Publications and papers on dynamics, vibrations and finite element analysis

Table of Contents

• Influence of the High Speeds of Moving Trains on the Dynamic Behaviour of Multi-Span Bridges
• An Efficient Program for the Dynamic Analysis of Structures using exact approach
• Application of Asymptotic Method to Transient Dynamic Problems with Non Periodic Loading
• On the Investigation of Material Damping Parameter, identification Based on Laboratory Test Results, using Neural Network
• AN EFFICIENT ALGORITHM FOR DYNAMIC ANALYSIS OF BRIDGES UNDER MOVING VEHICLES USING A COUPLED MODAL AND PHYSICAL COMPONENTS APPROACH
• Application of the Artificial Neural Networks in Structural and Bridge Damage Detection and Identification
• Dynamic Analysis of the Structure-Vehicule Interaction in the Highway Bridges. Part I: Numerical Aspect
• Dynamic Analysis of the Structure-Vehicule Interaction in the Highway Bridges. Part II: Application to the Senneterre Bridge in Quebec.
• DYNAMIC BEHAVIOUR OF MULTI-SPAN BEAMS UNDER MOVING LOADS
• Dynamic Behavior of continuous beams Under Moving Loads. Finite Elements and semi-Analytical Approaches
• On the investigation of material damping parameter identification based on laboratory test results using neural network
• Numerical Solution of Transient Dynamic Problems Using Asymptotic Method

1999. On the Investigation of Material Damping Parameter, identification Based on Laboratory Test Results, using Neural Network. The Fourth International Conference of the European Association for Structural Dynamics (EASD, EURODYN'99), 7-10 June 1999. Prague, Czech Republic.

AN EFFICIENT ALGORITHM FOR DYNAMIC ANALYSIS OF BRIDGES UNDER MOVING VEHICLES USING A COUPLED MODAL AND PHYSICAL COMPONENTS APPROACH

Abstract: A general and efficient method is proposed for the resolution of the dynamic interaction problem between a bridge, discretized by a three-dimensional finite element model, and a dynamic system of vehicles running at a prescribed speed. The resolution is easily performed with a step-by-step solution technique using the central difference scheme to solve the coupled equation system. This leads to a modified mass matrix called a pseudo-static matrix, for which its inverse is known at each time step without any numerical effort. The method uses a modal superposition technique for the bridge components. The coupled system vectors contain both physical and modal components. The physical components are the degrees of freedom of a vehicle modelled as linear discrete mass-spring_damper systems. The modal components are the degrees of freedom of a linear finite element model of the bridge. In this context, the resolution of the eigenvalue problem for the bridge is indispensable. The elimination of the interaction forces between the two systems (bridge and vehicles) gives a unique coupled system (supersystem) containing the modal and physical components. In this study, we duly consider the bridge pavement as a random irregularity surface. The comparison between this study and the uncoupled iterative method is performed.

Application of the Artificial Neural Networks in Structural and Bridge Damage Detection and Identification

Resume. Cet article presente Ie developpement d'une methode d'identification d'endommagement dans les structures. Celie etude est basee sur l'utilisation des reseaux neuronaux artificiels et de leur auto-organisation dans l'evaluation de l'endommagement structural. L'idée de base est d'entralner Ie reseau pour comprendre Ie comportement de la structure avec diffirents etats d'endommagement. Quand les resultat.f experimentaux .w'rmzt presentes au reseau, il sera capable de detecter avec succes la presence ou non de l'endommagement dans la structure. Trois exemples SOlll examines etles resultats obtenus sont prometteurs.MOTS-CLES: dynamique, elemeents finis, idetification, reseaux de neurones, retro-propagation, structures.

