STABILIZATION OF THE GENERALIZED RAO-NAKRA BEAM BY PARTIAL VISCOUS DAMPING

In this paper, we consider the stabilization of the generalized Rao-Nakra beam equation, which consists of four wave equations for the longitudinal displacements and the shear angle of the top and bottom layers and one Euler-Bernoulli beam equation for the transversal displacement. Dissipative mechanism are provided through viscous damping for two displacements. The location of the viscous damping are divided into two groups, characterized by whether both of the top and bottom layers are directly damped or otherwise. Each group consists of three cases. We obtain the necessary and sufficient conditions for the cases in group two to be strongly stable. Furthermore, polynomial stability of certain orders are proved. The cases in group one are left for future study.

Design analysis and performance evaluation of a novel Multi-Cantilever Foil Bearing

This study gives an explanation to design analysis and performance evaluation of a novel multi-cantilever foil bearing (MCFB). The aim of this study is to develop a theoretical model that will explain the working principles of the cantilever foil bearing. A theoretical derivation of structural and vibration models were developed to find structural stiffness, equivalent viscous damping and maximum deflection. Findings show that the theoretical results of structural models have an equivalent structural stiffness of 58.59kN/mm, equivalent viscous damping of 0.599kNs/m and maximum deflection of 0.5675mm. The equivalent viscous damping is computed at a near zero circumferential coordinate (0.0350). The results obtained from vibration models show an equivalent structural stiffness of 58.74kN/mm, equivalent viscous damping of 0.228kNs/m and maximum deflection of 0.5675mm. Theoretical viscous damping coefficient varies from 0.23kNs/m at 24Hz to 0.026kNs/m at 200Hz when determined at maximum deflection of 0.5675mm and phase angle of 0.0350. This means the higher the frequency, the lower the viscous damping coefficient. The validation was done over frequency range 24-200Hz and at amplitude of 50mm at a 450 phase angle. The models were found to have compared well with experimental results in the prediction of equivalent viscous damping coefficient. The models can be relied upon to analyze the behaviour of MCFB and it can also form a theoretical background for the design and manufacture of Multi-Cantilever Foil Bearing.