This paper presents a novel approach to the study of shock in elastic structures. An energy storage property for linear elastic non-dissipative structures is demonstrated, then extrapolated also to damped systems. This property relates locations of energy accumulation along the structure to the form of its stiffness and mass matrices. This result can be profitable used at a design stage of complex structures undergoing shock excitations. On the theoretical ground, the obtained results disclose indeed general properties of energy distribution in dynamical systems with implications on energy localization as well as on energy equipartitioning. Finally, these findings open a new point of view on energy transmission in structures, with potential application in the context of Statistical Energy Analysis.

A. Carcaterra

N. Roveri

Energy Distribution in Impulsively Excited Structures

The forces applied to a structure from the soil ground during an earthquake and the dynamic response of a structure are problems that are not well understood. In recent years, seismic design technology aided by numerical simulation is under active development. Successful improvement of the accuracy and reliability of numerically simulated results relies on a clear understanding of the seismic force transmission mechanism between the soil and a structure associated with mechanical properties of soil.In this study, laboratory shaking tests were conducted using the unique apparatus designed to have a structure move only by its inertial force and the lateral earth pressure that comes from surrounding sandy soils. The earth pressure at the structure surface and the relative displacement between the soil and the structure were measured in the experiments under various conditions. A new Finite Element interface model for sandy soil-structure dynamic interaction is proposed from the experimental results. Estimated seismic responses of a bridge pier calculated by the proposed interface model, conventional linear elastic model and tension cut-off model are compared.

N. Kodama

K. Komiya

Model Tests and FE-Modelling of Dynamic Soil-Structure Interaction

Stator vanes which are found in axial compressors are subject to vibratory fatigue. Their division into monoblock sectors makes the prediction of their vibratory behaviour difficult by deterministic methods due to the loss of the cyclic symmetry properties and also to a high sensitivity to mistuning. The purpose is to present a robust calculation strategy based on a stochastic modelisation of the structure. The methodology has been developed first on a simplified model and then applied to an industrial case. Polynomial chaos based results are in good agreement with reference Monte Carlo simulations.

A.C. Sall

F. Thouverez

L. Blanc

P. Jean

Stochastic Behaviour of Mistuned Stator Vane Sectors: An Industrial Application

This paper presents a new semi-analytical solution for the Timoshenko beam subjected to a moving load in case of a nonlinear medium underneath. The finite series of distributed moving loads harmonically varying in time is considered as a representation of a moving train. The solution for vibrations is obtained by using the Adomian's decomposition combined with the Fourier transform and a wavelet-based procedure for its computation. The adapted approximating method uses wavelet filters of Coiflet type that appeared a very effective tool for vibration analysis in a few earlier papers. The developed approach provides solutions for both transverse displacement and angular rotation of the beam, which allows parametric analysis of the investigated dynamic system to be conducted in an efficient manner. The aim of this article is to present an effective method of approximation for the analysis of complex dynamic nonlinear models related to the moving load problems.

Piotr Koziol

Zdzislaw Hryniewicz

Dynamic Response of a Beam Resting on a Nonlinear Foundation to a Moving Load: Coiflet-Based Solution

Comfort, road holding and safety of passenger cars are mainly influenced by an appropriate design of suspension systems. Improvements of the dynamic behaviour can be achieved by implementing semi-active or active suspension systems. In these cases, the correct design of a well-performing suspension control strategy is of fundamental importance to obtain satisfying results. Operational Modal Analysis allows the experimental structural identification in those that are the real operating conditions: Moving from output-only data, leading to modal models linearised around the more interesting working points and, in the case of controlled systems, providing the needed information for the optimal design and verification of the controller performance. All these characters are needed for the experimental assessment of vehicle suspension systems. In the paper two suspension architectures are considered equipping the same car type. The former is a semi-active commercial system, the latter a novel prototypic active system. For the assessment of suspension performance, two different kinds of tests have been considered, proving ground tests on different road profiles and laboratory four poster rig tests. By OMA-processing the signals acquired in the different testing conditions and by comparing the results, it is shown how this tool can be effectively utilised to verify the operation and the performance of those systems, by only carrying out a simple, cost-effective road test.

L. Soria

B. Peeters

J. Anthonis

H. Van der Auweraer

Operational Modal Analysis and the Performance Assessment of Vehicle Suspension Systems

This paper presents an integrated approach to optimize for design and control of mechanical systems with random input parameters. Random parameters are represented by probability density functions. A numerical technique defining directly the representative values and the associated probabilities is implemented by modeling the stochastic parameters as generalized Wiener processes. The Monte Carlo&#x2019;s method is also implemented to deal with correlated parameters. A design and control sensitivity analysis optimization formulation is derived. A conceptual separation between time variant and time invariant design parameters is presented, this way including the design space into the control space and considering the design variables as control variables not depending on time. By using time integrals through all the derivations, the design and control problems are unified. In the optimization process we can use both types of variables simultaneously or by interdependent levels. The dynamic response is modeled via space and time finite elements, and is integrated either by at-once integration or step-by-step. The formulation is applied to a numerical example.

