Adjustment of the Force Transmissibility of a SDOF Vibrating System; Part II: Fraction Transmissibility

The purpose of this paper is to present an efficient technique for the adjustment of the transmissibility of a SDOF system through the optimal selection of the damping ratio of the SDOF vibrating system. As an application a case of fraction transmissibility. Different objective function relationships are presented and the best one is assigned leading to the desired unit force transmissibility and a frequency spectrum of the system vibration amplitude ratio having a settling frequency ratio above 4.2. Five objective function expressions (ISE, IAE, ITAE, ITSE and ISTSE) are considered and their impact on the force transmissibility and other related parameters is investigated. Desired force transmissibility in the range 0.1 to 0.5 is considered. The force transmissibility of the vibrating system is adjusted around the mean value with standard deviation less than 0.085. System optimal damping ratio of the system is less than 1.3 depending on the desired force transmissibility and the objective function used. The optimum vibration amplitude ratio settles within a 0.05 band at an exciting frequency ratio greater than 4.2.