Thus, the contact stiffness is affected by the interaction between the string, bridge and top plate. In addition, some of the plate structure changes may be very sensitive to the bridge-corpus interaction, for example the cutting of the slot-like f-holes which are close to the bridge feet. Thus, the dynamic contact stiffness is sensitive to such structure changes.Evidently, in this paper the term isolated bridge does not mean the bridge is completely independent of the strings and the corpus. In fact, the bridge is linked to the strings and corpus through the dynamic contact stiffness. However, the dynamic contact stiffness is difficult to determine analytically. Moreover, the violin bridge vibration is very complicated with many vibration modes.
An accurate analytical dynamic contact vibration model is difficult to deduce to predict the bridge mobility. The impact of the dynamic contact stiffness on the bridge mobility is studied through finite element modeling and experimental measurements in this paper.3.?Finite Element Modeling of a Violin Bridge under the Contact Vibration ModelFrequency response analysis of a violin bridge is carried out using ANSYS Workbench 12. The bridge geometric model in Figure 1a was built using the CAD software SOLIDWORKS according to the physical parameters of a real violin bridge. The maximum length, height and thickness of the bridge are 49.5, 34.5 and 4.5 mm, respectively. The top edge width of the bridge is 2 mm. The bridge material is maple. The material properties of ��maple red�� published in [13] were used in the simulation as listed in Table 1, where the X, Y, Z directions are as defined in Figure 1.
No pre-stress has been considered in any of the simulations of this paper.Figure 1.Geometrical models. (a) A real bridge; (b) A plate solid bridge.Table 1.Material properties of the violin bridge used in the Dacomitinib simulation.Elastic supports (elastic support B in Figure 2) were applied to the bottom surfaces of the two bridge feet, which are the contact surfaces between the two bridge feet and violin top plate, and the elastic foundation contact stiffness in this contact interface is denoted as EFS1. Elastic supports were also applied to the groove/notch surfaces of the bridge top, which are the contact surfaces between the bridge and four strings. In a violin the strings are just placed on the arched notches of the bridge top.
Thus, the elastic supports in the notch surfaces are appropriate to model the constraints exerted by the strings. According to the contact mechanics theory [14,15], which studies the deformation of solids that touch each other at one or more points, the contact vibration involves compressive and adhesive forces in the direction perpendicular to the interface, and frictional forces in the tangential direction. These interface forces act on the bridge notch surfaces, constraining the bridge dynamic motion.Figure 2.