P.P. Moita

J.B. Cardoso

A. Barreiros

Optimal Design and Control of Mechanical Systems with Uncertain Input

Structures include elements designated as load bearing and non-load bearing. While non-load bearing elements, such as facades and internal partitions, are acknowledged to add mass to the system, the structural stiffness and strength is generally attributed to load bearing elements only. This paper investigates the contribution of non-load bearing elements to the dynamic response of a new structure, the Charles Institute, in the grounds of University College Dublin (UCD) Ireland. The vertical vibration response of the first floor and the lateral response at each floor level were recorded at different construction stages. The evolution of the structural response as well as the generation of a finite element (FE) model is discussed. It was found that the addition of the non-load bearing facades increased the first floor natural frequency from 10.7 Hz to 11.4?Hz, a change of approximately +6.5&#x25;. Similarly these external facades resulted in the first sway mode having its frequency increased by 6&#x25;. The subsequent addition of internal partitions, mechanical services and furnishings resulted in the floor natural frequency reducing to 9.2 Hz. It is concluded that external facades have the net effect of adding stiffness and the effect of internal partitions and furnishings is to add mass. In the context of finite element modelling of structures there is a significant challenge to represent these non-structural elements correctly so as to enable the generation of truly predictive FE models.

A. Devin

P.J. Fanning

The Evolving Dynamic Response of a Four Storey Reinforced Concrete Structure during Construction

We describe a multi-component boundary element method for predicting wave energy distributions in a complex built-up system with material properties changing discontinuously at boundaries between sub-components. We point out that depending on the boundary conditions and the number of interfaces between sub-components, it may be advantageous to use a normal derivative method to set up the integral kernels. We describe how the resulting hypersingular integral kernels can be regularised. The method can be used to minimise the number of weakly singular integrals thus leading to BEM formulations which are easier to handle.

H.A.M. Ben Hamdin

G. Tanner

Multi-Component BEM for the Helmholtz Equation: A Normal Derivative Method

We investigate non-linear dynamics of flexible rectangular plates subjected to external shear harmonic load action. We show that an application of the classical and widely used Fourier analysis does not allow to obtain real picture of the frequency vibration characteristics in each time instant. On the other hand, we show that application of the wavelets approach allows to follow frequency time evolutions. Our numerical results indicate that vibrations in different plate points occur with the same frequencies set although their power is different. Hence, the vibration characteristics can be represented by one arbitrary taken plate point. Furthermore, using wavelets scenarios of transitions from regular to chaotic dynamics are illustrated and discussed including two novel scenarios not reported so far in the existing literature.

J. Awrejcewicz

I.V. Papkova

E.U. Krylova

V.A. Krysko

Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading

It is well known that nonlinear systems, as well as linear time-varying systems, are characterized by non-stationary response signals. In this sense, they both show natural frequencies that are not constant over time; this variation has however different origins: for a time-varying system the mass, and possibly the stiffness distributions, are changing over time, while for a nonlinear system the natural frequencies are amplitude-dependent. An interesting case of time-varying system occurs when analyzing the transit of a train over a railway bridge, easily simulated by the crossing of a moving load over a beam. In this case, the presence of a nonlinearity in the beam behaviour can cause a significant alteration of the modal parameters extracted from the linearized model, such that the contributions of the two effects are no more distinguishable.For this study, some reinforced concrete beams have been tested in the framework of a vast project: these beams show a clear softening nonlinear behaviour, well detectable when the excitation is produced by a hammer (free response). If the passage of a carriage is considered, moreover, the variation of natural frequencies is always larger than expected because of this softening nonlinearity.The article first analyzes theoretically the two effects on the natural frequencies of a simply supported beam, then a numerical and an experimental tests are presented. The identification procedure is conducted with a linear algorithm called ST-SSI, which has been demonstrated to be appropriate for the analysis of non-stationary signals, in particular in presence of moving masses. The article shows that the nonlinear contribution can be well estimated by using this linear tool but, on the contrary, when also moving masses are present, it is difficult to separate the nonlinear effects from the time varying ones.

A. Bellino

S. Marchesiello

L. Garibaldi

Experimental Dynamic Analysis of Nonlinear Beams under Moving Loads

About this journal

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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Shock and Vibration

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