Effects of a Scalloped and Rectangular Brace on the Modeshapes of a Brace-Plate System

Abstract

Shaping the soundboard braces on a wooden stringed musical instrument has long been a way in which instrument makers optimize their musical instruments. Reasons for these methods are scientifically not well understood. Various bracing patterns have successfully been used to create different-sounding wooden stringed musical instruments. These bracing patterns stimulate the modeshapes that are specific to the soundboard of the instrument. However, a higher adjustment resolution is required in order to specify the frequency spectrum of the musical instrument. This paper demonstrates how the shape of the braces affects the modeshapes of the vibrating system. A simple analytical model composed of a plate and brace is analyzed in order to see these effects. The results are plotted together for three cases: the plate by itself, the plate with a rectangular brace and the plate with a scalloped brace. For clarity, the modeshapes are analysed in 2D at different locations and along both the x and y directions of the plate. It is shown that any brace affects modeshapes for which the brace does not run along a nodal line. The different shapes of the brace are shown to affect different modeshapes by various degrees. If braces are stiffened at locations of maximum amplitude for a given modeshape, then that modeshape will be significantly affected. It is clear that by properly designing the shape of a brace, instrument makers can exert great control over the shape of the instrument's modeshapes and therefore also their frequencies.

An analytical model for computing the sound power of an unbraced irregular-shaped plate of variable thickness

“…The implication of the simulated support is that it allows unlimited motion of the irregular-shaped plate in the x- and y-directions compared to the simple support of the analytical model and hence affects the magnitudes of the natural frequencies for higher modes. It is worthy to note that control of natural frequencies is also possible with the use of scalloped braces 6 , 26 , 27 .…”

Mathematical Modelling and Acoustical Analysis of Classical Guitars and Their Soundboards

“…Dumond and Baddour [25,26] studied the effects of scalloped braces on mode shapes. A simple analytical model based on Kirchhoff plate theory was used to study the vibration of a rectangular board with and without braces.…”

Structured Approaches to General Inverse Eigenvalue Problems

“…It is clear that the brace affects the maximum amplitude of this modeshape, thus also affecting the associated frequency. In order to adjust the fundamental frequency of the brace-plate system to a desired value, it is necessary to adjust the thickness of the brace [20].…”

“…Substituting equation (20) into equation (21), the following equation for kinetic energy is obtained…”