Structural dynamic analysis of a musical instrument: Tibetan singing bowl

Abstract

Operational Modal Analysis (OMA) of Tibetan singing bowl is performed to extract natural frequencies and mode shapes without measuring excitation data. It is kept free on a rigid surface, which is a common way of playing this musical instrument. OMA results are validated using Experimental Modal Analysis (EMA) and Numerical Methods using FEA. Numerical simulations using ANSYS® software establishes a benchmark for EMA results. The input and response data for 144 response points are collected using instrumented hammer and accelerometer, connected to a four-channel FFT analyser. A self-generated MATLAB® code processes the response signals for EMA and OMA. For natural frequencies, the absolute error lies within 6%, except for the first mode. For mode shapes, the Modal Assurance Criteria (MAC) value is more than 70%, except for the fourth mode. Thus, OMA is the best available method compared to the EMA and Numerical method using FEA for structural analysis under actual performance conditions.