Комп’ютерне моделювання коливань дзвону

Abstract

Проведені експериментальні дослідження звучання корабельного дзвону «ринда» та визначені частоти власних коливань. Побудована комп’ютерна модель дзвону яка повністтю відповідає реальному дзвону за геометричними розмірами та фізико-механічними властивостями. Були визначені власні частоти та моди коливань. За експериментальними даними показано, що похибка визначення частот коливань дзвону в комп’ютерній моделі не перевищує 5 % та встановлено відповідність мод коливань частотам в спектрі звуку дзвона.

The bell is a musical instrument with the speech which is not characteristic for most instruments. The speech of bells contains a large number of overtones but the frequencies do not constitute an arithmetic progression. The studies of the bell oscillations are of interest to predict its speech. Since the bell has a shape difficult enough and variable thickness, it is not possible to solve the problem by rigorous analytical methods. Therefore, to determine modes and natural oscillation frequency it was suggested using numerical methods, namely the finite-element method. A computer model of the bell having geometrical dimensions and physical and mechanical properties fully identical to a real bell was developed. The calculated frequencies were compared to the frequencies obtained during the experiment with a real bell. It was found that the relative error of the calculated natural oscillation frequency of the bell made up not more than ± 5%. Furthermore oscillation modes were obtained. According to the results of calculations it can be claimed that only axially symmetric oscillations take part in the creation of the bell sound, while asymmetric and vertical oscillations are not excited in the bell. The developed model allows designing the bells with predetermined timbre characteristics as well as analyzing the influence of different parts of the bell on the generated sound.