Foundation Damping Research Articles

Modelling of foundation damping in time-domain analysis of monopile supported offshore wind turbine structures

Foundation damping holds large potential for design optimisations of monopile-supported offshore wind turbine structures. However, the contribution of foundation damping is not well understood, in part due to lack of suitable method for incorporating foundation damping in the time-domain analysis of wind turbine structures. This paper presents a practical approach for this purpose in which a dashpot is attached in parallel to each p-y spring along the monopile. In this way, the distributed soil-pile interaction stiffness and damping are accurately modelled. To demonstrate the validity of the proposed approach, a case study exploring the influence of foundation damping on the dynamic response of an IEA 15 MW reference turbine founded on monopile is carried out. The results demonstrate that the foundation damping has relatively limited impact on the overall dynamic response and fatigue loads in power production states. However, inclusion of foundation damping is shown to significantly reduce the structural response after emergency shutdown and under parked conditions. The findings of the case study show promising potential for wind turbine structure design optimization through consideration of foundation damping.

New method for incorporating foundation damping in time-domain analysis of integrated offshore wind turbine structures

Foundation damping has significant potential for reducing the loads of monopile-supported offshore wind turbines. However, the contribution of foundation damping is not well understood, primarily because of the absence of suitable methods for incorporating it into the time-domain analysis of wind turbine structures. This paper presents a novel approach for this purpose. In this approach, a dashpot is attached parallel to each of the p-y springs along a monopile, which models the stiffness and damping of soil-pile interactions. Employing this approach, the influence of foundation damping on the structural dynamic response is investigated using the time-domain analysis of a monopile-supported IEA 15 MW reference wind turbine. The results demonstrate that foundation damping has a limited impact on the overall dynamic response and fatigue loads of wind turbines during power production. However, the foundation fatigue loads after an emergency shutdown can be reduced by 29-46% owing to the inclusion of foundation damping. In addition, foundation damping is found to significantly influence the bending moment, horizontal displacement, and angular rotation of the monopile at the mudline under parked conditions, with load reductions of up to 20%.

A case study of foundation damping in a piled offshore wind jacket structure

This paper presents an assessment of foundation damping in piled offshore wind jacket structures through a case study of the Block Island Wind Farm (BIWF). Foundation damping is one of several sources of energy dissipation which can improve fatigue performance in offshore wind structures. Damping was quantified through operational model analysis (i.e. system identification) using structural health monitoring data combined with foundation damping modeling. The results showed that for the 1st bending mode the hysteretic damping ratio of the pile under axial cyclic loading was estimated to range from 0.2% to 1.5%. This range was comparable in magnitude to the foundation damping ratios documented for operational offshore wind monopiles under lateral loading.

Analytical Studies of Fluid Conveying Pipes on Viscoelastic Foundation Using Differential Transforms Method

This study presents an analytical investigation of the vibration of fluid-conveying pipes on viscoelastic foundations using the differential transform method. The effects of a new time dependent viscosity parameter in the modified Winkler viscoelastic foundation is studied and analyzed. The governing equation is a fourth-order partial differential equation with pinned-pinned boundary conditions, which required a special analytical method for solution. The differential transform method was applied to obtain the solution of the governing partial differential equation for the fluid-conveying pipes on viscoelastic foundations. The time-dependent viscosity parameter in the modified Winkler viscoelastic model was implemented and simulated to determine the behavior of the viscoelastic foundation. The obtained analytical solution was validated with Runge-Kutta order four numerical method. The effects of foundation stiffness , coefficient of foundation damping and the frequency mass ratio on the governing model equation were investigated. In addition, the bending and deflection of the pipe on a viscoelastic foundation are compared with those on an elastic foundation. The analytical and the numerical solutions are in good agreement. From the study, it is observed that an increase in the foundation stiffness results in increase in the pipe inherent frequencies. Furthermore, the vibration of the pipe on a viscoelastic foundation shows better control and reduction compared with its vibration on an elastic foundation.

