The majority of sports enthusiasts favor tennis. Tennis has long since become an important event in the Olympic Games. Therefore, it is of theoretical significance to study the dynamic characteristics of the tennis racket hitting process to guide the design of tennis rackets and improve the level of tennis players . A tennis racket consists of a network cable and a frame. Due to the strong nonlinear vibration characteristics of the racket’s net under the tennis ball’s impact, it is difficult to model the tennis racket mechanically. As a result, many scholars use interlaced beams to replace the tennis racket net while ignoring the nonlinear characteristics of the tennis racket net. Some scholars have studied the serve action of tennis . Some scholars have studied the dynamic characteristics of tennis rackets. Some scholars have discussed the striking center of a tennis racket. The relationship between tennis racket net string tension and hitting speed was studied . None of the above-related studies have considered the nonlinear factors of the net. Based on the above reasons, this paper regards the net of the tennis racket as a cable net, uses the nonlinear vibration theory to study the dynamic characteristics of the tennis racket during the hitting process, and obtains some useful conclusions.
The tennis racket frame is assumed to be rigid . From the elastic vibration theory, it can be known that the vibration equation of the tennis racket cable net is:
In the formula,
When the net is an ellipse, its boundary area can be expressed by the following equation:
In the formula,
Assuming that the part where the tennis racket hits the tennis ball is in the center of the net, we can express
Therefore, we can obtain the function expressions of the natural vibration frequency of the net and the nonlinear vibration displacement of the net as:
Finally, we use
After ignoring the inertia term, we can see that the relationship between the displacement
In the formula
We simplify the analysis of tennis. The experiment transforms the nonlinear elasticity of the net into an equivalent linear elasticity . Assume that the equivalent linear elastic coefficient of the net after transformation is
Suppose the stiffness of the tennis ball is
It is assumed that the moment when the center of the net of the tennis racket produces the maximum displacement
Suppose the tennis ball has a diameter
We can transform Equation (25) into the following form:
When the tennis racket is separated from the tennis ball, the following conditions should be met:
We now take a certain type of tennis racket as an example to analyze the dynamic characteristics of the tennis racket during the hitting process [12-13]. The long axis of the tennis racket net is 2
Because the average spacing of the net chords in the
From the analysis of Figure 3, we can see that with the increase of the initial speed of the tennis ball, the change of the tennis motion curve becomes steeper and more complex. As the initial velocity of the tennis ball gradually decreases, the movement curve of the tennis ball tends to be gentle . This means that tennis players who hit the ball faster have a relatively higher success rate in the same situation. From the analysis of Table 1, we can see that as the initial speed of the tennis ball gradually decreases, the separation time of the tennis ball and the tennis racket gradually becomes longer.
Separation time between tennis and tennis rackets
The greater the initial velocity of the tennis ball, the greater the displacement of the net. Tennis players who hit the ball quickly have a relatively high success rate on their serve. As the initial velocity of the tennis ball gradually decreased, the separation time of the tennis ball and the tennis racket gradually became longer.
Separation time between tennis and tennis rackets
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