Abstract: This paper presellls the development of an automatic monitoring method for the detection of structural damage. In this feasibility study, we have explored the use of fell-organisation of artificial neural networks in structural damage assesment combined with the finite element method. The basic strategy is to train the network to recognise the behaviour of the structure with various possible damage states. When the trained network is subjected to the measurements of the structural response, it should be able to detect any existing damage. Three examples are examined and the results are promising. KEY WORDS: back propagation, dynamic, finite elements, identification, neural networks, structural

Dynamic Analysis of the Structure-Vehicule Interaction in the Highway Bridges. Part I: Numerical Aspect

Resume: Dans cet article, nous presentons une methode generale et efficace pour l'analyse dynamique des ponts routiers avec la prise en compte de l'interaction pont-vehicules et du profil de la route d'une maniere tres realiste. Dans cette approche, la structure du pont peut etre modelisee par elements finis d'une fayon tridimensionnelle en utilisant des elements de coques et de poutres. Le modele de vehicule est represente d'une maniere discrete it partir des equations de Lagrange. Cette methode utilise la technique de la superposition modale pour les composantes du pont, avec une correction du deplacement basee sur la methode d'acceleration modale. La methode de resolution des equations de mouvement de chaque systeme pont et vehicules est celle de Newmark et la solution est obtenue it partir d'un processus iteratif des forces d'interaction entre Ie pont et les vehicules. Un exemple academique simple est presente pour montrer la validite de l'algorithme ainsi developpe. Mots cles: coque, dynamique, elements finis, interaction, pont, rugosite, vehicule.

Abstract: In this paper,a general and efficient procedure for the dynamic analysis of road bridges is presented, that takes into account bridge-vehicle interaction and the road profile in a realistic way. With this approach, the bridge structure can be modeled with a tridimensional finite element method using shell and beam elements. The vehicle model is represented using a discrete method based on Lagrange equations. This method uses the modal superposition technique for the bridge components, with a correction for the displacement based on the method of modal acceleration. The Newmark-_ method is used to solve the movement equations of each bridge and vehicles system and the solution is obtained through an iterative process of the interactive forces between the bridge and the vehicles. A simple academic example is presented to show the validity of the proposed algorithm. Key words: shell,dynamics, finite elements, interaction, bridge, roughness, vehicle.

Dynamic Analysis of the Structure-Vehicule Interaction in the Highway Bridges. Part II: Application to the Senneterre Bridge in Quebec.

Resume: Dans cet article, nous presentons une application de l'algorithme de l'interaction dynamique pont-vehicules que nous avons developpe et presente dans l'article qui precede. Nous comparons les resultats numeriques et ceux obtenus a partir de tests experimentaux des frequences et modes propres et en vibrations forcees effectues sur Ie pont de Senneterre situe au Québec. Le modele numerique du pont est obtenu par une modelisation tridimensionnelle par elements finis, en utilisant des elements de coques et de poutres, en tenant compte de l'interaction pont-vehicules et du profil de la route d'une fayon realiste. Le modele numerique du vehicule utilise dans la province de Quebec est represente d'une maniere discrete selon des parametres mecaniques calibres et ajustes a partir des resultats experimentaux. Vne etude parametrique a ete realisee par la suite. Cette etude permet de mettre en evidence quelques recommandations quant a la resistance des ponts aux effets dynamiques et l'etablissement d'un facteur d'amplification dynamique adapte aux conditions specifiques de chargement des ponts. Mots cles: coque, dynamique,elements finis, interaction, pont, rugosite, vehicule, facteur d'amplification, essais experimentaux.

Abstract: In this paper, an application ofthe algorithm for the dynamic analysis of bridge-vehicles interaction that the authors developed in the preceeding paper is presented. The numerical results are compared to the results obtained from experimental tests of frequencies and mode shapes and from forced vibrations carried out on the Senneterre bridge located in Quebec. The numerical model ofthe bridge is obtained by tridimensional finite element modeling, using shell and beam elements, and taking into account bridge-vehicles interaction and the road profile in a realistic way. The numerical vehicle model used in the province of Quebec is represented in a discrete form based on mechanical parameters calibrated and adjusted according to experimental results. A parametric siudy was then carried out. The results of this study allow us to present some recommendations with regard to bridge resistance to dynamic effects and the determination of a dynamic amplification factor based on the specific loading conditions of the bridge. Key words: shell, dynamic, finite elements, interaction, bridge, roughness, vehicle, amplification factor, experimental tests.