Natural Frequency and Foundation Damping of Colocated and Hybrid Systems Sharing Wind Turbine Monopiles under Operational Conditions

Natural Frequency and Foundation Damping of Colocated and Hybrid Systems Sharing Wind Turbine Monopiles under Operational Conditions

Evaluation of the Seismic Response of Reinforced Concrete (RC) Buildings Considering Soil-Structure-Interaction Effects

The dynamic response of the structure is influenced by soil-structure interaction (SSI), and is distinct from the fixed-base one. When stiff structures are supported by soft to very soft soil, SSI has a substantial effect. This work intends to investigate the effects of SSI using various estimation techniques in order to quantify the foundation damping effect on the response of reinforced concrete (RC) buildings. Generalized and completely viscous damping formulas were utilized to estimate the damping of the soil-foundation system. The investigated structures are 4, 8, and 12-story RC buildings built on very soft soil in a high seismic zone. In comparison to the fixed base condition, the study demonstrated an increase in the natural period, damping of the system, and a decrease in base shear. The study's response parameters are compared to those obtained in accordance with ASCE7-16 code provisions.

Influence of groundwater level on the first natural frequency of monopile

The variation of groundwater level caused by tides is a unique feature of intertidal wind turbines (IWTs). The groundwater level affects the natural frequency of the IWTs' monopile by changing the seabed characteristics. Therefore, it is necessary to reveal the influence of groundwater level on the natural frequency of monopile to ensure the stable operation and maintenance of IWTs. Based on model experiments, the laws of the change in groundwater level and the number of groundwater level cycles on the first natural frequency of the monopile in fine sand foundation is revealed, and is explained according to the stiffness and damping characteristics of the fine sand foundation. Moreover, the stiffness and damping characteristics of the fine sand foundation have different effects on the first natural frequency under different variation states of groundwater level: The stiffness of sand foundation is the main factor affecting the first natural frequency; with the groundwater level rising, the influence of the damping of sand foundation on the first natural frequency is getting stronger. In the designing and maintenance of IWTs, the seabed groundwater level should be focused on.

Auto-parametric resonance of flexible viscoelastic beams under interaction between longitudinal and transverse modes

For a system encompassing subsystems, dynamic modal interaction may experience unanticipated vibrations among subsystems that are excited indirectly. This paper focuses attention to a nonlinear auto-parametric resonance phenomenon of a flexible beam introduced via modal coupling of longitudinal forced resonance and transverse parametric resonance under longitudinal pulsatile excitation. The coupled resonance equations are first modeled based on the Euler-Bernoulli beam theory by incorporating nonlinear curvature, von Kármán's nonlinear strain-displacement relationship and the flexible beam model characterizing nonlinear inertia and displacement interaction. The Galerkin truncation-incremental harmonic balance method (IHBM) is then introduced to obtain both the stability boundary and amplitude-frequency bifurcation maps. Through the corresponding relationship between stability boundary and bifurcation diagram, the energy exchange between two modes is identified as well as the instability region and bifurcation topology can be tuned. It is found that the modal interaction greatly widens the instability region with at most two resonance bands of lateral resonance. By tuning structural and foundation damping, resonance can be controlled to occur only in one frequency band of the pair as desired. This research provides guidance to design broadband energy harvesting or vibration suppression equipment with tunable working frequency band for using the strategy of auto-parametric resonance.

Seismic damage characteristics of high arch dams under oblique incidence of SV waves

This study investigates the seismic damage characteristics of high arch dams considering the oblique incidence of seismic waves. Based on the dynamic implicit finite element method, a viscous-spring artificial boundary is applied to consider radiation damping of the infinite foundation, the seismic wave input is converted into an equivalent nodal force of the artificial boundary, and the equivalent nodal loads of the wave input under oblique incidence of the SV wave is deduced. Taking JP Ⅰ arch dam as an example, combined with the concrete damaged plasticity (CDP) model, the nonlinear dynamic response of the dam under 25° oblique incidence of the SV wave is conducted considering the geometrical nonlinearity of contraction joints and the dynamic mechanical properties of concrete materials. Based on the incremental dynamic analysis (IDA) method, the relative displacement and transverse joint opening are selected as the damage measures for fragility analysis of the arch dam. According to the damage distribution from the analysis of a large number of seismic time-history responses, the damage levels of the arch dam are classified. Three limit states of slight damage, moderate damage and severe damage are proposed for the arch dam. The average responses of the 10 earthquakes are considered as the limit values to quantitatively describe the damage of the arch dam. By fitting the results of incremental dynamic analysis, the seismic probabilistic demand model and seismic fragility curves for the two damage measures to predict the probability of the arch dam reaching damage levels under different seismic actions have been established. The fragility curve shows that the probability of severe damage is almost zero under the maximum design earthquake (PGA = 0.1971 g) and less than 5% under the maximum credible earthquake (PGA = 0.2299 g). It is concluded that JP Ⅰ arch dam has a high degree of safety redundancy and fully satisfies the “two levels” design requirements.

