Four simplified gradient elasticity models for the simulation of dispersive wave propagation

Gradient elasticity theories can be used to simulate dispersive wave propagation as it occurs in heterogeneous materials. Compared to the second-order partial differential equations of classical elasticity, in its most general format gradient elasticity also contains fourth-order spatial, temporal as well as mixed spatial temporal derivatives. The inclusion of the various higher-order terms has been motivated through arguments of causality and asymptotic accuracy, but for numerical implementations it is also important that standard discretization tools can be used for the interpolation in space and the integration in time. In this paper, we will formulate four different simplifications of the general gradient elasticity theory. We will study the dispersive properties of the models, their causality according to Einstein and their behavior in simple initial/boundary value problems

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

On stability of a clamped-pinned pipe conveying fluid

Civil Engineering and Geoscience

Comparison of the Dynamic Response of One- and Two-Dimensional Models for an Embedded Railway Track to a Moving Load,

In this paper, the steady-state response of an embedded track to the axle loading of a moving train is studied theoretically using two models. The first and the second models are one-dimensional (1D) and two-dimensional (2D), respectively, and differ by the fact that the latter model accounts for the lateral flexibility of the concrete slab of the track. The loading is modelled by a harmonically varying load that uniformly moves along the track. The response to this load is studied analytically with the help of the Fourier integral transforms. The study is accomplished performing the following steps, every of which is accompanied by comparison of two models under consideration. Firstly, the dispersion curves are calculated and critical parameters (frequency and velocity) of the load are found that could lead to resonance in the structure. Secondly, displacements of the rails and stresses in the concrete slab are studied for various velocities and frequencies of the load. The results obtained from both models are compared to that one calculated using a Finite Element program. On the basis of a comparative analysis of results obtained from the 1D and 2D models it is concluded that in engineering calculations, the 1D model can be employed for a quick and sufficiently accurate assessment of the dynamic behaviour of the embedded track under a high-speed train.Civil Engineering and Geoscience

Plasticity Detection and Quantification in Monopile Support Structures Due to Axial Impact Loading

Recent developments in the construction of offshore wind turbines have created the need for a method to detect whether a monopile foundation is plastically deformed during the installation procedure. Since measurements at the pile head are difficult to perform, a method based on measurements at a certain distance below the pile head is proposed in this work for quantification of the amount of plasticity. By considering a onedimensional rod model with an elastic-perfectly plastic constitutive relation, it is shown that the occurrence of plastic deformation caused by an impact load can be detected from these measurements. Furthermore, this plastic deformation can be quantified by the same measurement with the help of an energy balance. The effectiveness of the proposed method is demonstrated via a numerical example

Comparison of the dynamic resonse of one-and two-dimensional models for an embedded railway track to a moving load

Civil Engineering and Geoscience

The influence of friction at the ice-structure interface on the induced vibrations

Vertically-sided offshore structures occasionally experience sustained vibration due to drifting ice sheets crushing against them. These vibrations may lead to problems associated with structural integrity and safety. Traditionally, three regimes of interaction are distinguished: intermittent crushing, frequency lock-in and continuous brittle crushing. These regimes correspond to the dynamic ice-structure interaction at low-, intermediate- and high ice sheet velocities respectively. In this paper the effect of friction at the ice-structure interface on the frequency lock-in regime is studied. This investigation is a follow-up of a comparison between prediction models and full-scale data for ice induced vibrations which has been carried out in the framework of an Ice Induced Vibrations JIP (IIV JIP). This comparison showed that no simultaneous match could be found for both the structural acceleration of and ice force on cylindrical structures. This raised the question of whether or not the neglected in the models frictional interaction at the ice-structure interface could be a reason for such an inconsistency. In order to answer this question the interaction at the ice-structure interface is implemented, in a simplified manner, according to the Coulomb friction law in one of the models tested in the framework of the IIV JIP. In this model it is assumed that the three regimes of the dynamic ice-structure interaction can be described based on the distribution of ice strength in the ice sheet. It is concluded that friction alone cannot explain the large inconsistency in case of cylindrical shaped structures. It is suggested that the way the current models translate the available measurement data to input might be worth further investigation. Effects of friction on the range of velocities for which frequency lock-in might occur are expected to be minimal when a fully confined scenario is considered, although an overall increase in loads is predicted. The influence of friction for scenarios with marginal confinement needs further investigation with a more advanced model.Structural EngineeringCivil Engineering and Geoscience

Dynamic behaviour of a layer of discrete particles, Part 1: Analysis of body waves and eigenmodes

This paper is one in a series of two, and discusses the body wave propagation and the eigenmodes for a layer of discrete particles. This configuration is a representation for a ballast layer used in ordinary railway tracks. The discrete nature of the ballast is simulated via an elastic nine-cell square lattice. After deriving the equations of motion for the lattice, the long-wave approximation for the equations of motion is compared with the equations of motion for a classic elastic continuum. This comparison yields relations between the macroscopic continuum parameters and the microscopic lattice parameters. Then, the dispersion curves that characterize the eigenmodes of the discrete layer are derived. The differences between these dispersion curves and those of a continuous layer are elucidated. By means of a parametric study, the influence is shown of the particle diameter and thickness of the layer on the dynamic response. In an accompanying paper, the layer response to a moving, harmonically vibrating load is analyzed, which is a representation for a ballast track that is subjected to an instantaneous train axle passage