During the last decades a great variety of methods have been proposed for damage detection by using the dynamic structure characteristics, however, most of them require modal data of the structure for the healthy state as a reference. In this paper the applicability of the mode shape curvature squares determined from only the damaged state of the structure for damage detection in a beam structure is studied. To establish the method, two aluminium beams containing different-size mill-cut damage at different locations are tested by using the experimentally measured modal data. The experimental modal frequencies and the corresponding mode shapes are obtained by using a scanning laser vibrometer with a PZT actuator. From the mode shapes, mode shape curvatures are obtained by using a central difference approximation. With the example of the beams with free-free and clamped boundary conditions, it is shown that the mode shape curvature squares can be used to detect damage in the structures. Further, the extent of a mill-cut damage is identified via modal frequencies by using a mixed numerical-experimental technique. The method is based on the minimization of the discrepancy between the numerically calculated and experimentally measured frequencies.

S. Rucevskis

M. Wesolowski

Identification of Damage in a Beam Structure by Using Mode Shape Curvature Squares

Annoying building floor vibrations have become a serious serviceability issue. This is mainly due to decrease in the system mass resulting from the use of higher strength materials; use of computer-assisted design and the Load and Resistance Factor Design Method to optimize the structure based on the strength requirements; fewer partitions and more innovative designs by architects achieving long, column free spans resulting in a reduction in the natural frequency and damping. This paper provides details of the vibration analysis and design of a novel office building. Three-dimensional computer models of the structure were created and various modifications were made to the original structure, designed based on static loads, to reduce the possible excessive floor vibrations when subjected to walking excitations. Tuned mass dampers were also designed as a back-up vibration control system. A series of dynamic tests were conducted on the building floor to identify the dynamic properties of the structure and these were then used to update the original computer model. Finally, various forcing functions representing human walks and the updated computer model of the structure were used to evaluate the accuracy of the walking excitation force models to predict the structural response. Conclusions are made on the validity of each forcing function studied here.

M. Setareh

M. Lovelace

Vibration Analysis and Design of a Structure Subjected to Human Walking Excitations

This paper analyses theoretically the response of a solid for fast moving trains using models related to real situations: a load moving in a tunnel and a load moving on a surface. The mathematical model is described by Navier's elastodynamic equation of motion for the soil and Euler-Bernoulli equation for the beam with appropriate boundary conditions. Two modelling approaches are investigated: the model with half space under the beam and the model with finite thickness of supporting medium. The problem of singularities for displacements calculation is discussed in relation with boundary conditions and types of considered loads: harmonic and constant, point and distributed moving loads. The analysis in frequency-time and frequency-velocity domains is presented and discussed with regard to critical velocities.A wavelet approximation method based on application of coiflet filters is used for the derivation of displacements in physical domain. A new, modified filter is used in numerical calculations allowing to alleviate numerical difficulties related to the form of approximating sequences based on classical filters, formulated in previous publications. The effectiveness of the coiflet approach is discussed for filter coefficients with different order of accuracy. This methodology is very efficient for the analysis in the range of relatively high and low load frequencies (treated as an approximation of a constant load) which are especially important for the analysis of vibrations generated by trains moving with velocities near critical values.Results of numerical simulations are presented, demonstrating their utility for modelling and preliminary analysis of complex models.

Piotr Koziol

Cristinel Mares

Wavelet Approach for Vibration Analysis of Fast Moving Load on a Viscoelastic Medium

This article presents a study on the use of the dynamical response of multi-laminated periodic bars to create resonance band gaps within useful frequency ranges. The objective is to control, in a passive form, the longitudinal vibration transmissibility in specific and wide enough frequency ranges of interest. This is achieved by the separation of two adjacent eigenfrequencies. A relation between the modal analysis, the harmonic analysis and the Bloch wave theory is proposed, for which no reference was found in the searched literature. As shown, the selection of appropriate material pairs is essential to obtain useful frequency ranges. The use of pairs of steel and cork agglomerate is proposed, since it allows the design of attenuators at lower frequencies through a prediction based on finite element analysis (FEA). This approach requires the storage modulus of cork for which analytical and numerical FEA models were verified and validated. A methodology to obtain experimentally the storage modulus of cork is presented. Regarding the structural improvement problem, we discuss a methodology to design periodic bars for a specific location of the first attenuation's frequency range and illustrate the main results through several examples.

