Non-Linear analysis of compressively/thermally stressed elastic shell structures on the steelpan and the underlying theory of the tuning process

摘要

This paper presents a non-linear analysis of the dome-shaped notes on the steeplan under compressive and thermal stresses. Equations are derived for the static and dynamic response of symmetrically distorted notes. Analytical results are obtained for modal frequencies, non-linear coupling coefficients and the buckling parameter. Experimental results demonstrate the vibration characteristics and their dependence on temperature. Experimental results were also obtained for the effects of stress relaxation which follows the shaping and tuning process of these notes by hammer peening. The results of the analysis are applicable to other shell-likes structures not necessarily designed for musical purposes.