DYNAMIC BEHAVIOUR OF MULTI-SPAN BEAMS UNDER MOVING LOADS

Abstract:In this paper, an exact dynamic stiffness element under the frame work of finite element approximation is presented to study the dynamic response of multi-span structures under a convoy of moving loads. A dynamic model coupled,with a FFT algorithm is developed. Tffe model is highly efficient for calculating the response of bridges under multiaxle moving forces. All the vibration frequencies and mode shapes of the beam-structure may be calculated exactly using the Wittrick and Williams algorithm. Examples show that with only one element per span, exact frequeneies and modes could be obtained. Some results on the dynamic amplification factor are presented also as a function of the speed of the moving loads.

Dynamic Behavior of continuous beams Under Moving Loads. Finite Elements and semi-Analytical Approaches

RESUME. Nous presentons dans cet article une etude comparative des effets de la force et de la masse mobiles sur Ie comportement dynamique des poutres. Nous presentons une nouvelle approche appelee approche semi-analytique des vibrations des poutres sous les effets des masses mobiles, pour les problemes de poutres continues ou ponts multi-travees, en utilisant la methode de la matrice de rigidite dynamique exacte. Une approche par elements finis pour les problemes de structures (ponts) sollicitees par des forces et masses mobiles est egalement presentee. De plus, les resulrats obtenus montrent que pour des cas de vitesses importantes et des rapports importants de la masse mobile la masse totale de la poutre (cas des ponts rails pour trains a grandes vitesses), la reponse des structures sous masses mobiles doit etre prise en compte a cause des effets significatifs d'inertie qui sont negliges da1ls Ie modele des forces mobiles.

ABSTRACT. In this work, a comparative study between the effects of moving force and the moving mass on the dynamic beheviour of beams is presented.

Abstract: A new semi-analytical approach of beam vibrations under the effect of moving masses for the problems of continuous beams or multi-span bridges using the exact dynamic stiffness matrix method is presented. We also present, finite element approach on structural problem (bridges) under mobile forces and masses. Moreover, in this study, we demonstrate that in the case of high mass speed and high ratio between the moving mass and the mass of the beam (case of fast train railway bridges), the structural response under moving masses must be taken into account because of their significant effects which are neglected in moving force models. MOTS-CLES: elements finis, force mobile, masse mobile, matrice de rigidite dynamique, pont KEY WORDS: finite element, moving force, moving mass, dynamic stiffness matrix, bridge, bridge

1999. Application of Asymptotic Method to Transient Dynamic Problems with Non Periodic Loading. In the Fourth International Conference of the European Association for Structural Dynamics (EASD, EURODYN'99), 7-10 June 1999. Prague, Czech Republic.

Abstract: A new method to solve linear dynamics problems using an asymptotic method is presented. Asymptotic methods have been efficiently used for many decades to solve non-linear quasi static structural problems. Generally, structural dynamics problems are solved using finite elements for the discretization of the space domain of the differential equations, and explicit or implicit schemes for the time domain. With the asymptotic method, time schemes are not necessary to solve the discretized (space) equations. Using the analytical solution of a single degree of freedom (DOF) problem, it is demonstrate, that the Dynamic Asymptotic Method (DAM) converges to the exact solution when an infinite series expansion is used. The stability of the method has been studied. DAM is conditionally stable for a finite series expansion and unconditionally stable for an infinite series expansion. This method is similar to the analytical method of undetermined coefficients or to power series method being used to solve ordinary differential equations. For a multi-degree-of-freedom (MDOF) problem with a lumped mass matrix, no factorization or explicit inversion of global matrices is necessary. Jt is shown that this conditionally stable method is more efficient than other conditionally stable explicit central difference integration techniques. The solution is continuous irrespective of the time segment (step) and the derivatives are continuous up to orderN-l where N is the order of the series expansion.

2003. Influence of the High Speeds of Moving Trains on the Dynamic Behaviour of Multi-Span Bridges: Comparative Study with Various Types of French Bridges Proceedings of the Ninth International Conference on Civil and Structural Engineering Computing, 2-4 Sept 2003, paper (85). Amsterdam, Holland.

Keywords: Bedas software, bridge, dynamic amplification factor, dynamic stiffness, moving load, high frequencies, TGV, vibrations.