H. Policarpo

M.M. Neves

A.M.R. Ribeiro

Dynamical Response of a Multi-Laminated Periodic Bar: Analytical, Numerical and Experimental Study

This paper presents a novel approach in the field of experimental and numerical investigation of mechanical properties of composite structures. It takes into account test data variability resulting from structural dynamic properties measurement and uses them to quantify uncertainties in model parameters updating. The main goal of the conducted research is to investigate the dynamic properties of fibre reinforced composite structures. Non-destructive experimental and numerical simulation methods are used hereto. In the experimental part, different test configurations were taken into account. The excitation was performed by means of random and harmonic, single and multi point stimuli while the response measurement was done through contact and non-contact acceleration, velocity and dynamic strain sensing. The test results are applied in two ways: for the structural identification of the object and for non-deterministic updating of the numerical model according to a range of experimental models obtained from test. The sources of the test data variabilities were related to the excitation and measurement technique applied for the investigated object. Non &#x2013; deterministic model updating and verification &#x26; validation included uncertainties of its parameters by means of interval and stochastic methods. A number of variable test modal models were statistically assessed to investigate impact of variability source onto modal model parameters. The presented research was conducted in the context of the FP6 Marie Curie project UNVICO-2.

Marcin Luczak

Antonio Vecchio

Bart Peeters

Ludo Gielen

Herman Van der Auweraer

Uncertain Parameter Numerical Model Updating According to Variable Modal Test Data in Application of Large Composite Fuselage Panel

Unique conductor-pole couplings complicate the dynamic behaviors of electric transmission pole line systems. Finite element modeling is performed on two typical transmission poles used in southeastern USA &#x2013; a steel pole and a prestressed concrete pole. The two poles are representative of unique structure types: a heavy rod-like structure and a lightweight, shell-type structure. Since coupling issues between the pole and the cable introduce great complexities for modeling the pole line system, simplified numerical models are used. Limited full-scale modal test results are presented to verify the numerical models. The prestressed concrete pole is shown to be easier for mode identification than the steel pole &#x2013; but both numerical models show complicated coupled vibration modes. This study is part of a larger study to establish an understanding of the dynamic response analyses of power grid under ground vibrations.

Shen-En Chen

Kaoshan Dai

Modal Characteristics of Two Operating Power Transmission Poles

Mode Indicator Functions (MIFs) are real-valued frequency-dependent scalars that exhibit local minima or maxima at the modal frequencies of the system. This paper presents an overview of the currently used and some recently developed MIFs, revealing their features and limitations. Eigenvalue or singular value based MIFs use rectangular frequency response function (FRF) matrices calculated in turn at each excitation frequency. Their plots have as many curves as the number of references. Recently developed MIFs do the simultaneous analysis of all FRF information organized in a compound FRF (CFRF) matrix. The left singular vectors or the Q-vectors obtained from the pivoted QLP decomposition of this matrix contain the frequency information and are used to construct MIFs. The number of curves in such a MIF plot is equal to the effective rank of the CFRF matrix. If the number of response coordinates is larger than this rank, a single point excitation can locate even double modes. The condition to use as many input points as the multiplicity of modal frequencies is no more imposed.

