Theoretical and experimental studies on the vibration of membranes of Mridangam

Abstract

A notable exception to percussion instruments not having harmonic overtones are drums belonging to the Indian musical family, particularly Tabla and Mridangam. A common aspect in both these instruments is the presence of an applied mass on the membrane to change its density distribution. While considerable work has been done to improve such membrane models for Tabla, relatively less has been done for Mridangam. It has been shown in past literature that the first few overtones are nearly and almost exclusively harmonic for such drums. Such a behaviour has been attributed to the aforementioned applied mass. While this inference has remained the same after improvements in membrane models of Tabla, the same is not true for Mridangam. The importance of this work is to show that while the applied mass does in fact lead to nearly harmonic overtones it doesn’t do so exclusively (i.e. there are non–harmonic overtones present as well). In this work, a new membrane model for Mridangam based on extensive measurements and testing is developed. The pseudospectral method and FEM are used to solve the vibration problem using this new membrane model. Since the results from simulation based on the current membrane model present new findings that were not captured by simpler models of the past, experimental modal analysis was done to support these findings and to ascertain the assumption of treating the multiple layers as a single layer of effective density. A reconciliation is provided to the apparent harmonic nature of these drums by studying the transient response of membrane under excitation by Chaapu stroke and comparing it to similar studies done in the literature. Such a study serves to illustrate that there are perhaps some other reasons as to why these non–harmonic overtones might be suppressed. It is important to note that the current work deals exclusively with the vibration of the Mridangam membrane and does not consider any other effects like that of the air-cavity or the shells, which may or may not affect the acoustic response of the actual instrument.