Slender Vertical Structures Research Articles

Alongwind dynamic response of slender vertical structures: thunderstorm outflows vs extra-tropical cyclones

Alongwind dynamic response of slender vertical structures: thunderstorm outflows vs extra-tropical cyclones

The contribution of higher order modes in the dynamic response of slender vertical structures with application to wind turbine towers

Understanding the contribution of the vibration modes to the response of a tower-like structure subjected to base excitations is crucial for a safe and optimized design. The modal contributions to the structural response are generally assessed through modal participation factors and effective masses; however, relatively recent studies pointed out the variability of the modal contributions depending on the response effect (e.g., top displacement, base shear force, base bending moment). The formulation proposed here derives the shear force and the bending moment at the base of a tower-like structure by combining the influence function technique with the quasi-static equivalent forces technique. The resulting formulation of the tower response relies on the concept of modal contribution factors, which provides a straightforward indication of the modal contributions associated with a given response effect. The proposed methodology is applied to the case of wind turbine towers erected on temporary foundations at the port quayside without rotor nacelle assembly to assess the forces on the foundations due to the seismic loading on the towers. This technique may be of great relevance for assessing the tower integrity during installation and for the design of the temporary foundations at the quayside of harbors in seismic area, also considering the quick expansion of the offshore wind energy in countries prone to earthquakes.

Dynamic Response of Slender Vertical Structures Subjected to Thunderstorm Outflows

This study examines the maximum alongwind dynamic response of slender vertical structures subjected to thunderstorms, comparing the induced maximum response with the one induced via synoptic events. Two real structures are considered as case studies: a lighting pole and a telecommunications tower. The comparison between thunderstorm- and synoptic-induced dynamic responses is performed through a critical analysis of three ratios characterizing the difference between the two phenomena: the reference wind speed, the mean wind profile, and the gust response factor. The comparison shows that the definition of the reference wind speed and the height of the nose tip of the thunderstorm mean wind profile are crucial for the maximum response, as well as for the dependence of the turbulence intensity on the roughness length. The results show that thunderstorms provide the design loading condition in most cases.

Coupled numerical simulation of liquid sloshing dampers and wind–structure simulation model

Long-span bridges, high-rise buildings, chimneys, or wind turbines are often susceptible to wind-induced vibrations due to their high flexibility and lightweight. Therefore, these structures should be carefully designed to sustain the wind loads. Employing robust solutions for vibration mitigation, such as tuned liquid dampers (TLDs), enables energy dissipation at reduced structural and maintenance costs. This study presents a numerical coupling methodology for evaluating the wind-induced response of slender vertical structures that include a TLD. The methodology is based on coupling a Computational Fluid Dynamics (CFD) model of a TLD, a semi-analytical aerodynamic force model, and a structural model. The coupling is realized in a time-domain fashion by continuously exchanging sloshing forces, aerodynamic forces, and structural response. The highlight is the use of the volume of fluid (VOF) method as a CFD strategy to represent the sloshing damping forces, including an experimental validation. The methodology is applied to (i) a chimney-type structure to mitigate the buffeting and vortex-induced vibrations and (ii) a high-rise building to reduce the acceleration buffeting response for human comfort. In both cases, strategy for TLD predesign is employed based on free- and forced-vibration analysis, an equivalent tuned mass damper model, and wind vibrations, respectively. The results of the dynamic analyses show that there is a significant reduction in structural response for both cases. The outcome of this study is intended to showcase the applicability of CFD for TLD predesign and modeling nonlinear sloshing forces during dynamic analysis as an alternative to experiments. Thus, it is intended to serve academics as well as practitioners.

