Nonlinear membrane stiffness model of a tennis racquet string bed - Hong, H.; Han, L.; Perkins, N. C.; Hu, C.; Barber, J. R. (Proceedings of the Institution of Mechanical Engineers, Part P: Journal of Sports Engineering and Technology, 2018)
The overall stiffness of the string bed of a tennis racquet depends on numerous factors including the size and shape of the string bed, initial string tension, string spacing, and string geometric and material properties. This article contributes an analytical model of the string bed that employs nonlinear membrane theory to estimate static stiffness. The partial differential equation governing string bed deformation is discretized using a one-term Galerkin approximation that employs a logarithmic shape function for the string bed deflection. The resulting force-displacement relation at the centre of the string bed yields the string bed stiffness as a function of the major design parameters, including the shape and size of the frame, string tension used during stringing, and string spacing, diameter, and elastic modulus. To assess the accuracy of this model, the predicted force-displacement relation was compared to that measured from experiments on a string bed instrumented with a load cell and photoelectric (laser) displacement sensor. Experimental results confirm that the analytical model yields accurate estimates of the string bed load-displacement characteristics, especially for displacements of 5?mm or less.