The Feasibility of Statistical Energy Analysis in the Modeling of Stringed Musical Instruments

Abstract

Stringed musical instruments are complex vibrating systems both from structural and fluid-structure coupling perspectives; hence, their modeling is one of the most challenging tasks in the area of vibration and acoustics. Making a reliable model not only broadens our knowledge of the physics of these instruments, but also it simplifies the procedure of structural modification and optimization on them. In this regard, a Finite Element Model has been previously made from Setar and is verified with the experimental results. Although that model could precisely simulate the instrument in lower frequencies (i.e. below 2.5 KHz), its results showed a weak correlation with reality in higher frequencies. In fact, unreliable results and high computational demand are common drawbacks of finite element method in higher frequencies. To avoid these problems, in this study Setar is modeled with Statistical Energy Analysis (SEA) approach. This method is more efficient in dealing with high degree of uncertainty in the system. SEA does this by averaging the response over the frequency and location to gain a more general and reliable result. Application of SEA in higher frequencies is, in fact, compatible with the nature of musical instruments where in higher frequencies we are mostly interested in the trend of the response rather than the location of each individual peak.