Asymptotic equivalence of homogenisation procedures and fine-tuning of continuum theories

Long-wave models obtained in the process of asymptotic homogenisation of structures with a characteristic length scale are known to be non-unique. The term non-uniqueness is used here in the sense that various homogenisation strategies may lead to distinct governing equations that usually, for a given order of the governing equation, approximate the original problem with the same asymptotic accuracy. A constructive procedure presented in this paper generates a class of asymptotically equivalent long-wave models from an original homogenised theory. The described non-uniqueness manifests itself in the occurrence of additional parameters characterising the model. A simple problem of long-wave propagation in a regular one-dimensional lattice structure is used to illustrate important criteria for selecting these parameters. The procedure is then applied to derive a class of continuum theories for a two-dimensional square array of particles. Applications to asymptotic structural theories are also discussed. In particular, we demonstrate how to improve the governing equation for the Rayleigh-Love rod and explain the reasons for the well-known numerical accuracy of the Mindlin plate theory

Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures. Part I: model description and validation

This paper is first of the two papers dealing with the nonlinear modelling and investigation of coupled cross-flow and in-line vortex-induced vibrations (VIVs) of flexible cylindrical structures. As a continuation of the previous work (Qu and Metrikine in Ocean Eng 196:106732, 2020) where a new single wake oscillator model was proposed and studied for VIVs of rigid cylinders, the present paper focuses on applying it to flexible cylinders. In this paper, the structure is modelled as an extensible Euler–Bernoulli beam and its 3D nonlinear coupling motion is described in the absolute coordinate system. The single van der Pol wake oscillator model with nonlinear coupling to the in-line motion of the structure, in addition to the classic linear cross-flow motion coupling, is uniformly distributed along the structure to model the hydrodynamic force acting on it. The finite element method has been applied to solve the dynamics of the coupled system, and the experiments of the VIV of a top-tensioned straight riser subjected to a step flow have been taken for the validation of the model. The model has been shown to be able to capture most features of VIVs of flexible cylinders, and a good agreement between the simulation results and the experimental measurements has been observed with regard to the amplitude, frequency and excited mode of both cross-flow and in-line vibrations, as well as the mean in-line deflection due to the amplified in-line force. While it is conventionally expected that the VIV of a flexible cylinder subjected to a uniform flow is dominated by a single frequency, a multi-frequency response is observed in the simulation results over the range of flow velocities through which the transition of the dominant mode of vibration occurs.</p

1997], Critical velocities of a harmonic load moving uniformly along an elastic layer, J.Appl

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Modelling of coupled cross-flow and in-line vortex-induced vibrations of flexible cylindrical structures: Part II: on the importance of in-line coupling

To illustrate the influence of the in-line coupling on the prediction of vortex-induced vibration (VIV), the simulation results of the coupled cross-flow and in-line VIVs of flexible cylinders- obtained with three different wake oscillator models with and without the in-line coupling- are compared and studied in this paper. Both the cases of uniform and linearly sheared flow are analysed and the simulation results of the three models are compared with each other from the viewpoints of response pattern, fluid force, energy transfer and fatigue damage. The differences between the simulation results from the three models highlight the importance of the in-line coupling on the prediction of coupled cross-flow and in-line VIVs of flexible cylindrical structures.</p

Wave radiation from vibratory and impact pile driving in a layered acousto-elastic medium

A steel monopile is the most common foundation type of a wind turbine installed offshore and is driven into place with the help of vibratory or impact hammers. Underwater noise generated during the installation of steel monopiles has recently received considerable attention from international environmental organizations and regulatory bodies in various nations. Collected data regarding underwater noise measurements indicate that pile driving operations, especially when impact hammers are used, can be potentially harmful for the marine ecosystem. In this paper, a linear semi-analytical model is developed for the study of the vibroacoustic behaviour of a coupled pile-soil-water system. The hammer is substituted by an external force applied at the head of the pile. The pile is described by a thin shell theory, whereas both soil and water are modelled as threedimensional continua. The solution is based on the dynamic sub-structuring technique. The total system is divided into two subsystems namely, the shell structure and the soil-fluid medium. The response of each sub-domain is expressed as a summation over a complete set of eigenfunctions. The orthogonality of the shell modes in vacuo and the bi-orthogonality of the acoustoelastic modes is utilized in order to meet the displacement compatibility and the force equilibrium at the interface of the two sub-systems. With the developed model, the wave radiation due to vibratory and impact pile driving is analysed. The influence of soil elasticity and soil stratification on the dynamics of the coupled system is examined. In addition, the energy launched by the hammer into the water and into the soil is investigated for both excitation types in order to highlight the main differences in the generated wave field.Structural EngineeringCivil Engineering and Geoscience

