Passive vibration control in mid-frequency region

This paper deals with passive vibration control of structures exhibiting both long and short wavelength deformations within the same frequency range. Such behaviour is often observed in complex build-up structures such as rib-stiffened plates, automotive vehicles, aeroplane fuselages and so on, and is inherent property of any structure comprising of both stiff and flexible structural elements. Addressing both short- and long-wavelength vibrations within the same frequency range is often referred to as the mid-frequency problem, and presents considerable difficulties since it is not amendable for deterministic (e.q. finite element method, FEM) or statistical (statistical energy analysis, SAE) analysis techniques alone. Furthermore, mid-frequency vibrations exhibit intrinsic sensitivity to system uncertainties (e.q. structure variability, uncertainty in boundary conditions). Mid-frequency vibration problem has attracted considerable interest in the past decade, and a number of hybrid FE/SAE methods for predicting the vibration response has been developed. Yet, passive vibration control of the structures exhibiting mid-frequency vibration has not been fully addressed. In this paper, we discuss an optimal passive control technique for a generic mid-frequency vibration problem via multiple tuned mass dampers (TMDs). The problem at hand is tackled as reducer-order optimal H1 control of uncertain system with controller order and structure constraints. We address several issues of the proposed approach, such as system uncertainty modelling, applicable optimization algorithms and computational costs. To illustrate the applicability and the efficiency of the proposed approach, we present an example comprising of beam-stiffened plate with multiple TMDs. We also investigate the influence of total TMDs mass, number of TMDs and distribution of individual TMDs resonant frequencies on vibration attenuation efficiency.