Unlike the body, the frame of th e tennis racket is hard to be dimensioned using conventional common techniques. The reason for this is not only the specific shape of the frame but also the nature of the load it is subjected to. Therefore, we shall only submit some approximate formulas in the present paragraph to determine the nature of the load. One of the things that are possible to be determined in the present paragraph is the force occurring in the strings of the racket mesh. This can be achieved by means of calculating their elongation. The latter can in turn be performed by means of direct measuring of the slack observed in every individual string when in static position and using a dial indicator. The idea of this suggestion lies in the following: The central point of the string is being subjected to a certain load force by the tennis ball and the value of this force corresponds to the maximum deflection of the tennis racket tip point. It is also possible to establish in this same racket position the chamfer radii for each individual string [24].
Acquiring this information allows me to calculate the effort force at every individual string using the following expression:Si δs i, (Eq. 23)
where cs is the string elasticity coefficient and δI is the calculated elongation of the i-th string. Afterwards, we can make an imaginative cut of the section of the frame, which is on the left-hand or right-hand side of the vertical axis of the tennis racket and is situated under the horizontal axis running through the central point of the mesh. The choice for this particular frame section is not incidental. It is based on information acquired from the practice according to which frames are most often broken in this section. Meanwhile, internal stress occurs at the location of the imaginative sections and this stress is hard to be defined. Therefore, the finite element method is recommended, which is adopted in the modules of some well-known software products, such as I-deas, and the ProEngineer Firewall.
7.3.6 Tennis racket vibrationsE stablishing the parameters of the vibration movement of the tennis racket is an important task because the results obtained from this study would give valuable information about the effect of vibrations on the human arm. The differential equation for transverse vibration of a straight beam having a distributed mass can be formulated using the method of kinetostatics [24]. Also, we shall have to use the differential equation for the elastic line we have learned from the material resistance course of education, which is expressed as follows:
EJ =′′ M, (Eq. 24) Where y=y(x,t) is the slack on whichever point from the beam and Mbnd. Is the bending momentum in the given section. Also, we shall have to use the existing relation between distributed load q(x,t) and Mbnd. :
∂
2
y
m
∂2 y= ρt2, (Eq. 26) ∂t2 ∂
where ml is the mass per unit length, F is the cross-sectional area of the beam and ρ is its density. Having differentiated the differential equation for the elastic line twice and relating it to the expression for the distributed load we obtain a new differential equation as follows:
∂2yEJ∂4 y= −F ρt2 or k4 ∂4y+∂2 y= 0 . (Eq. 27) ∂x4 ∂ ∂x4 ∂t2The solution to this differential equation is as follows: