“Computational Civil Engineering - "Intersections" International Journal

238 C. C. Comisu1. INTRODUCTIONSince a superstructure of bridge when excited vibrates in several modessimultaneously, and thus causes difficulties in the analysis of the results, theunwanted modes have to be somehow eliminated. This can be achieved for simplestructures by placing the exciters or pick-ups at nodal points of the unwantedmodes, or by making use of the symmetrical and anti-symmetrical properties of themode shapes. In complex structures such as superstructures of bridge, this is notalways possible, and systematic methods have to be used for exciting the structurewith multiple shakers and forcing them to vibrate in their principal modes.However, this requires rather sophisticated equipment both on the excitation side,as well as on the data acquisition side, because of the large number of pick-ups,necessary for determining the mode shapes. To facilitate understanding of themultiple exciter techniques, it is necessary to first illustrate in practical terms thetheoretical considerations and describe the instrumentation required, and thefeatures that have been incorporated, that are obligatory for functioning of the test[1], [2].2. EXPERIMENTAL PROCEDUREThat if a structure is proportionally damped, it can be excited at any frequency by aparticular set of forces which are in phase or anti-phase with each other, such thatthe measured responses at all points are all in phase, or anti-phase, and that thecommon phase lag between the force and the response is unique at this frequency.At this frequency there are as many characteristic phase lags with their associatedlinearly independent force distribution, as there are degrees of freedom in thestructure. The structure when excited in this manner for a particular ratio of forceswill vibrate in the principal mode, and thus as a single degree of freedom system.If the structure is non-proportionally damped, the structure can be excited in itsprincipal mode, only at the corresponding natural frequency by a set of monophaseforces. In this case, the response will be in quadrature with the forces at allpoints on the structure.If the structure has n degrees of freedom, n number of shakers is required ideally toisolate a mode. To exemplify this statement, consider the mode shapes of the firstthree degrees of freedom of a free-free beam shown in figure 1.In order to excite the third mode only, three shakers in phase would be required,one at each of points A, B and C. If only two shakers with equal force amplitudeswere used in phase at A and B, the second mode could be eliminated, as points Aand B move in anti-phase, however, the first mode would be excited together withthe third one. Again, if only two shakers were used in phase at A and C, the first