M. Rade&#x15f;

Performance of Various Mode Indicator Functions

The paper presents a structural health monitoring system based on propagation of tuned Lamb waves and their interference with discontinuities. The dispersion curves are studied to determine the appropriate type and dimension of transducers and to select the optimum scanning frequencies and relevant propagation modes. A piezoelectric sensor network was implemented in an aluminum plate in order to generate and to sense the wave propagation and associated reflections. The algorithm developed for damage detection relies on the comparison of undamaged and damaged responses of the structure. Combinations of filters and statistical methods were applied to detect differences in the sensor signals acquired for the two different states (damaged and undamaged), corresponding to damage reflections. In order to eliminate the false positives due to noise, a probability analysis is performed to obtain the final damage position. The software designed for the current application allows the automatic calculation of dispersion curves, it executes the scans, performs data processing, executes the detection algorithm and presents the probable damages and their positions in a graphical form. Experiments were performed with the introduction of cumulative damages in the plate such as surface and through-the-thickness holes and cuts, ranging from 7 mm to 1 mm in diameter. Additionally, a stringer was attached to the plate by a single rivet line to simulate an aircraft skin structure. Cuts originating from rivet holes and connecting adjacent rivets, as well as loosened rivets were detected by the system. The introduction of the stringer resulted in a loss of precision in the determination of the radial position of the damages near it. Also, the network revealed significant difficulties in the detection of damages beyond the stringer.

Bruno Rocha

Carlos Silva

Afzal Suleman

Structural Health Monitoring System Using Piezoelectric Networks with Tuned Lamb Waves

A sensitivity analysis and multicriteria control optimization formulation is derived for mechanical systems. This formulation is implemented into an interactive optimum design code and it is applied to optimize protection systems for the prevention of injuries. The limiting isolation capabilities of the systems are determined. The effect of pre-acting control is investigated. Control forces as well as the time at which the control should act before the instant of impact are considered as design variables. The same idea used by the authors in previous articles for minimum time control problems is applied here to find the preview time. Dynamic response index, maximum acceleration, rattlespace, or maximum power of the resisting force among others can be used as performance criteria. In order to handle the multicriteria problem, both the reduced feasible region method and a min-max upper bound method are utilized. The adjoint system approach is used to calculate the sensitivities. The dynamic response of the systems and its sensitivity are discretized via space-time finite elements. The equations of motion and the sensitivity equations are integrated at-once as it is typical for the static response. This way, displacement, velocity or acceleration control conditions can be imposed easily at any point in time. Also, adjoint system response is obtained without needing primary response memorization. Mathematical programming is used for the optimal control process.

J.B. Cardoso

P.P. Moita

A.J. Valido

Multicriteria Optimization of Injury Prevention Systems to Impact

The design of passive damping treatments using viscoelastic materials requires both an accurate numerical analysis approach, usually making use of the finite element method, and a realistic means of material description. While the former has been widely studied and several and valuable approaches have become available during the last years, the latter is still an issue requiring additional efforts. The experimental characterization, the data modeling and finally the constitutive models able to be directly used along analytic and numerical analysis, are still important research areas. Several viscoelastic models, able to be directly applied into a finite element analysis either in a time or in a frequency domain analysis, are available and have been widely used during the last years in most of the published work. Despite the general description and straightforward use that such modeling approaches may provide, temperature effect is usually disregarded and isothermal analysis are usually performed. Moreover, this temperature effect is naturally not directly considered as an input parameter for most of the viscoelastic material models and isothermal conditions are also considered in the experimental characterization data analysis. This work presents an extended viscoelastic model, based on well known isothermal models, where the temperature-frequency superposition effect is directly considered. The extended model is applied to the analysis of the experimental data using a data fitting procedure to identify a set of global parameters able to represent the effect of the frequency and the temperature.

R.A.S. Moreira

J.D. Corte-Real

J. Dias Rodrigues

A Gneralized Frequency-Temperature Viscoelastic Model

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Shock and Vibration publishes papers on all aspects of shock and vibration, especially in relation to civil, mechanical and aerospace engineering applications, as well as transport, materials and geoscience.&nbsp;

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Chief Editor&nbsp;Dr Tai Thai&nbsp;is based at the University of Melbourne and his current research focuses on high strength materials for sustainable construction of buildings, bridges and other infrastructure.

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