existence of two dilatational waves and a transverse wave. Conditions required to couple the porous medium to the panel and an adjacent fluid will be discussed. A formal solution for the plate response may be obtained easily in the wavenumber domain. Although it is not possible to obtain the spatial response analytically in this instance, it will be shown that under practical circumstances the required inversion integral may be evaluated efficiently and “exactly” by using the fast fourier transform algorithm. Results will be given illustrating the damping potential of thick layers of porous materials.