A STUDY OF MATERIAL DAMPING OF CIRCULAR PLATE OF UNIFORM THICKNESS UNDER DIFFERENT MODES OF VIBRATION

Abstract

Modern engineering demands that engineers must have a sound knowledge of the vibration response of plates. Plates are widely used in many fields of engineering applications such as missiles, architectural structures, etc. Due to presence of intense sources of broad-band excitation, such structures are always subjected to some type of loading. Whenever, a plate is caused to vibrate, it may happen that due_ to resonance, the amplitude of vibration becomes very large. To control this large amplitude of vibration, various types of damping may be used. Sometimes, it may not be possible to provide an external .damping, -then- the internal damping of the plate remains the only option to control the amplitude of vibration. In this dissertation, the material damping of a thin circular plate with uniform thickness under different modes of vibration is studied. After a brief introduction in the first chapter, the second chapter consists of literature review. In brief, it consists of: (i) Introduction of various types of damping, (ii) Importance of material damping under resonant condition, (iii) Description of material and member properties, (iv) Definition of loss factor and review of pastwork done on forced vibration of plates. Third chapter deals with analytical formulation of modal loss factor for the case of thin, elastic, isotropic and homogeneous clamped edge circular plate subjected to an eccentric harmonic point force. Starting with the fundamental equation of forced transverse vibration of circular plate using Green's function, the expression for deflection is determined. Then stresses are calculated with the help of general stress equations. Criteria of equivalent uniaxial: stress is used. At the end, modal loss factor is calculated for different modes. In this formulation, Bessels functions are used for solution. It also deals with analytical formulation of modal loss factor for fundamental mode for the case of thin, elastic, isotropic and homogeneous clamped edge circular plate subjected to a central point load. Due to geometry of plate, polar co-ordinate system is chosen. After this, in the fourth chapter, computer programming is discussed, in brief. This consists of two flow charts; one for eccentric harmonic point load another for central point load. On the basis of these flow charts, two simple computer programs in FORTRAN 77 are developed-. Computer— programs are given in the appendix I and II. In Chapter Five, results obtained from formulation are discussed. An attempt has also-. been made to calculate modal loss factor graphically for a similar plate for first seven modes for different load, thickness and eccentricity. It also deals with the further scope of work.