Acoustic resonance of xylophone bars: experimental and analytic approaches of frequency shift phenomenon during the tuning operation of xylophone bars

The xylophone is a percussion instrument made of vibrating wooden bars, the free ends of which can be struck by a mallet. The cross section of xylophone bars is not uniform for tuning purposes. The aim of this study is to impart a better understanding of the frequency shift phenomenon in acoustic resonance of xylophone bars during their tuning operation. A new analytic approach is, therefore, proposed based on the presence of one or several defects (weak elements) in a bar considered as a one-dimensional system in free–free longitudinal and transversal vibration. A weak element mechanically represents one or several real structural irregularities in the wood; this element corresponds to a mechanical behaviour analogy. This weak element is physically characterized by two positional parameters and by its Young’s modulus. Dynamic tests and numerical computations by the finite elements method give results in good accordance with those of the weak element method. It is shown that when the element weakens, the natural frequencies decrease. Furthermore, the frequency shift depends on the weak element position along the bar. It is also reported that longitudinal and transverse dynamic behaviours are similar regarding the presence of a weak element in a bar.