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Abstract :
Timila is an hour glass shaped Indian rhythmic drum with a circular membrane drum head, popularly used in percussion ensemble Panchavadhyam played in temples of Kerala. The basic strokes produced by the instrument are Tha and Thom. Variable separable method and Greenâ€™s function technique are often used to study the vibrations of circular membrane like that of timila. Hankel transform technique is another powerful tool which can be used to study drum heads like that of timila. In our study we use zero order Hankel transform method for studying the vibrations. Initial conditions like initial velocity and initial displacement are chosen as functions of radius of the membrane. The amplitude of the displacement for the first six modes are found for different initial velocities and initial displacements for a circular membrane of radius 0.082 m. Three initial displacement and three initial velocity functions are used to study the displacement of different modes of timila membrane. A constant function, a quadratic function and a cubic function are chosen as initial velocity. The functions used are 1, (2-r/2)^2 and r(2-r/2)^2 for initial velocity. The functions r^2-r^4 , 3r-r^3 and (R^2-r^2)^2 are the initial displacements chosen in this study. The first function resembles the shape of the timila drum head. For different initial velocity functions, all the modes vibrate in phase. In the paper it is shown that different initial velocity functions and initial displacement functions does not change the shape of the modes. When the functions are changed it is found that the amplitude of modes changes. The values of displacements are tabulated and compared. In the case of initial velocity functions, quadratic function produced highest displacement for the membrane and cubic function has got lowest value. For initial displacement functions maximum displacement of the membrane is observed for second function and lowest value is obtained for the third function. For our studies it is assumed that the membrane is struck at the centre.