Vibration control of structural members by mutiple TMDs and multiple beam- and plate-types dynamic absorbing system : 1st report, approximate tuning method as a single TMD

In this paper, tuning method of several sets of TMDs and dynamic absorbing systems attached to the arbitrary positions of the main member (beam or plate) subjected to the harmonic excitation are considered. TMD is consisted of a mass, a spring and a damper and dynamic absorbing system is consisted of the dynamic absorbing member (beam or plate) with completely free boundary and connecting spring and damper distributed uniformly. Under the assumptions that natural frequencies of the main member are not very close to each other and flexural rigidity of the dynamic absorbing member is so small that it may be neglected, approximate modal equation of the main member with multiple TMDs or multiple dynamic absorbing systems have shown the equivalents to the equations of motion of the main system with multiple subsystem. When natural frequencies and damping ratios of subsystems are equal to each other, it has shown modal equations for above system to the equivalent to those of a two-degrees-of-freedom (TDOF) system. The approximate tuning method of the multiple TMDs and multiple dynamic absorbing systems was presented as a single TMD by applying the tuning method of an absorber in the TDOF system. Effectiveness of this method will be shown by numerical investigations in the second report.