RJAV vol IX issue 2/2012 77 ISSN 1584-7284 Modal Analysis of the Viaducts Supported on the Elastomeric Insulators within the Bechtel Constructive Solution for the Transilvania Highway Polidor BRATU “Dun<rea de Jos” University of GalaYi, Faculty of Engineering of Br<ila,, e-mail: icecon@icecon.ro Ovidiu VASILE Department of Mechanics, University Politehnica of Bucharest, Splaiul Independentei, 313, Bucharest, Romania, ovidiu_vasile2002@yahoo.co.uk Abstract: - The article presents an approach of six degrees dynamic model of a rigid-solid with some types of symmetries. These symmetries lead to simplified mathematical models, which are easier to solve. If the rigid-solid is jointed of the structure by four elastic bonds, the mathematical model becomes still simple and the vibrations are decoupled into four subsystems of movements: side slipping and rolling, forward motion and pitching, galloping motion, gyration. There is also a case study: the modal analysis of a bridge with the total length of 200 meters, 13.2 meters width and 2.5 meters height, modeled as a rigid solid supported elastically for the Transilvania highway. Keywords: - bearings, proper modes, decoupled vibrations 1. DYNAMIC AND PHYSICAL MODELLING OF AN ELASTICALLY SUPPORTED VIADUCT The developed physical model is based on the rigid solid hypotheses with six degrees of dynamic freedom with trirectangular elastic bonds, definited as discrete elastic bearings. The elastic and inertial characteristics are represented by measurable parameters depending on the structure and the configuration of the system. The differential equations of motion of the linear vibrations for the rigid solid with visco-elastic bonds are coupled elastically, as a rule. As matric form this system can be written: f q C q B q A ? - - % % % , (1) where A is the matrix of inertia (masses, statical moments, moments of inertia) B - the (damping) viscous dissipation matrix) C - the (of elasticities) rigidity matrix q / q % / q % % - the vectors of the generalized accelerations/velocities/coordinates f - the vector of the generalized forces Since the system (1) is difficul to be solved analytically or using the matric formalism, it takes into consideration certain geometric and structural conditions for the rigid solid as vibratory system, that leads to the equations system decoupling into the simpler subsystems and easy to be integrated. In addition, it can be considered that the rigid bonds are elastic or with small dampings, the equations of motion simplifying itself by the cancellation of the dampings. In this hypothesis, the system of the differential equations of motion, under the action of some outer disturbances, reduces becoming: f q K q M ? - % % (2) For the determination of the vibration proper modes, the rigid solid is considered in state of non- disturbed stable static balance. The matric formalism applied for the transpose of the differential equation of motion, can lead to the form: 0 ? - q K q M % % (3) To adopt the main and central system of axes, the inertia matrix becomes diagonal, the system of differential equations of motion, remaining coupled elastically but decoupled inertial. In this case, the inertia matrix is diagonal, as follows: ] _ z y x J J J m m m DIAG M , , , , , ? , (4) where m is the mass of the rigid, and x J , y J and z J are the main inertia moments. 2. STRUCTURAL SYMMETRIES OF THE VIADUCT The viaduct is constituted of five sections, each section being carried out of four “Bechtel”