Rigid Body Response Research Articles

Dynamic response of multi-unit floating offshore wind turbines to wave, current, and wind loads

Motion of a multi-unit wind-tracing floating offshore wind turbine (FOWT) to combined wave–current and wind is obtained in the frequency-domain. The linear diffraction wave theory with a Green function for small current speeds and the blade-element momentum method are used for the hydrodynamic and aerodynamic analysis, respectively. A finite-element method is coupled with the hydrodynamic and aerodynamic equations to obtain the elastic responses of the FOWT to the environmental loads. The wind-tracing FOWT consists of three 5 MW wind turbines installed at the corners of an equilateral triangular platform. The platform is connected to the seabed through a turret-bearing mooring system, allowing the structure to rotate and face the dominant wind direction; hence, the multi-unit FOWT is called the wind-tracing FOWT. In this study, rigid-body responses of the wind-tracing FOWT to waves and wind are compared with those to combined wave, current, and wind loads for several current speeds and various wave heading angles. For a chosen current speed and wave heading angle, hydro- and aeroelastic responses of the wind-tracing FOWT to combined waves, current, and wind are obtained and compared with those of the rigid structure. Discussion is provided on the effect of the wave–current interaction on the motion and elastic responses of the wind-tracing FOWT. The numerical results show that under the rated wind speed, the motion of the wind-tracing FOWT is mainly governed by the wave-induced hydrodynamic forces and moments and the presence of current results in larger elastic motion of the FOWT to the environmental loads.

Numerical Framework for the Coupled Analysis of Floating Offshore Multi-Wind Turbines

Floating offshore multi-wind turbines (FOMWTs) are an interesting alternative to the up-scaling of wind turbines. Since this is a novel concept, there are few numerical tools for its coupled dynamic assessment at the present time. In this work, a numerical framework is implemented for the simulation of multi-rotor systems under environmental excitations. It is capable of analyzing a platform using leaning towers that handle wind turbines with their own features and control systems. This tool is obtained by coupling the seakeeping hydrodynamics solver SeaFEM with the single wind turbine simulation tool OpenFAST. The coupling of SeaFEM provides a higher fidelity hydrodynamic solution, allowing the simulation of any structural design using the finite element method (FEM). Additionally, a methodology is proposed for the extension of the single wind solver, allowing for the analysis of multi-rotor configurations. To do so, the solutions of the wind turbines are computed independently using several OpenFAST instances, performing its dynamic interaction through the floater. This method is applied to the single turbine Hywind concept and the twin-turbine W2Power floating platform, supporting NREL 5-MW wind turbines. The rigid-body response amplitude operators (RAOs) are computed and compared with other numerical tools. The results showed consistency in the developed framework. An agreement was also obtained in simulations with aerodynamic loads. This resulting tool is a complete time-domain aero–hydro–servo–elastic solver that is able to compute the combined response and power generation performance of multi-rotor systems.

Reducing wave impacts on high-speed catamarans through deployment of ride control: Analysis of full-scale measurements

Full-scale trials on a 98 m wave piercer catamaran were conducted in the North Sea and North Atlantic region. In order to examine, amongst other things, the effectiveness of the ride control system, the ship was deliberately operated in sea conditions likely to induce a large number of wave impact events. Primary ship motion and structural response parameters, such as angles, rates and accelerations, and strains at various locations were recorded. Slam and minor wave impact events were identified in the data records and analysed to determine the influence of wave headings, vessel speeds, sea states and ride control system activation on their occurrence rates and severity. The Empirical Mode Decomposition technique was used to remove both noise and the rigid body response from the acceleration signals. This was based on prior work by the authors and found to provide more reliable slam identification than traditional methods. A prediction of extreme slam occurrences was modelled using logistic regression. A key outcome of the study was the finding that the activation of ride control significantly reduces the probability of extreme slams occurring.

Scaling Laws for Rigid-Body Response of Masonry Structures under Blast Loads

The response of masonry structures to explosions can be hardly investigated relying only on numerical and analytical tools. Experimental tests are of paramount importance for improving the current comprehension and validate existing models. However, experiments involving blast scenarios are, at present, partial and limited in number, compared to tests under different dynamic conditions, such as earthquakes. The reason lies on the fact that full-scale blast experiments present many difficulties, mainly due to the nature of the loading action. Experiments in reduced-scale offer instead greater flexibility. Nevertheless, appropriate scaling laws for the response of masonry structures under blast excitations are needed before performing such tests. We propose here new scaling laws for the dynamic, rigid-body response and failure modes of masonry structures under blast loads. This work takes its roots from previous studies, where closed-form solutions for the rocking response of slender blocks due to explosions have been derived and validated against numerical and experimental tests. The proposed scaling laws are here validated with detailed numerical simulations accounting for combined rocking, up-lifting, and sliding mechanisms of monolithic structures. Then, the application to multi-drum stone columns is considered. In particular, we show that, whilst the presence of complex behaviors, such as wobbling and impacts, similarity is assured. The developments demonstrate their applicability in the design of reduced-scale experiments of masonry structures.

