Vibration Analysis of a Guitar considered as a Symmetrical Mechanical System

Abstract

This paper aimed to use the symmetry that exists to the body of a guitar to ease the analysis behavior to vibrations. Symmetries can produce interesting properties when studying the dynamic and steady-state response of such systems. These properties can, in some cases, considerably decrease the effort made for dynamic analysis at the design stage. For a real guitar, these properties are used to determine the eigenvalues and eigenvectors. Finite element method (FEM) is used for a numerical modeling and to prove the theoretically determined properties in this case. In this paper, different types of guitar plates related to symmetrical reinforcement patterns were studied in terms of modal analysis performed using finite element analysis (FEA). The dynamic response differs in terms of amplitude, eigenvalues, modal shapes in accordance with number and pattern of stiffening bars. In this study, the symmetrical and asymmetric modes of modal analysis were highlighted in the case of constructive symmetrical structures.Symmetry 2019, 11, 727 2 of 16 symmetrical system of the guitar is analyzed and the vibration properties that are the result of considering this symmetry are revealed. An example for a real system is made in the second part of the paper. Derveaux et al. [9] developed a guitar model based on advanced numerical methods to simulate the three-dimensional sound-pressure field of a guitar in the time domain. Due to the complexity of the problem, the main parts of guitar (plates, body, strings, air from cavity, holes) that are implied in acoustic radiation and vibration were simplified in terms of mathematical models and interactions. Compare to [9], in this paper, the frequency spectrum and eigenmodes of different symmetric types of guitar plates were analyzed and in future works, the guitars bodies with different bars pattern will be numerical modeled. Elejabarrieta et al. [10] analyzed the influence of each component from acoustic box of guitar on the vibrational behavior using finite element method in a progressive manner of constructive system.These types of problems occur frequently in practical applications; many mechanical systems exhibit different kinds of symmetry properties, resulting from a design process for constructive, simplistic, logistic or cost considerations. Knowing these properties allows to increase the precision of calculations in such issues. Properties determined by symmetries have been observed by researchers and are mainly used in the static analysis. They are presented in the classical courses of Strength of Material or Structural Analysis. From a historical point of view, the symmetries in mechanics have been studied by mathematicians [11,12]. Symmetry effects occur in the writing the motion equations, but the solutions can be symmetric and antisymmetric according to the assumed boundary conditions [7]. In accordance with [13], the methods of mechanics (Lagrangian and Hamiltonian) use symmetry to solve complex problems. Moreover, these methods and symmetry principles are based on the ...

Frequency Response Evaluation of Guitar Bodies with Different Bracing Systems

“…These generate higher harmonics. The dynamics of the guitar body differs from that of the individually analyzed plates presented in previous papers [34,36,37]. This is due to the new bordering conditions created by attaching the sides to the top and back plates, as well as due to the aerodynamic phenomena inside the cavity that leads to delaying the transmission of vibration from the top plate to the backplate and to the sides [17,39].…”

“…The eigenmodes can be classified into two classes: symmetrical and skew-symmetrical eigenmodes. The properties of the symmetric systems were less used in the field of applied mechanics, but some papers study applications in the field [32][33][34].…”

Symmetry in Applied Continuous Mechanics

“…The statistics of papers called for this Special Issue related to published or rejected items were [7][8][9][10][11][12][13][14][15][16][17][18][19][20]: total submissions (21), published (13; 62%), and rejected (8; 38%). The authors' geographical distribution by countries of authors in published papers is shown in Table 1, and it can be seen that 35 authors are from 11 different countries.…”