The mode shapes of a tennis racket and the effects of vibration dampers on those mode shapes

Abstract

The vibrational behavior of a tennis racket was studied using a speckle-pattern interferometry system. Specifically, the first 12 mode shapes of a racket are shown and discussed. In addition, the speckle-pattern interferometry system was used to compare the effects of four commercially available vibration damping systems. It was found that these vibration dampers produce a variety of effects on the vibrational behavior of the racket, though these effects may not be noticeable during play.

A simple and inexpensive optical technique to help students visualize mode shapes

“…ESPI images captured using an inexpensive array with an inexpensive lens have produced interferograms of sufficient quality to perform publishable research. 6 Regardless of which imaging algorithm is used (TBSI or DTBSI), two-beam speckle imaging requires two beams of light to be derived from the same laser, and some of the light must be directed at an angle different from the direction normal to the surface. Therefore, mirrors and some mounting hardware are required.…”

Tennis Racket Vibrations and Shock Transmission to the Wrist during Forehand Drive

“…In order to limit such risks, equipment companies offer innovative designs, composite materials, and grips or damping devices intended to reduce racket vibrations. While string dampers are claimed to reduce discomfort in the hand and arm, previous studies concluded that they have no other effect on player’s sensations than reducing the sound of impact [ 2 , 4 ]. A multi-layered core damper inserted in the racket handle as for it reduces racket stiffness, and in turn limits the dampening time and amplitudes of vibrations [ 5 ].The claimed benefits are mainly based on results obtained by laboratory-testing-based simulation.…”

Understanding the Dynamic Behaviour of a Tennis Racket under Play Conditions

“…The bending and torsional modes are relatively easy to visualize, as the racket behaves in a similar manner to a freely suspended vibrating beam. For stringbed mode shapes, the labelling method used by Timme et al [21] has been adopted. The nomenclature for labelling is (x,y), where x is the number of nodal lines and y is the number of nodal circles.…”

“…Korte et al [20] investigated the differences between conventional midsize rackets and the, then new, wide body rackets and found that the wide body racket's bending and torsional natural frequencies were far higher than those of the midsize racket. More recently, Timme et al [21] used electronic speckle-pattern interferometry to identify twelve mode shapes of a clamped tennis racket up to 1500 Hz, including seven stringbed modes, the first of which was found to be at 562 Hz. Computational modal analyses of finite element models of tennis rackets have been performed by a number of researchers [22,23] and, while the mode shapes of the lower frequency modes correlate well with experimental data, far more mode shapes have been identified up to a frequency of 745 Hz.…”