Stanciu Mariana Domnica, Cosnita Mihaela, Cretu Constantin Nicolae, Teodorescu Horatiu Draghicescu, Trandafir Mihai
Faculty of Mechanical Engineering, Transilvania University of Brașov, B-dul Eroilor 29, 500036 Brasov, Romania.
Department of Product Design Mechatronics and Environment, Transilvania University of Brasov, B-dul Eroilor 29, 500036 Brasov, Romania.
Materials (Basel). 2022 Jul 26;15(15):5192. doi: 10.3390/ma15155192.
Music should be integrated into our daily activities due to its great effects on human holistic health, through its characteristics of melody, rhythm and harmony. Music orchestras use different instruments, with strings, bow, percussion, wind, keyboards, etc. Musical triangles, although not so well known by the general public, are appreciated for their crystalline and percussive sound. Even if it is a seemingly simple instrument being made of a bent metal bar, the problem of the dynamics of the musical triangle is complex. The novelty of the paper consists in the ways of investigating the elastic and dynamic properties of the two types of materials used for musical triangles. Thus, to determine the mechanical properties, samples of material from the two types of triangles were obtained and tested by the tensile test. The validation of the results was carried out by means of another method, based on the modal analysis of a ternary system; by applying the intrinsic transfer matrix, the difference between the obtained values was less than 5%. As the two materials behaved differently at rupture, one having a ductile character and the other brittle, the morphology of the fracture surface and the elementary chemical composition were investigated by scanning electron microscopy (SEM) and analysis by X-ray spectroscopy with dispersion energy (EDX). The results were further transferred to the finite element modal analysis in order to obtain the frequency spectrum and vibration modes of the musical triangles. The modal analysis indicated that the first eigenfrequency differs by about 5.17% from one material to another. The first mode of vibration takes place in the plane of the triangle (transverse mode), at a frequency of 156 Hz and the second mode at 162 Hz, which occurs due to vibrations of the free sides of the triangle outside the plane, called the torsion mode. The highest dominant frequency of 1876 Hz and the sound speed of 5089 m/s were recorded for the aluminum sample with the ductile fracture in comparison with the dominant frequency of 1637 Hz and the sound speed of 4889 m/s in the case of the stainless steel sample, characterized by brittle fracture.
由于音乐通过其旋律、节奏与和声的特性对人类整体健康具有巨大影响，所以应将其融入我们的日常活动中。交响乐团使用不同的乐器，如弦乐器、弓弦乐器、打击乐器、管乐器、键盘乐器等。三角铁虽不为大众所熟知，但其清脆的敲击声备受赞赏。即便它看似是由一根弯曲金属棒制成的简单乐器，三角铁的动力学问题却很复杂。本文的新颖之处在于研究用于制作三角铁的两种材料的弹性和动态特性的方法。因此，为了确定力学性能，获取了两种三角铁的材料样本并通过拉伸试验进行测试。结果的验证通过另一种基于三元系统模态分析的方法进行；通过应用固有传递矩阵，所得值之间的差异小于5%。由于两种材料在断裂时表现不同，一种具有韧性特征，另一种具有脆性特征，通过扫描电子显微镜（SEM）和能量色散X射线光谱分析（EDX）研究了断裂表面的形态和基本化学成分。结果进一步被应用于有限元模态分析，以获得三角铁的频谱和振动模式。模态分析表明，两种材料的第一固有频率相差约5.17%。第一种振动模式发生在三角铁平面内（横向模式），频率为156赫兹，第二种模式频率为162赫兹，它是由三角铁平面外自由边的振动引起的，称为扭转模式。与不锈钢样本（具有脆性断裂特征）的主导频率1637赫兹和声速4889米/秒相比，铝样本（具有韧性断裂）记录到的最高主导频率为1876赫兹，声速为5089米/秒。
