Vortex-induced vibrations of a rigid cylinder on elastic supports with endstops. Part 1: Experimental Results

This paper describes an experimental investigation into the effect of restricting the vortex-induced vibrations of a spring-mounted rigid cylinder by means of stiff mechanical endstops. Cases of both asymmetric and symmetric restraint are investigated. Results show that limiting the amplitude of the vibrations strongly affects the dynamics of the cylinder, particularly when the offset is small. Fluid-structure interaction is profoundly affected, and the well-known modes of vortex shedding observed with a linear elastic system are modified or absent. There is no evidence of lock-in, and the dominant impact frequency corresponds to a constant Strouhal number of 0.18. The presence of an endstop on one side of the motion can lead to large increases in displacements in the opposite direction. Attention is also given to the nature of the developing chaotic motion, and to impact velocities, which in single-sided impacts approach the maximum velocity of a cylinder with linear compliance undergoing VIV at lock-in. With symmetrical endstops, impact velocities were about one-half of this. Lift coefficients are computed from an analysis of the cylinder’s motion between impacts.

Changes in modal parameters of a steel truss bridge due to artificial damage

This study investigated how damage changes the modal parameters of a real bridge by means of a field experiment which was conducted on a real steel truss bridge consecutively subjected to four artificial damage scenarios. In the experiment, both the forced and free vibrations of the bridge were recorded, the former for identifying higher modes available exclusively and the latter for lower modes with higher resolution. Results show that modal parameters are little affected by damage causing low stress redistribution. Modal frequencies decrease as damage causing high stress redistribution is applied; such a change can be observed if the damage is at the non-nodal point of the corresponding mode shape. Mode shapes are distorted due to asymmetric damage; they show an amplification in the damaged side as damage is applied at the non-nodal point. Torsion modes become more dominant as damage is applied either asymmetrically or on an element against large design loads. © 2013 Taylor & Francis Group, London.

Numerical Simulation of Tanpura String Vibrations

A numerical model of a tanpura string is presented, based on a recently developed, stability-preserving way of incorporating the non-smooth forces involved in the impactive distributed contact between the string and the bridge. By defining and modelling the string-bridge contact over the full length of the bridge, the simulated vibrations can be monitored through the force signals at both the bridge and the nut. As such it offers a reference model for both measurements and sound synthesis. Simulations starting from different types of initial conditions demonstrate that the model reproduces the main characteristic feature of the tanpura, namely the sustained appearance of a precursor in the force waveforms, carrying a band of overtones which decrease in frequency as the string vibrations decay. Results obtained with the numerical model are used to examine, through comparison, the effect of the bridge and of the thread on the vibrations.

Extracting statistically dominant modes of a steel truss bridge from vehicle-induced vibrations

This study is intended to investigate the validity of the stability diagram (SD) aided multivariate autoregressive (MAR) analysis for identifying modal parameters of a real truss bridge. The MAR models are adopted to fit the time series of the dynamic accelerations recorded from a number of observation points on the bridge; then the modal parameters are extracted from the MAR model coefficient matrix. The SD is adopted to determine statistically dominant modes. In plotting the SD, a number of stability criteria are further adopted for filtering out those modes with unstable modal parameters. By the present method, the first five modal frequencies and mode shapes are identified with very high precision, while the damping ratios are identified with high precision for the 1st mode but with poorer precision for higher modes. Moreover, the ability of the SD in selecting structural modes without getting involved in any model-order optimization problem is highlighted through a comparison study.

Investigation of tanpura string vibrations using a two-dimensional time-domain model incorporating coupling and bridge friction

Tanpura string vibrations have been investigated previously using numerical models based on energy conserving schemes derived from a Hamiltonian description in one-dimensional form. Such time-domain models have the property that, for the lossless case, the numerical Hamiltonian (representing total energy of the system) can be proven to be constant from one time step
to the next, irrespective of any of the system parameters; in practice the Hamiltonian can be shown to be conserved within machine precision. Models of this kind can reproduce a jvari effect, which results from the bridge-string interaction. However the one-dimensional formulation has recently been shown to fail to replicate the jvaris strong dependence on the thread placement. As a first step towards simulations which accurately emulate this sensitivity to the thread placement, a twodimensional model is proposed, incorporating coupling of controllable level between the two string polarisations at the string termination opposite from the barrier. In addition, a friction force acting when the string slides across the bridge in horizontal direction is introduced, thus effecting a further damping mechanism. In this preliminary study, the string is terminated at the position of the thread. As in the one-dimensional model, an implicit scheme has to be used to solve the system, employing Newton's method to calculate the updated positions and momentums of each string segment. The two-dimensional model is proven to be energy conserving when the loss parameters are set to zero, irrespective of the coupling constant. Both frequency-dependent and independent losses are then added to the string, so that the model can be compared to analogous instruments. The influence of coupling and the bridge friction are investigated.