Identification of wave impacts and separation of responses using EMD

Various marine and off-shore structures experience rare extreme, and frequent substantial wave impacts, and these impacts have significant implications respectively for the ultimate strength and fatigue life of these structures. Likewise, many other structures experience forms of impact among their environmental loads that are critical for their design. One way of exploring these impacts is to study the vibration signal of the structure. However, due to the complexity of the non-stationary signal, the wave impacts on marine and off-shore structures are difficult to analyse. Using signals acquired during trials of a high-speed catamaran as a case study, this paper proposes employing the Empirical Mode Decomposition (EMD) to detect, identify and characterise significant wave impacts (known as ‘slams’), which is shown to be significantly better at classifying events than traditional methods of slam detection. With the application of EMD, the vibration signal is decomposed into many components that may be grouped into three categories: (1) the rigid-body response comprising two parts: the quasi-static response to the underlying wave spectrum (hydrostatic) and rigid-body resonance (hydrodynamic); (2) the elastic structural response (hydroelastic); and (3) local high frequency vibrations and/or noise. It is the second category that responds significantly to wave impact loads. By identifying the gap between the rigid body and structural resonant frequencies, a threshold is established to automate the physically rational separation of this hydroelastic response. Wave impact detection methods are then applied to this separated component, showing 94% true positive classification, compared with 64% for a recently published slam detection method that uses traditional filtering applied to the whole signal. Further, it allows for more targeted subsequent characterisation of the impact response. Thus, this paper concludes that EMD is an effective method to detect and identify wave impacts.

Bistatic scattering of an elastic object using the structural admittance and noise-based holographic measurements.

This paper presents a method to calculate the bistatic response of an elastic object immersed in a fluid using its structural Green's function (in vacuo structural admittance matrix), calculated by placing the object in a spatially random noise field in air. The field separation technique and equivalent source method are used to reconstruct pressure and velocity fields at the object's surface from pressure measurements recorded on two conformal holographic surfaces surrounding the object. Accurate reconstruction of the surface velocity requires subtraction of the rigid body response computed using a finite element approach. The velocity and pressure fields on the surface lead to the extraction of the in vacuo structural admittance matrix of the elastic object, which is manipulated to yield the farfield bistatic response for a fluid-loaded target for several angles of incidence. This method allows the computation of the scattering properties of an elastic object using exclusive information calculated on its surface (no knowledge of the internal structure required). A numerical experiment involving a cylindrical shell with hemispherical caps is presented, and its bistatic response in water shows excellent agreement with a finite element solution.

Nonlinear electrostatic effects in MEMS ring-based rate sensors under shock excitation

The vibration response of a capacitive ring-based Coriolis Vibrating Gyroscope (CVG) subjected to in-plane shock is modelled and analysed to quantify the effect of shock on angular velocity measurement. The model developed considers a ring resonator with 8 uniformly spaced support legs and describes the in-plane ring response as the sum of the first 3 modes of a perfect ring and the nonlinear electrostatic force as a Taylor series. When a severe in-plane shock is applied, the rigid body response of the ring reduces the electrode gap significantly and a high order expansion is needed to represent the electrostatic force. These nonlinear forces are shown to cause direct and mixed mode coupling to occur, which can significantly modify the response characteristics. Numerical results are presented and interpreted for a range of shock cases to demonstrate the importance of mode coupling, and estimates are made to quantify the angular rate measurement error caused by shock for devices based on 2θ- and 3θ-modes of operation. To aid the design of devices that are more resilient to shock, a parameter study is performed to identify the modal frequency ratios that minimise this coupling.

