STUDY OF MATERIAL DAMPING IN CIRCULAR PLATES OF UNIFORM THICKNESS

Abstract

The state of the art of modern engineering demands that engineers have a good knowledge of the vibration behaviour of structures where the plates are used. It is well known that plates are used in many fields of engineering applications, such as architectural structures, missiles, jets, electronic devices etc. When ever a plate is caused to vibrate, it is possible that due to resonance the amplitude of vibration becomes very large. To suppress the vibration amplitude at resonance condition various types of dampings are used. Some times it may not be possible to provide the external damping to control the vibratory resonant response. In those cases internal damping is the only means available to reduce the resonant response.' The present work deals with the study of material damping in circular plates of uniform thickness. Second chapter consists of literature review. It gives a brief introduction to various types of dampings. Special emphasis is given to the importance of material damping under resonant conditions. Member and material properties are described and loss factor is also defined. Past work done on the forced vibration of rectangular and circular plates is reviewed. Third chapter deals with the analytical formulation of modal loss factor for the case of thin, elastic, isotropic and homogeneous circular plate. A uniformly distributed harmonic force is considered. Plate is assumed to be clamped at the boundary. Starting with the fundamental equation of forced transverse vibration of circular plate, the expression for deflection is determined. Then with the help of general stress equations stresses are determined. After that criteria of equivalent uniaxial stress is applied and modal loss factor is evaluated for the first three modes. Solution of the problem requires the use of Bessels functions. Due to the geometry of plate,polar coordinate system is chosen. Fourth chapter deals with the computer programming. Here a flow chart is given, on the basis of which a simple computer programme is developed. Computer program is given in the appendix. Chapter five discusses the results and gives the scope for further work