Determining the Presence of Scour around Bridge Foundations Using Vehicle-Induced Vibrations

Bridge scour is the number one cause of failure in bridges located over waterways. Scour leads to rapid losses in foundation stiffness and can cause sudden collapse. Previous research on bridge health monitoring has used changes in natural frequency to identify damage in bridge beams. The possibility of using a similar approach to identifying scour is investigated in this paper. To assess if this approach is feasible, it is necessary to establish how scour affects the natural frequency of a bridge, and if it is possible to measure changes in frequency using the bridge dynamic response to a passing vehicle. To address these questions, a novel vehicle–bridge–soil interaction (VBSI) model was developed. By carrying out a modal study in this model, it is shown that for a wide range of possible soil states, there is a clear reduction in the natural frequency of the first mode of the bridge with scour. Moreover, it is shown that the response signals on the bridge from vehicular loading are sufficient to allow these changes in frequency to be detected.

Mode III interlaminar fracture of carbon/epoxy laminates using the edge crack torsion (ECT) test

The mode III interlaminar fracture of carbon/epoxy laminates was evaluated with the edge crack torsion (ECT) test. Three-dimensional finite element analyses were performed in order to select two specimen geometries and an experimental data reduction scheme. Test results showed considerable non-linearity before the maximum load point and a significant R-curve effect. These features prevented an accurate definition of the initiation point. Nevertheless, analyses of non-linearity zones showed two likely initiation points corresponding to GIIIc values between 850 and 1100 J/m2 for both specimen geometries. Although any of these values is realistic, the range is too broad, thus showing the limitations of the ECT test and the need for further research.

Transverse Vibrations in Beams Supported by a Piece-Wise Homogeneous Visco- Elastic Foundation

Transversal vibrations induced by a load moving uniformly along an infinite beam resting on a piece-wise homogeneous visco-elastic foundation are studied. Special attention is paid to the additional vibrations, conventionally referred to as transition radiations, which arise as the point load traverses the place of foundation discontinuity. The governing equations of the problem are solved by the normalmode analysis. The solution is expressed in a form of infinite sum of orthogonal natural modes multiplied by the generalized coordinate of displacement. The natural frequencies are obtained numerically exploiting the concept of the global dynamic stiffness matrix. This ensures that the frequencies obtained are exact. The methodology has restrictions neither on velocity nor on damping. The approach looks simple, though, the numerical expression of the results is not straightforward. A general procedure for numerical implementation is presented and verified. To illustrate the utility of the methodology parametric optimization is presented and influence of the load mass is studied. The results obtained have direct application in analysis of railway track vibrations induced by high-speed trains when passing regions with significantly different foundation stiffness.

Discrete fractional order system vibrations

A theory of free vibrations of discrete fractional order (FO) systems with a finite number of degrees of freedom (dof) is developed. A FO system with a finite number of dof is defined by means of three matrices: mass inertia, system rigidity and FO elements. By adopting a matrix formulation, a mathematical description of FO discrete system free vibrations is determined in the form of coupled fractional order differential equations (FODE). The corresponding solutions in analytical form, for the special case of the matrix of FO properties elements, are determined and expressed as a polynomial series along time. For the eigen characteristic numbers, the system eigen main coordinates and the independent eigen FO modes are determined. A generalized function of visoelastic creep FO dissipation of energy and generalized forces of system with no ideal visoelastic creep FO dissipation of energy for generalized coordinates are formulated. Extended Lagrange FODE of second kind, for FO system dynamics, are also introduced. Two examples of FO chain systems are analyzed and the corresponding eigen characteristic numbers determined. It is shown that the oscillatory phenomena of a FO mechanical chain have analogies to electrical FO circuits. A FO electrical resistor is introduced and its constitutive voltage–current is formulated. Also a function of thermal energy FO dissipation of a FO electrical relation is discussed.