Spectral element formulation for rock-socketed mono-pile under horizontal dynamic loads

The current study entails a thorough investigation of the dynamic response of a mono-pile foundation in homogeneous soil and varied layered soil–rock conditions under horizontal dynamic loads. A sequence of visco-elastic springs linked along its length represents the mono-pile immersed in elastic half space. The frequency dependent stiffness and damping of a mono-pile foundation embedded in layered elastic half space are developed using spectral element formulation. The variations in stiffness and damping with frequency for various soil–rock systems are demonstrated. The dynamic response characteristics of the pile were found to be influenced by the depth of the rock-socketed pile. The presence of the underlying layer of stiffer layer of rock enhances the overall stiffness of the system. The frequency versus amplitude responses of a mono-pile supported heavy mass block for both horizontal translation and rocking motion are calculated using the stiffness and damping of the mono-pile under various soil rock conditions. The horizontal amplitude of the pile decreases with increasing pile rock socketing depth. The resonant amplitudes for rocking motion increases as the pile’s rock socketing depth increases. Finally, the changes in natural frequency and peak amplitudes with varied pile slenderness ratios are investigated for diverse pile–soil–rock conditions.

Prediction of foundation stiffness and damping ratio under horizontal translation and rocking motion

In this paper, the results of snapback, cyclic and forced-vibration tests performed by laboratory and full-scale facilities are collected and analysed to investigate the nonlinear response of shallow foundations. The outcomes of tests on a full-scale soil-foundation-structure prototype, performed during the EU-research project SISIFO, were exploited to fill the lack of data on foundation damping and stiffness associated with the translation motion and enrich the database relevant to low-amplitude rocking motion. Predictive equations are calibrated to estimate the nonlinear variation of the foundation stiffness and damping ratio with the increasing amplitude of the foundation translation and rocking motions. In the latter case, the availability of numerous experimental data allows differentiating the predictive damping equation according to the so-called ‘critical foundation-soil contact area’, which is the most influencing factor on the energy dissipation capacity of the foundation. To prove the reliability of the proposed approach, two different applications with an increasing level of complexity are discussed. First, simplified analytical formulas are employed to calculate the fundamental period and damping ratio of the prototype tested during the SISIFO project. Then, a flexible-base model of the same structure is calibrated to simulate the experimental forced-vibration tests. The outcomes of both applications successfully match the experimental measurements.

Dizajn i razvoj nove podesive elektroreološke tečnosti (ERF) prigušivača za ublažavanje zaostalih vibracija u mašinskim alatima

Residual vibrations in machine tools hamper accuracy and productivity. The attenuation of residual vibrations has been an industrial concern for decades. Meanwhile, the residual vibrations' vibration pattern reveals that the support foundation's damping capabilities predominantly influence them. Therefore, inserting dampers in any other location on a machine tool (such as a machine column) is ineffective. Hence, the scope of inserting the damper into the machine foundation needs to be verified. However, conventional machine mounting systems (concrete foundation and rubber mounts) equally respond to all variable inputs. Both these flocks resulted in inadequate dampening and perhaps poor accuracy. This paper provides a first-generation model of a semiactive-viscous damper (ERF damper-foundation) with tunable damping facilitating machine installation. Controlled experimentation by exposing the developed damper foundation to excitations of medium duty lathe machine confirms its effectiveness and obtains over 48% attenuation compared to a conventional concrete foundation.