A non-collocated method to quantify plastic deformation caused by impact pile driving

The use of bolted connections between the tower and a support structure of an offshore wind turbine has created the need for a method to detect whether a monopile foundation plastically deforms during the installation procedure. Small permanent deformations are undesirable, not only because they can accelerate fatigue of the structure; but also because they can lead to misalignment between the tower and the foundation. Since direct measurements at the pile head are difficult to perform, a method based on non-collocated strain measurements is highly desirable. This paper proposes such a method. First, a physically non-linear one-dimensional model is proposed, which accounts for wave dispersion, effects that are relevant for large-diameter piles currently used by the industry. The proposed model, combined with an energy balance principle, gives an upper bound for the amount of plastic deformation caused by an impact load based on simple strain measurements. This is verified by a lab-scale experiment with a uni-axial stress state. Second, measurement data collected during pile driving of a large-diameter pile show that the proposed one-dimensional model, while able to predict the peak stresses, fails to accurately predict the full time history of the measured stress state. In contrast, an advanced model based on shell membrane theory is able to do that, showing that a bi-axial stress state is needed for these type of structures. This requires an extension of the theory for plasticity quantification presented in this paper.</p

A non-linear three-dimensional pile–soil model for vibratory pile installation in layered media

This paper presents a computationally efficient model for vibratory pile installation. A semi-analytical finite element (SAFE) model for thin cylindrical shells is derived to represent the pile. The linear dynamic response of the soil medium is described by means of Green's functions via the Thin-Layer Method (TLM) coupled with Perfectly Matched Layers (PMLs) to account for the underlying elastic half-space. Furthermore, the non-linear pile–soil interaction is addressed through a history-dependent frictional interface and a visco-elasto-plastic tip reaction model that can be characterized on the basis of standard geotechnical in-situ measurements. The solution to the non-linear dynamic pile–soil interaction problem is based on the sequential application of the Harmonic Balance Method (HBM). The constituent components of the model are first benchmarked against established numerical schemes. Subsequently, model predictions are compared with experimental data collected from field tests. It is demonstrated that the proposed model amalgamates rigorous theoretical elements and promising prediction capabilities in a computationally efficient framework, applicable to engineering practice.</p

Simulating interaction between level ice and conical structures with a 2D lattice model

Structures with a downward sloping waterline shape in Arctic or sub-Arctic regions experience reduced loading from ice on the structure and its foundation compared to vertical structures as the slope causes the ice to fail in bending. For the design of these structures, a numerical model is desired that can predict the loading from the ice on the structure by simulating the physical processes that occur when the ice fails. A numerical 2D lattice model has been developed to simulate level ice behavior. The model is composed of masses and interconnecting springs, taking into account deformation in tension, compression, bending, shear and torsion in the ice sheet. Deformation and failure criteria in the model are based on first principles, enabling a physically sound simulation of breaking processes. In addition, the discrete lattice model avoids stress singularities in fracture modeling since the model only describes displacements and forces in the connections and no stresses are present. In this paper interaction between ice and a downward sloping conical structure is simulated with the lattice model and compared with data from scale model tests. From the model test results it was observed that level ice and larger ice floes fail in sequential bending during interaction with a structure, giving a repetitive load pattern. Smaller ice floes split and break in bending into smaller parts and a sequential breaking pattern does not develop. The lattice model is capable of simulating failure in bending, splitting and combinations of these. In contrast, predictions of the model presented herein suffer from limitations of the contact model between the ice and the structure, the lack of a clearing mechanism and the use of a regular lattice mesh.</p