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“Computational Civil Engineering - "Intersections" International Journal

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“Computational <strong>Civil</strong> <strong>Engineering</strong> 2005”, <strong>International</strong> Symposium 245In the special case when ω = ω 1 one of the undamped natural frequencies,one of the roots0θ i= θ = and equation (13) reduces to:190[ ]{ ψ } = { }ω c (14)1 1Γ 15. CONCLUSIONSIn conclusion:1. For each frequency of excitation there are as many characteristic phaseangle as there are number of degree of freedom, corresponding to certain sets offorces.2. For each characteristic phase lag there is a corresponding mode shapewhich varies with frequency. At the undamped natural frequencies one of the modeshapes is identical to the corresponding undamped principal mode.3. The mode shapes depend on the shape of the damping matrix and not onthe intensity of damping.4. In each mode the response at the coordinates are all in phase, but lag0behind the excitation force by an angle θ. At the undamped frequncy θ = 90 forone of the modes which is the principal mode.References1. Ibanez, P., Identification of dynamic structural models from experimental data. Univ. of Calif. AtLos Angeles Engrg. Report, UCLA–ENG-7725, Univ. Of California at Los Angeles, Los Angeles,California, 19722. Zaveri K., Phil M., Modal Analysis of Large Structures. Multiple Exciter Systems. Bruel & Kjaer,1984.3. Kennedy C. C., Pancu C. D. P., Use of Vectors in Vibration Measurement and Analysis, J.Aeronautical Sciences, Vpl. 14, No. 11, 1947, pp. 603-6254. Stahle C. V. Jr. Phase Separation Technique for Ground Vibration Testing, Aerospace <strong>Engineering</strong>,19625. Comisu Cristian., Contribuţii la studiul caracteristicilor dinamice ale tablierelor de poduri custructură compusă (mixtă)”, Facultatea de Construcţii Iaşi, martie 19986. Comisu Cristian., Identificarea în concept dinamic a stării tehnice a podurilor cu structură mixtăoţel-beton, Editura Societăţii Academice “Matei-Teiu Botez”, Iaşi, 240 pg., ISBN:973-7962-12-5,20037. Cristian Claudiu Comisu, Constantin Ionescu, Metodologia de investigare analitico-experimentalăşi de identificare în concept dinamic a tablierelor de poduri. Studii de caz. Simpozion cu participareinternaţională “Computational <strong>Civil</strong> <strong>Engineering</strong> 2004” Iaşi, 11 iunie 2004.

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