Residual vibration reduction for translation unconstrained or partially unconstrained structures by structural optimization

This paper studies residual vibration reduction in translation unconstrained or partially unconstrained structures by structural optimization. Suppression of elastic residual vibration is of great concern in many fields, and several approaches have been proposed to deal with it through structural optimization. However, these approaches are suitable for completely constrained structures, while unconstrained and partially unconstrained structures are not considered in particular. The dynamic responses of the latter include not only elastic responses but also rigid body responses. The rigid body responses make several effective structural optimization approaches inapplicable. This paper proposes two methods to solve the problem arising from the rigid body responses. Then the abovementioned effective approaches based on completely constrained models are applied to study the optimization of translation unconstrained or partially unconstrained structures to minimize the residual vibration. To reduce the computational burden of optimization, model reduction is further applied in this research. Finally, several numerical examples are presented to illustrate the effectiveness of the proposed approaches. The optimized results for residual vibration minimization show superiority over those obtained with classical objective functions.

Displacement response analysis of the SCR rigid body rotation under the wave and X direction motion of the riser hanging point effects based on Cable3D

The steel catenary riser has a rigid body swing around the top suspension point and the bottom touch down point. The effect of rigid body oscillation on the displacement response of the transverse flow is not negligible. It is very important to calculate the swing displacement response of structural rigid body. The structure was imposed the wave action and the X direction action of the top suspension point that makes the rotation axies change. Based on the slender beam with large deflection model, wave model and the rigid body swing model, the influence of rigid body swing to the structure is studied. Calculation shows that structure under wave loading and X direction action, the percentage of rigid body swing impact on the structural is about 10%, increasing as the radius vector S, while decreasing with the decrease of the S. The trend is different from the waves and the top action decreasing with increasing of the depth of water. It is hoped that the above research can provide some reasonable and practical suggestions to the calculation of steel catenary riser.

Full-scale measurements of slamming loads and responses on high-speed planing craft in waves

Full-scale trials on a high-speed planing craft in waves were conducted to investigate the characteristics of slamming impacts and related rigid body and structural response. Measurements of acceleration, pressure, strain and global hull deflection were made in different sea conditions and at different speeds and headings. Low pass filtering is used to remove unwanted noise from the acceleration signals and extract the rigid body response. Methods for removing trends from the strain signals and identifying the peaks in the pressure and strain signals are established. Characteristic results including time series, distributions of peak values, averages of the largest 1/3rd and 1/10th peak values and individual impact events, are presented and discussed. The Weibull and Generalized Pareto models are used to describe the pressure and strain peak values and for estimating extreme loads and responses. Automated algorithms for fitting the statistical models to the peak value distributions are developed and the goodness-of-fit of the models to the data is examined.

System identification of flexible aircraft in frequency domain

PurposeThe purpose of this paper is to identify the flexible aircraft model accurately from the frequency responses.Design/methodology/approachThe frequency domain output error method is used to estimate the aerodynamic (rigid body and elastic body) derivatives, and mode shape parameters in the process of identification of flexible aircraft model. The accurate identification of lightly damped low frequency rigid-body response modes requires a careful selection of the frequency sweep length and the fast Fourier transform (FFT) window size, as the FFT window length cannot be longer than any individual sweep records. To address this issue, an effort is made to derive the FFT window length for the application of frequency domain estimation approach.FindingsThe investigations are initially made to select a suitable FFT window size for the accurate identification of the lightly damped low frequency rigid-body response modes of the flexible aircraft. Subsequently, frequency domain estimation approach is applied to simulated data of flexible aircraft. Besides the stability and control derivatives, the structural modes of the flexible aircraft are also estimated as part of state space model identification, and it is shown that all the model parameter estimates are accurate. Identification of such flexible aircraft aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters will lead to mathematical models of flexible aircraft that are accurate over a wide frequency range. The identified models are validated using the time response of frequency sweep data.Research limitations/implicationsAircraft system identification is an integral part of aerospace system design and life cycle process. This becomes a complex process when the aircraft has significant effects of flexibility on the flight dynamics, especially as the frequencies of the elastic modes become lower and approach those of the rigid body modes. Thus, an integrated mathematical model of flexible aircraft is required to develop, and it should be valid for a wide frequency range and relevant for the design of flight control system.Originality/valueThis paper focuses on the application of frequency domain approach to identify the valid model of flexible aircraft by estimating the aerodynamic (rigid body and elastic body) derivatives and structural mode shape parameters of flexible aircraft. The unknown frequencies of structural modes are also able to identify accurately in frequency domain. This gives more value addition to analyze the flight data of flexible aircraft, as it is challenging problem in parameter estimation of flexible aircraft.

