Dynamic Analysis of the Musical Triangles—Experimental and Numerical Approaches

Abstract

This paper addresses the experimental and numerical dynamic analysis of curved bars used as percussion musical instruments. These structures are known as triangles, being made of various metal materials. The study was based on the experimental analysis of the dynamic response over time and the frequency of three types of triangles, different in material and size. Subsequently, finite element analysis of the same structures modeled with the SimCenter 12 program was performed. The results were compared, highlighting the contribution of material type and geometry in obtaining vibration modes, frequency spectrum, and structural damping coefficient. Between the experimental and the numerical analysis, the obtained errors were below 2.2% in terms of their natural frequencies. The study also highlights the complementarity of the two methods in understanding the vibration modes of triangles.

Mechanical and Acoustic Properties of Alloys Used for Musical Instruments

“…As the analyzed triangles were purchased on the market for musical instruments, there was no information on the type and characteristics of the materials in the structure of the triangles. In previous studies, the dynamic characteristics of triangles were determined by using the experimental modal analysis, as indicated in [ 4 ], and afterwards the aluminum and stainless samples were extracted from the musical triangles in order to determine their mechanical properties. The mechanical properties were investigated by two different methods, tensile testing and intrinsic transfer matrix.…”

“…In the finite element analysis, the determination of the boundary conditions was carried out by blocking the translational movements on the three axes of a node in the real clamping area of the triangle, as can be seen in Figure 5 . In our previous work [ 4 ] the method and the results of the modal analysis are presented in more detail. The experimental values of the elastic characteristics of the materials were considered in this simulation.…”

“…Alloys are used in the construction of percussion and wind instruments, and have been used since ancient times. There are numerous studies on the constructive evolution of different instruments that contain metallic elements whose impact produces highly appreciated musical sounds [ 4 , 5 , 6 , 7 , 8 ]. Currently, many constructive forms of percussion instruments have been developed, based on systematic studies on the theory of musical sounds and the physical phenomena of sound production with implications for music.…”

“…The musical role of the triangle in the orchestra began with the Turkish music from the 18th century, the instrument being later used by Franz Liszt in the third part of the Piano Concerto no. 1 in E flat major, known as the Triangle Concerto [ 4 ].…”

“…In our previous study [ 4 ], the dynamic analysis of the triangles was investigated through the hammer hits on triangle sides and their signal were recorded.…”