Abstract: In this paper, we present a recent new efficient and practical method implemented in the Bedas software, to model the dynamic and transient vertical vibrations of trussed and multi-span railway bridges, induced by moving multi-axle high-speed train. The speeds of train varying from 150 to 400 km/h are considered. The influence of the speed of moving multi-axle train on the dynamic response especially in the resonance zones is studied on three existing multi-span two-beams bridges (concrete-steel section). These three bridges are located in France and they were designed for the French high-speed train TGV. This study presents a specially developed Bridges Exact Dynamic Analysis Software program called BEDAS, which can be routinely used to analyse the static and dynamic behaviours of common type bridge structures. The advantages of BEDAS are:

• the program uses an exact dynamic stiffness method and gives exact frequencies and mode shapes with only one element per span;
• finite dynamic model based on exact dynamic expression leads to higher precision of internal forces at any location of the bridge;
• the program is applicable for studying the dynamic behaviour of common type of bridge structure including slab on I-beam bridges

BEDAS has been developed in such a way that it is applicable to any bridge structure discretized by beam elements (continuous beams bridge, frames, trusses, etc.).

1999. An efficient program for the dynamic analysis of bridges using exact approach In the Fourth International Conference of the European Association for Structural Dynamics (EASD, EURODYN'99), 7-10 June 1999. Prague, Czech Republic.

Abstract:A method to model the dynamic behaviour of bridges under dynamic and multi axle moving loads using the exact dynamic stiffness is proposed. This method gives the exact frequencies and mode shapes by using only one element per span. Dynamic analysis in frequency domain offers an effective means of evaluating the dynamic response of linear structure excited by moving and fixed loads. A program has been developed to perform the previous proposed method. Some numerical examples using moving loads of a different types of fast speed train show the validity of the model. The developed program provides very good results with- few dynamic finite elements (DFEM) and computational effort is very low compared to the classical finite element method (FEM).

On the investigation of material damping parameter identification based on laboratory test results using neural network

Abstract: An original way for modelling material damping in dynamical systems together with an identification method that can be easily used to calibrate parameters using laboratory test results are presented. New approach for modelling material damping of structures based on thermodynamic principles has been developed recently. The main feature of the present investigation is the introduction of material dissipation energy at a constitutive level that has been separated into elastic and dissipative parts. This approach allows, when the finite element model is formulated, the use of the same assemblage techniques applied for mass and stiffuess matrices. The back-propagation neural networks model has been investigated for parameters identification of the proposed damping model using laboratory tests. A closed agreement between the numerical model results after calibration and the ones obtained experimentally was observed.

Numerical Solution of Transient Dynamic Problems Using Asymptotic Method

Abstract: The so called asymptotic method has been known for more than a century. It is being used to find the solution of problems through an asymptotic development. Until now the main difficulty was in the manipulation of the asymptotic development by hand calculations. Nowadays, using symbolic software, it is easier to manipulate algebra of asymptotic method even for very high order. Some researchers have adopted the asymptotic method in order to solve structural stability problems. Koiter [1] was one of the pioneers in this field and his Ph.D. thesis was on the stability of structures using the perturbation method. In the seventies, many developments were made by Budiansky [2] and Poitier-Ferry [3] which were based on Koiter's work. The first interesting article on the application of the asymptotic method with the finite element formulation to solve polynomial non-linear quasi-static problems was published by Damil and Poi tier-Ferry [4]. Subsequently, Cochelin et al. [5] have presented many results based on this approach and they have proved that numerical asymptotic method can be efficiently used to solve elastic non-linear problems using the finite element method. Recently, Ammar [6] has extended the asymptotic numerical method, in which the equilibrium equations are not based on a polynomial form of the displacement field, as it's the case of plate/shell finite element formulation using large rotation theory. In this paper, a new approach, called Dynamic Asymptotic Method (DAM), is presented for the solution of transient dynamic problems using the asymptotic method [7]. With the finite element discretization scheme in space, the linear dynamic problem gives rise to a set of ordinary differential equations of the form: [M]{A(t)} + [C]{V(t)}+ [K]{D(t)} = {F(t)}