Normal modes of a small gamelan gong.

Studies have been made of the normal modes of a 20.7 cm diameter steel gamelan gong. A finite-element model has been constructed and its predictions for normal modes compared with experimental results obtained using electronic speckle pattern interferometry. Agreement was reasonable in view of the lack of precision in the manufacture of the instrument. The results agree with expectations for an axially symmetric system subject to small symmetry breaking. The extent to which the results obey Chladni's law is discussed. Comparison with vibrational and acoustical spectra enabled the identification of the small number of modes responsible for the sound output when played normally. Evidence of non-linear behavior was found, mainly in the form of subharmonics of true modes. Experiments using scanning laser Doppler vibrometry gave satisfactory agreement with the other methods.

Normal modes of the Indian elephant bell.

The geometrical structure of the Indian elephant bell is presented and the requirements on its normal modes from group representation theory are described. These are in good agreement with the results of a finite-element model (FEM) for a specific 16-tine case. The spectrum consists of a sequence of families of modes lying on saturation curves, completely different from those of conventional bells. Physical explanations for the occurrence of these families are presented in terms of the tines behaving as a closed loop of coupled cantilevers with constraints from the dome. Each family is found to consist of modes in one of two specific sequences of symmetry types. Experimental measurements of the modes of this same 16-tine bell, using electronic speckle pattern interferometry (ESPI), have been made and are compared with the FEM predictions. Although the interpretation of the interferograms is difficult in all but the simpler cases, agreement in terms of frequencies is surprisingly good for the first few family sequences. The ESPI study also showed up numerous harmonics and subharmonics of true normal modes, showing the system to be rather non-linear and making comparisons with the FEM results tricky.