Effects of initial compression/tension, foundation damping and pasternak medium on the dynamics of shear and normal deformable GPLRC beams under moving load

An attempt is made in this research to investigation the free vibration and dynamic response of an arbitrary thick composite beam which is reinforced with graphene platelets (GPLs). Distribution of GPLs in the layers may be different which leads to a functionally graded media. To this end a shear and normal deformable beam is adopted. The developed beam model has four unknowns and takes the non-uniform shear strains and also thickness stretching into account. Also the effects of compressive or tensile force, a two parameter Pasternak elastic foundation and also foundation damping are taken into account for both free and forced vibration responses. The governing equations of the beam are established using the Hamilton principle. By applying the Navier solution method suitable for simply supported edges, results of the present studies are provided. It should be noted that for forced vibration problem, Newmark time marching method is applied. For dynamic response the case of moving load is assumed. Results of this study are first compared with the available data in the open literature especially with those developed by 3D elasticity to show the accuracy of the developed formulation. After that novel results are given to discuss the effects of different parameters. It is highlighted that weight fraction and distribution pattern of GPLs are two important factors on the dynamic response of the structure.

Axial force contribution to the out-of-plane response of horizontally curved beams under a moving mass excitation

Horizontally curved beams subjected to a moving mass do experience a time-varying axial force due to the in-plane centrifugal action of the inertial accelerations. The current study aims at investigating the contribution of the induced axial force to the out-of-plane dynamics of horizontally curved beams under the excitation of a moving mass. The governing differential equations of motion are established to account for the action of the axial force, and also the effect of mass inertia, Coriolis and centrifugal forces introduced by a moving object. In the course of dealing with the semi-analytical approach, a new system of ordinary differential equations is distilled utilizing the transition matrix method in order to be amenable for numerical computations. The veracity of the solution has been corroborated through comparison with the results attained by the previous studies addressed in the literature. Moreover, the efficiency of the proposed solution is demonstrated through conducting an extensive parametric study. In that regard, the dynamic impact factor spectra have been obtained for various design parameters including the geometrical and dynamic properties of the system. The findings reveal that, in general, the dynamic impact factor is highly affected by the mass and velocity of the moving object. Furthermore, the results indicate that the inclusion of the axial force can result in a reduction in the dynamic impact factor spectra, which is shown to be more substantial for the response evaluation of short-span horizontally curved beams excited by a high-velocity heavy mass. In this particular situation, the mitigating effect of the axial force becomes comparable to that of the foundation damping. This paper concludes with an investigation on the influence of the axial force on the time-history patterns, which is demonstrated to attenuate the response amplitudes at both the forced and free vibration phases.

A Comparative Study on the Interpretation Procedure of Field Tests for Measuring the Dynamic Impedance of a Surface Footing

ABSTRACT The paper analyses in detail and compares different interpretation procedures of snap-back and forced-vibration tests on a full-scale prototype founded on soft-soil, in order to assess their effectiveness for measuring the stiffness and damping of a shallow foundation under dynamic loads. Both properties were back-calculated through three alternative methods, i.e. through impedance functions computed in the frequency domain, or by interpreting force-displacement loops in terms of peak-to-peak amplitudes or of phase-shift. The damping was further calculated from the logarithmic decrement of free-vibration records. The resulting foundation stiffness and damping were observed to vary with the number of cycles and with the load frequency and amplitude. The comparison among the interpretation techniques revealed that the peak-to-peak approach fails when damping is high, because it neglects the delay between force and displacement.

Effects of scour on the first natural frequency of monopile in different layered foundations

Scour is ubiquitous in offshore wind farms and threatens the stable state of the natural frequency of offshore wind turbines. The foundation of offshore wind turbines is a layered seabed, which mainly consists of clay, silt, and fine sand layers. However, little published literature can be found on the natural frequencies of monopiles in layered foundations with scour. The objective of this study was to reveal the influence of scour in layered foundations on the natural frequencies of monopoles and study its mechanism based on the dynamic characteristics of layered foundations. Therefore, based on an actual layered seabed, three typical layered foundations were established, and the first natural frequency of the monopile in terms of sensitivity to scour as well as the ability to resist continuous scour in the layered foundations were revealed. Moreover, the experimental results were analysed based on the stiffness and damping variations of the layered foundations under scour conditions. Importantly, a competitive relationship between the stiffness and damping of the layered foundations on the variation of the first natural frequency with scour was found and elaborated for the first time. The competitive relationship was influenced by the proportion of clay in the layered foundation.

Wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to visco-Pasternak foundation and magnetic field

In this study, the wave propagation and vibration analysis of sandwich structure with a bio-based flexible core and composite face sheets subjected to magnetic field are studied. In the present analysis, the material properties of composite face sheets are assumed viscoelastic based on Kelvin -Voigt model, and high-order sandwich panels theory is used for core modeling. The analysis of wave propagation and vibration of the sandwich structure is performed assuming complete adhesion between core and face sheets, and the governing equations of motion are derived by Hamilton's principle. Finally, the semi-analytical solution is applied to obtain the effects of the structural and foundation damping coefficients, different angles of the layers, the ratio of width to thickness, the ratio of the thickness of the core to the procedures, temperature variations, wave number, aspect ratios, elastic properties and number of layers on the wave propagation behavior of the sandwich plate for complete adhesion between layers. The results show that by increasing the ratio of the thickness of the core to the layers, the velocity of the wave propagation initially increases, and then decreases. Also, the application of the magnetic field has an increasing effect on the sandwich plate frequency. Finally, with the increase in the number of layers and the number of waves, the phase velocity increases, while the hardness of the system decreases when the temperature and damping coefficient rises.

Vibration Response of Timoshenko Beam-Foundation Interaction Model under Accelerated Moving Load

Simulation of an infinite Timoshenko beam subjected to accelerated moving load rested on the finite depth is assessed in this study. Then, the dynamic response of the infinite beam is illustrated on the various theoretical models, including the Winkler, Pasternak, and visco-elastic foundations. Furthermore, the effects of various damping, such as foundation damping, beam damping, and hysteretic damping (damping between soil grains), are also studied on the dynamic behavior of the beam. It has been worked out that the type of basement and its depth have a remarkable effect on the dynamic behavior. In addition, the load velocity will also cause a maximum displacement in the beam as the critical velocity approaches. The deflection of the beam on the basements increases when the velocity approaches the critical one, and the maximum displacement of the beam occurs under the load. Finally, it was seen that the presented diagrams for all three types of Winkler’s, Pasternak’s, and visco-elastic foundations follow the usual properties related to the critical velocity.

Third order nonlinear vibration of viscoelastic circular microplate based on softening and hardening nonlinear viscoelastic foundation under thermal loading

The nonlinear free vibration of the viscoelastic solid and annular circular microplate is investigated. Nonlinear viscoelastic symmetric and asymmetric foundations are considered. Thermal loading is assumed as constant value. The nonlinear equations of the microplate are derived by Hamilton principle based on third order shear deformation theory (TSDT) and modified couple stress theory (MCST). The finite element methods (FEM) and Newton repeated algorithm are employed to obtain the nonlinear natural frequency. The obtained results are validated with the literatures. Then, the effects of various parameters such as, length scale parameter, outer radius to thickness ratio, maximum deflection to thickness ratio, softening and hardening nonlinear foundation, symmetric and asymmetric nonlinear viscoelastic foundations, different boundary conditions, structure and foundation damping are conducted. The obtained results are compared with several literature and a close agreement are observed between them. The results show that the symmetric and asymmetric nonlinear viscoelastic foundations affect more the nondimensional nonlinear frequency ratio. Reduction effect of temperature difference on MCST nondimensional nonlinear frequency ratio is higher than that of classical theory. The results can be applied micro and nanomachines and smart systems.

Influence of foundation damping on offshore wind turbine monopile design loads

The dynamic behavior of offshore wind turbines (OWTs) must be designed considering stochastic load amplitudes and frequencies from waves and mechanical loads associated with the spinning rotor during power production. The proximity of the OWT natural frequency to excitation frequencies combined with low damping necessitates a thorough analysis of sources of damping; of these sources of damping, least is known about the contributions of damping from soil-structure interaction (foundation damping). This paper studies the influence of foundation damping on cyclic load demand for monopile-supported OWTs considering the design situations of power production, emergency shutdown, and parked conditions. The NREL 5 MW Reference Turbine was modeled using the aero-hydro-elastic software FAST and included equivalent linear foundation stiffness and damping matrices. These matrices were determined using an iterative approach with FAST mudline loads as input to a soil-pile finite element software which calculates hysteretic material damping. Accounting for foundation damping in time history analysis can reduce cyclic foundation moment demand by as much as 30% during parked conditions, 25–33% during emergency shutdown, but only 2–3% reduction during power production without wave and wind misalignment. The calculated foundation damping from the emergency shutdown cases agreed with experimental testing performed in similar site conditions.