International Research Journal of Engineering and Technology (IRJET)
e-ISSN: 2395-0056
Volume: 12 Issue: 08 | Aug 2025
p-ISSN: 2395-0072
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Experimental Study of Natural Frequencies and Mode Shapes of a Nonuniform Circular Membrane (Dafli) Advay Khetan Student, DPS Faridabad, Haryana, India ------------------------------------------------------------------------------***------------------------------------------------------------------Abstract This paper presents experimental methods to determine natural frequencies and mode shapes of a circular membrane with concentric or eccentric non-uniformity as found in Indian musical drums. The Dafli, a frame drum with a non-uniform circular membrane, was studied using modal vibration analysis techniques. Rather than utilizing computational approaches, this study employed direct measurement methods including electronic speckle pattern interferometry (ESPI) and frequency response analysis. Experimental results reveal the relationships between membrane loading patterns and resulting acoustical properties. The findings are corroborated through comparison with theoretical predictions and provide insights into the harmonic properties of traditional percussion instruments with non-uniform membranes.
1. Introduction Vibration of non-uniform circular membranes has been an important topic of research since the publication of experimental results by Raman [1]. The Dafli, a traditional Indian frame drum, features a circular membrane that often contains nonuniform mass distribution due to the application of a tuning paste similar to the "Syahi" used in Tabla drums. This paste alters the mass of the membrane per unit area where applied, creating either concentric or eccentric loading patterns that significantly affect the instrument's acoustic properties. Previous research on Indian drums has largely focused on computational methods [2-8], with limited experimental validation. Ramakrishna and Sondhi [2] modelled the Dayan Tabla (circular membrane with concentric non-uniformity) mathematically, while Sathej and Adhikari [7] developed computational approaches for both concentric and eccentric loading patterns. While these mathematical models provide valuable insights, comprehensive experimental verification remains necessary to fully understand the complex vibrational behaviour of these instruments. This paper presents an experimental investigation of the Dafli drum, examining both the concentric and eccentric loading configurations. Through systematic measurement of frequency responses and direct visualisation of mode shapes, we explore how non-uniform mass distribution influences the acoustic characteristics of circular membranes.
2. Materials and Methods 2.1 Drum Specimens Two variants of the Dafli drum were studied: 1
A drum with concentric mass loading (similar to the Dayan Tabla)
2
A drum with eccentric mass loading (similar to the Bayan Tabla)
Both drums consist of a circular membrane stretched over a wooden frame. The membrane was made of mylar with a thickness of 0.2 mm and a diameter of 30 cm. The loading material (similar to Syahi) was composed of a mixture of flour, water, and iron filings, applied to specific regions of the membrane. For the concentric configuration, the loading paste was applied as a circular patch at the centre covering approximately 29% of the membrane radius. For the eccentric configuration, a similar-sized patch was applied with its centre displaced 18% of the membrane radius from the centre.
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