ABSTRACT:A simplified design procedure for foundations of offshore wind turbines is often useful as it can provide the types and sizes of foundation required to carry out financial viability analysis of a project and can also be used for tender design. This paper presents a simplified way of carrying out the design of monopiles based on necessary data (i.e. the least amount of data), namely site characteristics (wind speed at reference height, wind turbulence intensity, water depth, wave height and wave period), turbine characteristics (rated power, rated wind speed, rotor diameter, cut-in and cut-out -upper limit of the 1P frequency range -fixed base (cantilever beam) natural frequency of the tower -characteristic yield strength -gravitational constant -distance from zero shear force location to pile toe -air gap between the highest expected wave crest level and the platform -wave number 0 -equivalent stiffness of first tower mode ℎ -horizontal modulus of subgrade reaction -total structural mass, also strain accumulation exponent 0 -equivalent mass of first tower mode -mass of the pile -mass of the rotor-nacelle assembly -mass of the tower -mass of the transition piece ℎ -horizontal coefficient of subgrade reaction ℎ1 -coefficient of subgrade reaction at the first load cycle ℎ -coefficient of subgrade reaction after N load cycles -shape parameter of Weibull distribution -undrained shear strength of soil , , -time, also degradation parameters degradation model -grout thickness -pile wall thickness -tower wall thickness -wall thickness of the transition piece -transition piece wall thickness -turbulent wind speed component -extreme gust speed ,

On its opening day, the London Millennium Bridge (LMB) experienced unexpected large amplitude lateral vibrations due to crowd loading. This form of pedestrian-structure interaction has since been identified on several other bridges of various structural forms. The mechanism has generally been attributed to 'pedestrian synchronous lateral excitation' or 'pedestrian lock-in'. However, some of the more recent site measurements have shown a lack of evidence of pedestrian synchronization, at least at the onset of the behaviour. This paper considers a simple model of human balance from the biomechanics field-the inverted pendulum model-for which the most effective means of lateral stabilization is by the control of the position, rather than the timing, of foot placement. The same balance strategy as for normal walking on a stationary surface is applied to walking on a laterally oscillating bridge. As a result, without altering their pacing frequency, averaged over a large number of cycles, the pedestrian effectively acts as a negative (or positive) damper to the bridge motion, which may be at a different frequency. This is in agreement with the empirical model developed by Arup from the measurements on the LMB, leading to divergent amplitude vibrations above a critical number of pedestrians.

Offshore wind turbines (OWTs) are dynamically loaded structures and therefore the estimation of the natural frequency is an important design calculation to avoid resonance and resonance related effects (such as fatigue). Monopiles are currently the most used foundation type and are also being considered in deeper waters (>30 m) where a stiff transition piece will join the monopile and the tapered tall tower. While rather computationally expensive, high fidelity finite element analysis can be carried to find the Eigen solutions of the whole system considering soil–structure interaction; a quick hand calculation method is often convenient during the design optimisation stage or conceptual design stage. This paper proposes a simplified methodology to obtain the first natural frequency of the whole system using only limited data on the WTG (Wind Turbine Generator), tower dimensions, monopile dimensions and the ground. The most uncertain component is the ground and is characterised by two parameters: type of ground profile (i.e. soil stiffness variation with depth) and the soil stiffness at one monopile depth below mudline. In this framework, the fixed base natural frequency of the wind turbine is first calculated and is then multiplied by two non-dimensional factors to account for the foundation flexibility (i.e. the effect of soil–structure interaction). The theoretical background behind the model is the Euler–Bernoulli and Timoshenko beam theories where the foundation is idealised by three coupled springs (lateral, rocking and cross-coupling). 10 wind turbines founded in different ground conditions from 10 different wind farms in Europe (e.g. Walney, Gunfleet sand, Burbo Bank, Belwind, Barrow, Kentish flat, Blyth, Lely, Thanet Sand, Irene Vorrink) have been analysed and the results compared with the measured natural frequencies. The results show good accuracy (errors below 3.5%). A step by step sample calculation is also shown for practical use of the proposed methodology

No abstract

Detailed vibration measurements were taken on the Clifton Suspension Bridge in Bristol, England to define its basic dynamic characteristics in normal conditions and then to assess its dynamic response to crowd loading; 27 vibration modes were identified with natural frequencies below 3 Hz. When subject to crowd loading, quite large lateral vibrations occurred in two modes, with sudden onset. This phenomenon, often termed 'synchronous lateral excitation' or 'pedestrian lock-in', is similar to the behaviour observed on the London Millennium Bridge and a number of other bridges. Data analysis showed the behaviour to be consistent with the pedestrian negative damping model proposed by Arup in developing a solution for the Millennium Bridge. This model does not, however, explain the underlying mechanism causing the excitation, and a number of observations of the behaviour of the Clifton Suspension Bridge suggest that significant synchronisation of pedestrians did not actually occur. Although synchronisation may occur for large-amplitude vibrations on some bridges, the observations challenge the commonly held view that this mechanism is responsible for the initial rapid onset of lateral vibrations due to crowd loading.

Offshore wind turbines are subjected to multiple dynamic loads arising from the wind, waves, rotational frequency (1P) and blade passing frequency (3P) loads. In the literature, these loads are often represented using a frequency plot where the power spectral densities (PSDs) of wave height and wind turbulence are plotted against the corresponding frequency range. The PSD magnitudes are usually normalized to unity, probably because they have different units, and thus, the magnitudes are not directly comparable. In this paper, a generalized attempt has been made to evaluate the relative magnitudes of these four loadings by transforming them into bending moment spectra using site-specific and turbine-specific data. A formulation is proposed to construct bending moment spectra at the mudline, i.e. at the location where the highest fatigue damage is expected. Equally, this formulation can also be tailored to find the bending moment at any other critical cross section, e.g. the transition piece level. Finally, an example case study is considered to demonstrate the application of the proposed methodology. The constructed spectra serve as a basis for frequency-domain fatigue estimation methods available in the literatur

This is a repository copy of Modal stability of inclined cables subjected to vertical support excitation.

An analytical model to predict the natural frequency of offshore wind turbines on three-spring flexible foundations using two different beam models. Soil Dynamics and Earthquake Engineering, 74,[40][41][42][43][44][45] ABSTRACT: In this study an analytical model of offshore wind turbines (OWTs) supported on flexible foundation is presented to provide a fast and reasonably accurate natural frequency estimation suitable for preliminary design or verification of Finite Element calculations. Previous research modelled the problem using Euler-Bernoulli beam model where the foundation is represented by two springs (lateral and rotational). In contrast, this study improves on previous efforts by incorporating a cross-coupling stiffness thereby modelling the foundation using three springs. Furthermore, this study also derives the natural frequency using Timoshenko beam model by including rotary inertia and shear deformation. The results of the proposed model are also compared with measured values of the natural frequency of four OWTs obtained from literature. The results show that the Timoshenko beam model does not improve the results significantly and the slender beam assumption may be sufficient. The cross-coupling spring term has a significant effect on the natural frequency therefore needs to be included in the analysis. The model predicts the natural frequency of existing turbines with reasonable accuracy.