Dynamic fracture mechanics

The dynamic behavior of rigid-block structures resting on a rigid foundation subjected to horizontal harmonic excitation is examined. For slender structures, the nonlinear equation of motion is approximated by a piecewise linear equation. Using this approximation for an initially quiescent structure, safe or no-toppling and unsafe regions are identified in an excitation amplitude versus excitation frequency plane. Furthermore, several possible modes of steady-state response are detected, and analytical procedures are developed for determining the amplitudes of the predominant modes and for performing stability analyses. It is shown that the produced stability diagrams can be beneficial to assessing the toppling potential of a rigid-block structure under a given amplitude-frequency combination of harmonic excitation; in this manner the integration of the equation of motion is circumvented.

Closure of "Rocking of Rigid Blocks Due to Harmonic Shaking"

https://pureadmin.qub.ac.uk/ws/files/17180680/20120319_JSV_Manuscript_v2.pdf

Identification of damping in a bridge using a moving instrumented vehicle

This paper presents experiences and lessons from the structural health monitoring practice on the Tamar Bridge in Plymouth, UK, a 335-m span suspension bridge opened in 1961. After 40 years of operations, the bridge was strengthened and widened in 2001 to meet a European Union Directive to carry heavy goods vehicles up to 40 tonnes by a process in which additional stay cables and cantilever decks were added and the composite deck was replaced with a lightweight orthotropic steel deck. At that time, a structural monitoring system comprising wind, temperature, cable tension and deck level sensors was installed to monitor the bridge behaviour during and after the upgrading. In 2006 and 2009, respectively, a dynamic response monitoring system with real-time modal parameter identification and a robotic total station were added to provide a more complete picture of the bridge behaviour, and in 2006 a one-day ambient vibration survey of the bridge was carried out to characterize low-frequency vibration modes of the suspended structure. Practical aspects of the instrumentation, data processing and data management are discussed, and some key response observations are presented. The bridge is a surprisingly complex structure with a number of inter-linked load–response mechanisms evident, all of which have to be characterized as part of a long-term structural health monitoring exercise. Structural temperature leading to thermal expansion of the deck, main cables and additional stays is a major factor on global deformation, whereas vehicle loading and wind are usually secondary factors. Dynamic response levels and modal parameters show apparently complex relationships among themselves and with the quasi-static load and response. As well as the challenges of fusing and managing data from three distinct but parallel monitoring systems, there is a significant challenge in interpreting the load and response data firstly to diagnose the normal service behaviour and secondly to identify performance anomalies. Copyright © 2012 John Wiley & Sons, Ltd.

/pdf/structural-health-monitoring-of-the-tamar-suspension-bridge-u6h0yu5lis.pdf

Structural health monitoring of the Tamar suspension bridge

This study examines the rationale of Hilbert-Huang transform (HHT) for analyzing dynamic and earthquake motion recordings in studies of seismology and engineering. In particular, this paper first p...

Hilbert-Huang transform analysis of dynamic and earthquake motion recordings

Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor : EMD-HT method

An analysis is given of the statistical and probabilistic properties of the random time at which a piece of essential equipment, such as a computer, may topple under base excitations. The equipment is modeled as a rigid block, and the base accelerations are modeled as white noises in horizontal and vertical directions. The cases of a free-standing block and an anchored block are both considered. The white-noise idealization resembles the most intense portion of ground acceleration in a seismic event, which is an acceptable simplification provided that the correlation times of actual base excitations are short compared with the dominant quasi-periods of the induced rocking motion. It is shown that the presence of vertical excitation about one-half the level of horizontal excitation may increase the probability of toppling by 30–40%, and that larger blocks are more stable than the smaller ones of the same geometrical proportion. The analysis is applicable to such objects as monuments, storage tanks, and certain types of tall buildings.

Toppling of computer-type equipment under base excitation

Currently, the kriging and conditional probability density function (CPDF) methods are widely used in solving the conditional simulation problems involving stochastic processes and fields. For the fundamental understanding of these two methods, this paper considers their applications to the conditional simulation of a one-dimensional, univariate and stationary stochastic process or field. The major findings of this study are as follows. First, the two methods are completely equivalent if the stochastic process is Gaussian with a zero mean. Specifically, the best linear unbiased estimate (BLUE) and the kriging variance are identical to the corresponding conditional mean and variance, respectively. Second, when the kriging method is used, the conditional simulation of a nonzero mean stochastic process (with a known value of the mean) is not equivalent to the (nonzero) mean plus the conditional simulation of the zero mean stochastic process obtained by subtracting the nonzero mean from the original process. Third, it can be shown that the second moment of the process conditionally simulated with the help of the kriging method are not identical to the target second moment (a priori known statistics). Finally, the kriging method is not suitable for the conditional simulation of non-Gaussian stochastic processes if no other assumptions or conditions are made for the reasons indicated in the paper, although the estimation (BLUE) may still be performed, as claimed by its proponents.

Equivalence between Kriging and CPDF Methods for Conditional Simulation

Modeling, synthetics and engineering applications of strong earthquake wave motion

A model for earthquake ground motion is developed using principles of geophysics and stochastics in a sequence of two papers. In the first paper, the earth is idealized as being composed of horizontally stratified layers, with uniform physical properties for each layer. The seismic source is modeled as a concentrated seismic moment located within one of the layers. The partial differential equations for the seismic motion in each layer are solved using a Fourier finite-Hankel transformation approach, and solutions in terms of state vectors of displacements and forces are converted to wave vectors composed of up-going and down-going waves. Transmission and reflection matrices are obtained for each layer, for each layer-to-layer interface, and for the free ground-surface boundary to characterize their roles in transmitting and reflecting a wave motion. The use of these matrices allows the numerical calculation to be channeled in the directions of wave propagation, resulting in better numerical accuracy. An example is included for illustration.

Ruichong Zhang

Papers

Modal parameter identification of Tsing Ma suspension bridge under Typhoon Victor : EMD-HT method

Toppling of computer-type equipment under base excitation

Equivalence between Kriging and CPDF Methods for Conditional Simulation

Modeling, synthetics and engineering applications of strong earthquake wave motion

Earthquake Ground Motion Modeling. I: Deterministic Point Source