Universal Grey System Theory for Analysis of Uncertain Structural Systems

The uncertainty present in many structural systems is commonly modeled using probabilistic, fuzzy, or interval approaches depending on the nature of uncertainty present. The probabilistic approach is based on the probability distributions of the uncertain parameters, which are not known for most practical systems. The fuzzy analysis is applicable to systems whose parameters are described in terms of linguistic and imprecise or vague statements. In most practical systems, particularly structural systems, the parameters such as the geometry (sizes of members), material properties, and loads are available as ranges or intervals. For such systems, the use of interval analysis, coupled with the finite element analysis, appears to be appropriate for predicting the ranges of the response quantities such as nodal displacements and element stresses. However, the accuracy of the results given by the interval analysis suffers from the so-called dependency problem, which can lead to undesirable expansions of the ranges of the computed results. Depending on the nature of expressions involved in the computation and the width of the ranges (intervals) of the uncertain parameters, the computed response quantities may sometimes violate the physical laws. Although several approaches, such as numerical truncation during interval arithmetic operations, parameterization of intervals, and the use of subintervals within an interval, have been suggested to limit the growth of the intervals of the results predicted, there has not been a simple approach that can improve the accuracy of the basic interval analysis. This work presents a new methodology, called universal grey number (or system) theory, for the analysis of systems whose parameters are described as intervals or ranges. The computational feasibility and improved accuracy (compared to the interval analysis) of the methodology is demonstrated by considering three examples: the stress analysis of a stepped bar, the stress analysis of a planar 10-bar truss, and the rigid-body (vertical) response of an airplane taxiing on a wavy runway based on a single-degree-of-freedom model. This work demonstrates that the universal grey system approach is a viable methodology for the accurate analysis of structural and other engineering problems involving uncertain parameters that are described in terms of ranges or intervals.

A Simplified Model to Evaluate the Dynamic Rocking Behavior of Irregular Free-Standing Rigid Bodies Calibrated with Experimental Shaking-Table Tests

ABSTRACTA simplified model to evaluate the dynamic rocking behavior of free-standing irregular rigid bodies under earthquake-induced forces is proposed. The model analyzes the response of a three-dimensional irregular rigid body using a numerical approach that considers a critical section and two equivalent rectangular rigid blocks. Experimental shaking-table tests were carried out on modular prototypes, which allow the replication of representative mass distributions, sizes, and/or slenderness ratios for typical objects. The tests were used to calibrate the numerical model. It was found that the dynamic behavior under irregular conditions (asymmetrical shape and/or non-uniform mass distribution) can be estimated with the appropriate geometric and density considerations.

An advanced technology for structural crashworthiness analysis of a ship colliding with an ice-ridge: Numerical modelling and experiments

The structural engineering problem associated with a ship colliding with an ice-ridge involves highly nonlinear mechanisms including buckling, collapse, crushing, plasticity and fracture together with environmental and operational factors, such as the loading speed (strain rate), temperature and salinity. The objective of this paper is to develop an advanced technology for numerical computations of structural crashworthiness in the event of a ship colliding with an ice-ridge. The nonlinear finite element method is used for modelling the problem, in which the ship structures are modelled by plate-shell finite elements and the ice-ridge structures are modelled by solid elements together with the KOSORI ice material models. Two sets of experiments are performed to validate the numerical computations. In the first set of experiments, ice is dropped on a steel plate from a height of 2m, and in the second, a steel solid (rigid) body is dropped on a steel plate under the same conditions. The results of the two experiments are compared to determine the differences between the ice responses and solid (rigid) body responses on the steel plate. It is concluded that the developed technology is very useful for computing the structural crashworthiness of a ship when colliding with an ice-ridge. Details of the test results are documented.

First order coupled dynamic model of flexible space structures with time-varying configurations

This paper proposes a first order coupled dynamic modeling method for flexible space structures with time-varying configurations for the purpose of deriving the characteristics of the system. The model considers the first time derivative of the coordinate transformation matrix between the platform's body frame and the appendage's floating frame. As a result it can accurately predict characteristics of the system even if flexible appendages rotate with complex trajectory relative to the rigid part. In general, flexible appendages are fixed on the rigid platform or forced to rotate with a slow angular velocity. So only the zero order of the transformation matrix is considered in conventional models. However, due to neglecting of time-varying terms of the transformation matrix, these models introduce severe error when appendages, like antennas, for example, rotate with a fast speed relative to the platform. The first order coupled dynamic model for flexible space structures proposed in this paper resolve this problem by introducing the first time derivative of the transformation matrix. As a numerical example, a central core with a rotating solar panel is considered and the results are compared with those given by the conventional model. It has been shown that the first order terms are of great importance on the attitude of the rigid body and dynamic response of the flexible appendage.