Sobre a Modelagem Computacional de Estruturas Imersas em Escoamentos em Escala Subgrid

In the computational modeling of water environments there are cases where slender vertical structures, like bridge piers, are part of the modeling domain. In this work, four strategies for modeling the presence of bridge piers were studied: Mesh Refinement (MR), Nodal Island (NI), Additional Stress Term (AST) and Increasing Bottom Roughness (IBR). For each method, advantages and disadvantages were discussed. AST was the most favorable of the techniques studied due to the fact that it drastically decreases the time of computation, as well as providing the possibility to choose the drag coefficient according to the pier geometry and hydrodynamic condition. Comparing the results of longitudinal centerline velocity profiles, it has been observed that the AST method provides similar results to the RM method from a distance of 100 m downstream of the pier. For this reason, the research concludes that the AST method is appropriate to evaluate the flow distant from the structures, outside the near wake. This work presents a sensibility study of the pier drag coefficient to make the reader aware of the influence of this parameter.

Dynamic ice forces of slender vertical structures due to ice crushing

Abstract The dynamic ice forces and structure vibrations generated by crushing failure of ice sheet were investigated by full-scale tests conducted on a cylindrical compliant monopod platform in Bohai Bay, China. The load panels recorded three ice force modes distinguished by ice speed, which cause structure quasi-static, steady-state and random vibrations respectively. Based on the tests data, the physical process of dynamic ice forces in crushing failure was probed, by analysis of mechanical behaviour of ice under compressive loading related to relative loading speed of ice-structure interaction. It is proved that the three ice force modes takes place in loading speeds which make ice fail in ductile, ductile–brittle transition and brittle range respectively. In addition, the key problem from the structure design point of view involved in each ice force mode is discussed.

Directional Wind-Induced Fatigue of Slender Vertical Structures

The wind-excited vibrations of structures induce fluctuating stresses that lead to fatigue damage accumulation and may determine structural failure without exceeding ultimate strength. This paper proposes a mathematical model aimed at deriving the histogram of the stress cycles, the accumulated damage, and the fatigue life of slender vertical structures exposed to simultaneous alongwind and crosswind vibrations. Wind climate is modeled by the joint density function of the mean wind velocity and direction. Wind-induced actions consist of aerodynamic forces on the stationary structure and of aeroelastic forces due to the structural motion. Aerodynamic actions on the stationary structure are caused by the turbulence of the oncoming flow, dealt with through quasisteady theory, and by the vortex wake, considered as independent from turbulence. Aeroelastic forces are aimed at reproducing the lock-in phenomenon. The static and the quasistatic parts of the structural response are evaluated by the influence function technique, taking all modes of vibrations into consideration. The resonant part of the response is related to the fundamental alongwind and crosswind modes only. The probabilistic accumulation of damage due to aerodynamic actions on stationary structures is estimated by a counting cycle method inspired by narrow band processes. The damage in lock-in conditions is superimposed by counting stress cycles deterministically. The examples illustrate the application and the effectiveness of the proposed procedure, focusing attention on the role of upper modes and wind directionality.

Dynamic crosswind fatigue of slender vertical structures

Wind-excited vibrations of slender structures can induce fatigue damage and cause structural failure without exceeding ultimate limit state. Unfortunately, the growing importance of this problem is coupled with an evident lack of simple calculation criteria. This paper proposes a mathematical method for evaluating the crosswind fatigue of slender vertical structures, which represents the dual formulation of a parallel method that the authors recently developed with regard to alongwind vibrations. It takes into account the probability distribution of the mean wind velocity at the structural site. The aerodynamic crosswind actions on the stationary structure are caused by the vortex shedding and by the lateral turbulence, both schematised by spectral models. The structural response in the small displacement regime is expressed in closed form by considering only the contribution of the first vibration mode. The stress cycle counting is based on a probabilistic method for narrow-band processes and leads to analytical formulae of the stress cycles histogram, of the accumulated damage and of the fatigue life. The extension of this procedure to take into account aeroelastic vibrations due to lock-in is carried out by means of ESDU method. The examples point out the great importance of vortex shedding and especially of lock-in concerning fatigue.

