STRUCTURAL MODEL UPDATING USING VIBRATION MEASUREMENTS

Abstract. A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Paret

An improved computational strategy for vibration- proof structures equipped with nano-enhanced viscoelastic devices

Viscoelastic damping devices are effective in mitigating vibrations experienced by Civil Engineering structures subjected to natural actions, such as earthquakes, wind gusts or ocean waves. In this paper, an efficient computational framework for non-classically damped viscoelastic structures is proposed, allowing rheological information on nano-reinforced elastomeric devices to be incorporated in the time-domain dynamic analysis of structures equipped with such components. For thiss purpose, the Generalized Maxwell (GM) model and the Laguerre’s polynomial approximation (LPA) can be effectively adopted to represent the relaxation function of the viscoelastic materials, leading to an enlarged state-space model. It is also shown that these models can be used beyond the linear range, provided that the strain-dependent values of their mechanical parameters are identified

Transverse vibration of slender sandwich beams with viscoelastic inner layer via a Galerkin-type state-space approach

A novel state-space model for studying free and forced transverse vibrations of sandwich beams, made of two outer elastic beams of the same length, continuously joined by an inner shear-type viscoelastic layer, is presented. The proposed technique enables one to consider: i) inhomogeneous systems; ii) any boundary conditions; and iii) rate-dependent constitutive laws for the inner layer, which can be represented either through Generalised Maxwell's model or Laguerre's Polynomial Approximation. For the viscoelastic model of the inner layer, the dynamic behaviour is described by the Standard Linear Solid model, which is made of a primary elastic spring in parallel with a Maxwell's element. The kinematics of the outer beams is developed by means of Galerkin-type approximations for the fields of both axial and transverse displacements in the outer beams, and imposing the pertinent compatibility conditions at interface. In the proposed formulation, the assumed modes are selected as the first modes of axial vibration and of lateral buckling for each layer with homogenised mechanical properties and their own boundary conditions. Numerical examples using a novel direct integration method for calculating the response of the dynamic system demonstrate the accuracy and versatility of the proposed formulation, in both frequency- and time-domain analyses

Transverse vibrations of viscoelastic sandwich beams via a Galerkin-based state-space approach

A new state-space model is formulated for the dynamic analysis of sandwich beams that are made of two thin elastic layers continuously joined by a shear-type viscoelastic (VE) core. The model can accommodate different boundary conditions for each outer layer and accounts for the rate-dependent constitutive law of the core through additional state variables. The mathematical derivation is presented with the Standard Linear Solid (SLS) model (i.e., a primary elastic spring in parallel with a single Maxwell element) and then extended to the generalized Maxwell (GM) model. The kinematics equations are developed by means of Galerkin-type approximations for the fields of axial and transverse displacements in the outer layers, and imposing the pertinent compatibility conditions at the interface with the core. Numerical examples demonstrate the accuracy and versatility of the proposed approach, which endeavors to represent the effects of the VE memory on the vibration of composite beams

Structural model updating using vibration measurements

A multi-objective optimization framework is presented for updating finite element models of structures based on vibration measurements. The method results in multiple Pareto optimal structural models that are consistent with the measured data and the residuals used to measure the discrepancies between the measured and the finite element model predicted characteristics. The relation between the multi-objective identification method, Bayesian in-ference method, and conventional single-objective weighted residuals methods for model up-dating is discussed. Computational algorithms for the efficient and reliable solution of the resulting optimization problems are presented. The algorithms are classified to gradient-based, evolutionary strategies and hybrid techniques. In particular, efficient algorithms are introduced for reducing the computational cost involved in estimating the gradients of the ob-jective functions representing the modal residuals. Specifically, a formulation requiring the solution of the adjoint problem is presented, avoiding the explicit estimation of the gradients of the modal characteristics. The adjoint method is also extended to carry out efficiently the estimation of the Hessian of the objective function. The computational cost for estimating the gradients and Hessian is shown to be independent of the number of structural model parame-ters. The methodology is particularly efficient to system with several number of model param-eters and large number of DOFs where repeated gradient and Hessian evaluations are computationally time consuming. Component mode synthesis methods dividing the structure to linear substructural components with fixed properties and linear substructural components with uncertain properties are incorporated into the methodology to further reduce the compu-tational effort required in optimization problems. The linear substructures with fixed proper-ties are represented by their lower contributing modes which remain unchanged during the model updating process. The method is particular effective for finite element models with large number of DOF and for parameter estimation in localized areas of a structure. Theoret-ical and computational developments are illustrated by updating finite element models of a laboratory building using impact hammer measurements and multi-span reinforced concrete bridges using ambient vibration measurements

Effect of rail unevenness correlation on the prediction of ground-borne vibration from railways