Estimation of the ground shaking from the response of rigid bodies

<p>The paper illustrates and compares simplified approaches to interpret the mechanisms of damage observed on rigid bodies in the cemetery of Amatrice, after the main shock (August 24, 2016, M<sub>W</sub>=6.0) of the Central Italy earthquake. The final goal of the work is to link the observed movements of the fallen objects to specific characteristics of the ground motion occurred at the specific site.</p>

A finite element model for seismic response analysis of deformable rocking frames

SummaryA new finite element model to analyze the seismic response of deformable rocking bodies and rocking structures is presented. The model comprises a set of beam elements to represent the rocking body and zero‐length fiber cross‐section elements at the ends of the rocking body to represent the rocking surfaces. The energy dissipation during rocking motion is modeled using a Hilber–Hughes–Taylor numerically dissipative time step integration scheme. The model is verified through correct prediction of the horizontal and vertical displacements of a rigid rocking block and validated against the analytical Housner model solution for the rocking response of rigid bodies subjected to ground motion excitation. The proposed model is augmented by a dissipative model of the ground under the rocking surface to facilitate modeling of the rocking response of deformable bodies and structures. The augmented model is used to compute the overturning and uplift rocking response spectra for a deformable rocking frame structure to symmetric and anti‐symmetric Ricker pulse ground motion excitation. It is found that the deformability of the columns of a rocking frame does not jeopardize its stability under Ricker pulse ground motion excitation. In fact, there are cases where a deformable rocking frame is more stable than its rigid counterpart. Copyright © 2016 John Wiley & Sons, Ltd.

Seismic Response of Underground Structure under Vertical Seismic Excitation

Seismic response of shallowly buried underground under vertical seismic excitation is studied. In order to simplify the analysis two steps are adopted in the analysis. In the first step structure is looked at as rigid body, and the dynamic response of the structure under vertical seismic excitation is obtained on the basis of soil-structure dynamic interaction analysis. In the second step at first the natural frequencies and mode shapes of the structure are obtained with consideration of the bending restraint of the side walls to roof slab, and then the dynamic response is determined by taking the dynamic response of rigid body in the first step as input, and furthermore the bending moment of roof slab is obtained. Key words: vertical seismic excitation, roof slab, soil-structure interaction, dynamic response

Numerical analysis of low-velocity rigid-body impact response of composite panels

This paper investigates various modelling strategies to identify the most suitable approach for modelling the low-velocity impact response of laminated composite panels. The purpose of this paper is to thoroughly investigate a dropped tool scenario or a ground vehicle impact on an aircraft fuselage panel using detailed numerical models. Three-dimensional meso-scale finite element models have been developed and implemented with user-defined material subroutines in ABAQUS/Standard. The models predict the simultaneous evolution of inter-laminar and intra-laminar damage mechanisms that occur in composite panels during impact. The paper describes the implementation of the combined inter/intra-laminar models and assesses their performance. User-defined material models developed in previous work for quasi-static problems have been further developed in this paper for damage analysis under impact loading. Experimental drop-weight impact tests, representative of low-velocity high-energy rigid-body impacts, have been carried out for model validation. Impact energy levels were varied from 10 to 40 J to evaluate the damage threshold and damage area that develops within the laminate. The results of the combined inter/intra-laminar model are in excellent agreement with experimental data, especially in terms of energy absorbed during impact. Numerical results provide an accurate description of the threshold at which a significant change in laminate stiffness occurs. It is shown conclusively that the combined inter/intra-laminar damage model developed in this work can be employed as an accurate predictive tool for low-velocity impact events.

Long-term prediction of combined wave and whipping bending moments of container ships

The purpose of this paper is to propose a practical computational procedure for the long-term distribution of combined wave and whipping bending moments (BMs) of container ships. The problem is formulated in the frequency domain using standard engineering tools for load computation: a seakeeping code for the rigid-body response and a beam finite element model for transient vibratory response. The von Karman approach with correction for pile-up effect is employed for bow flare slamming load assessment. Correlation between wave and whipping BMs is considered. The procedure is demonstrated on the example of a 9200 TEU container ship. Long-term distributions of combined BMs are computed using the standard International Association of Classification Societies scatter diagram for the North Atlantic environment and two additional scatter diagrams for common shipping routes of container ships. The speed profile required for the long-term load prediction is calculated by the seakeeping analysis respecting operability limiting criteria. Conclusions about influence of various environmental and operability parameters are drawn.