3-D gust effect factor for slender vertical structures

Original studies on gust factor buffeting dealt with the alongwind displacement of structures. Research on this topic carried out since the nineties followed two distinct lines: the first determines the maximum effects due to the alongwind response; the second extends the original method from the alongwind response to crosswind and torsional responses. This paper represents the junction point of these research lines with reference to cantilever slender vertical structures. It derives the most relevant effects associated with the three-dimensional (3-D) wind-excited response of this structural type and shows that a suitable definition of one non-dimensional quantity, referred to as the 3-D gust effect factor, provides such effects at any level through a wide set of experimental, numerical and analytical procedures. A new definition of a 3-D equivalent static force consistent with this method is also introduced and critically compared with previous analogous statements.

Dynamic alongwind fatigue of slender vertical structures

The wind-excited vibrations of structures induce fluctuating stresses around mean deformation states that lead to fatigue damage accumulation and can determine structural failure without exceeding design wind actions. This paper proposes a mathematical model aimed at deriving a histogram of the stress cycles, the accumulated damage and the fatigue life of slender vertical structures (e.g. towers, chimneys, poles and masts) in alongwind vibrations. The formulation, integrally in closed form, is based on a probabilistic counting cycle method inspired by narrow-band processes. An example illustrates the proposed procedure and shows, through the comparison with Monte Carlo simulations, the entity of the approximations involved by treating the response as narrow-banded instead of broad-banded.

Dynamic behaviour of inflorescence-bearing Triticale and Triticum stems

The mechanical response of cereal plant shoots to load caused by wind and gravity in the field is swaying in flexure around the vertical or near vertical transient equilibrium position determined by the stationary component of the wind pressure. The aim of this work was to characterise the kinematic and dynamic attributes and their interrelations in freely swaying inflorescence-bearing stems of wheat (Triticum aestivum L.) and Triticale. The fundamental natural frequency of the stems appeared to be considerably lower than predicted from the theory of vibration using the model of a cantilever beam oscillator and assuming the spring constant to be equal to the force-deflection ratio. Because of the rate of deformation and visco-elastic behaviour of the plant material, a discrepancy of about 10% was found between the dynamic and static stem bending resistance. The presence of the tip inflorescence caused vibrating vertical stems to behave as compressed columns in which the effective spring constant was strongly biased by the apical load due to the weight of the inflorescence. At the late milk stage, in the freely swaying stems of wheat and Triticale, the resistance to dynamic lateral loads was reduced by about 30% as a result of compression exerted by the inflorescence. So the prominent effect of the tip inflorescence on the dynamic behaviour (the effective spring constant and the natural frequency) of the stem is attributed to the non-negligible magnitude of the inflorescence weight relative to the critical load producing elastic buckling in slender vertical structures. Stem softening as a consequence of increasing inflorescence weight is assumed to be one of the essential factors reducing the lodging resistance in cereal crops at the late milk stage. The feasibility of the compressed-column approach for predicting the dynamic bending performance of slender vertical plant organs is discussed.

Initial post-buckling of submerged slender vertical structures subjected to distributed axial tension

This paper proposes an analytical solution for determining the initial post-buckling behaviour of submerged slender vertical steel structures. These structures may have significant bending stiffness and self-weight so that the axial force varies linearly from one end to the other. Such structures constitute main components of drilling and production platforms used for the offshore exploitation of hydrocarbons. An understanding of their structural behaviour after buckling offers opportunities for cost reduction and design optimisation. The initial post-buckling behaviour is evaluated by retaining non-linear curvature terms and using an expansion in series to reduce the governing equation to a set of linear ordinary fourth order differential equations, which are then solved sequentially by power series functions. The paper also presents results from buckling and non-linear large deflection finite element analyses. The numerical results validate and establish a range of application for the analytical formulation. This solution technique is employed to explore the behaviour of slender structures dominated by geometrical (tension) or flexural stiffness.