This paper presents the influence of rail unevenness correlation on the predicted track and ground vibration. The study is based on an integrated railway model in the wavenumber-frequency domain with varying complexity describing the dynamic system of a ballasted track on layered elastic half-space. In order to investigate how ground vibration levels are influenced by taking into account different correlation levels between the two rails, the traction variation across the track-ground interface is included and the track model is discretised laterally including both rails separately and allowing for the pitching motion of the sleepers. The paper presents the effect of the different modelling approaches on the response predictions and compares the dynamic response calculated for a range of model/excitation parameter

The effect of track load correlation on ground-borne vibration from railways

In predictions of ground-borne vibration from railways, it is generally assumed that the unevenness profile of the wheel and rail is fully correlated between the two rails and the two wheels of an axle. This leads to identical contact forces at the two rails and can allow further simplifications of the vehicle model, the track model and the track/ground interface conditions. In the present paper, the level of correlation of the track loading at the wheel/rail interface due to rail unevenness and its influence on predictions of ground vibration is investigated. The extent to which the unevenness of the two rails is correlated has been estimated from measurements of track geometry obtained with track recording vehicles for four different tracks. It was found that for wavelengths longer than about 3 m the unevenness of the two rails can be considered to be strongly correlated and in phase. To investigate the effect of this on ground vibration, an existing model expressed in the wavenumber-frequency domain is extended to include separate inputs on the two rails. The track is modelled as an infinite invariant linear structure resting on an elastic stratified half-space. This is excited by the gravitational loading of a passing train and the irregularity of the contact surfaces between the wheels and the rails. The railway model is developed in this work to be versatile so that it can account or discard the effect of load correlations on the two rails beside the effects of variation of the tractions across the width of the track-ground interface and the vehicle sprung mass, as well as the roll motion of the sleepers and the axle. A comparative analysis is carried out on the influence of these factors on the response predictions using numerical simulations. It is shown that, when determining the vibration in the free field, it is important to include in the model the traction variation across the track-ground interface and the non-symmetrical loading at the two rails that occurs for unevenness wavelengths shorter than about 3 m.This work is undertaken as part of the MOTIV (Modelling of Train Induced Vibration) project which is funded by the EPSRC under EP/K006002/1 and EP/K005847/1. All data published in this paper are openly available from the University of Southampton repository at http://dx.doi.org/10.5258/SOTON/D0077.Scopu

Predictions of the dynamic response of piled foundations in a multi-layered half-space due to inertial and railway induced loadings

In this paper, the dynamic pile-soil-pile interaction (PSPI) in a multi-layered half-space is investigated for the prediction of the response of piled foundations due to railway vibrations. Two methods of modelling piled foundations in a multi-layered half-space are presented. The first is an efficient semi-analytical model that calculates the Green’s functions of the multi-layered half-space soil using the thin layer and the dynamic stiffness matrix methods. The second is a fully-coupled model that utilises the boundary element (BE) method to simulate the soil, where the Green’s functions are calculated using the ElastoDynamics Toolbox (EDT). The paper aims to investigate the accuracy and the efficiency of the semi-analytical model by comparing the predictions of the two methods. A set of comparisons is performed, including the driving point response of a single pile and the interaction between two piles. The comparisons reveal that, at most frequencies, the semi-analytical model can predict the driving point response and the dynamic interaction with acceptable accuracy and computational efficiency. The model is then used for predicting the response of a pile-group due to the vibration field generated by a railway in varying distance from the piles. The vibration field generated by the railway is modelled as the superposition of the response due to harmonic loadings generated at the wheel-rail interface and the vibration response is examined at different points on the free surface away from the piles. The comparisons highlight the efficiency and accuracy of the semi-analytical model and illustrate its practical application

THE EFFECT OF TRACK UNEVENNESS CORRELATION ON RAILWAY INDUCED GROUND VIBRATION

This paper focuses on quantifying the level of correlation of the track loading at the wheel/rail interface due to rail unevenness and its influence on predictions of ground vibration. The extent to which the unevenness of the two rails is correlated has been estimated from measurements of track geometry obtained with track recording vehicles for six different tracks. It was found that for wavelengths longer than about 3 m the unevenness of the two rails can be considered to be strongly correlated and in phase. To investigate the effect of this on ground vibration, a railway model that works in the wavenumber-frequency domain and includes separate inputs on the two rails has been used. In this model, the track is assumed as an infinite invariant linear structure resting on an elastic stratified half-space. This is excited by the gravitational loading of a passing train and the irregularity of the contact surfaces between the wheels and the rails. The railway model can account or discard the effect of load correlations on the two rails beside the effects of variation of the tractions across the width of the track-ground interface and the vehicle sprung mass, as well as the roll motion of the sleepers and the axle. A comparative analysis is carried out on the influence of these factors on the response predictions using numerical simulations. It is shown that, when determining the vibration in the free field, it is important to include in the model the non-symmetrical loading at the two rails that occurs for unevenness wavelengths shorter than about 3 m