Sporting Goods

Sports equipment exhibits unwanted vibration due to resonance response. Examples of this phenomenon include snow skis, aluminum baseball bats, tennis rackets, and golf clubs.. These resonances tend to be low-order, low-frequency resonances, though particular cases must be analyzed and understood.

Resonances are excited via use of the equipment. In the case of snow skis, impulsive excitation from irregularities in the snow field and variations in ski contact with the snow, and impulsive maneuvers will result in excitation of resonances of the ski. The resonance response of the ski is perceived by the skier and can interfere with the “feel” and stability of the ski.

Resonances of aluminum baseball bats are excited by contact with the baseball or softball. An impactive force in the time-domain exists as wide-frequency excitation in the frequency domain. Excitation of resonances of the bat is perceived as a tactile “buzz” in the handle of the bat. Also, motion in the barrel of the bat – where the ball contact should occur – can diminish the power of the hitter. If the hitter contacts the ball at the node line of the bat, more power will be generated, as the bat is extremely stiff at the node line – the so-called “sweet-spot”. Attenuating resonance response of the bat can increase the effective spatial node line area of the bat and increase the “sweet-spot”.

Tennis rackets are very similar to the baseball bat case, although the player’s arm tends to participate in the resonance response of the tennis racket. Attenuation of resonance response of the tennis racket can increase the “sweet spot” area. Golf clubs behave in a similar manner.

Damping is a very powerful attenuation tool for these types of applications.

In order to develop a solution, it is necessary to understand the particular structural dynamics of the structure. This means that operating data typically must be acquired to determine, for example, if resonance response is contributing to the detrimental performance -or is the issue related to forced-vibration? The answer will dictate the best countermeasure configuration.

Harvesting operating data can involve installing accelerometers on the test article and then “using” the sports equipment as-intended. If peak response levels are seen in the frequency domain at particular frequencies, then non-operating frequency response functions (FRF) are typically harvested via controlled artificial excitation to define the structural dynamics. If there is a resonance of the structure that correlates to the peak acceleration levels observed during use of the article, then it is very likely that resonance response is responsible for the detrimental behavior. At that point, modal analysis can be performed on the article to define the mode shapes of vibration. With the modal analysis data and FRFs, representative models of the structure can be created and countermeasures can be developed.

For low-frequency resonance response of baseball bats or tennis rackets, Tuned Mass Dampers (TMD) can be very effective. However, the TMD mass must be defined and optimized, the TMD must be located and installed appropriately, and the TMD must be tuned properly (for the resonance of interest). Viscoelastic materials which are very stable with respect to temperature must be selected to ensure that the TMD remains tuned for a wide variety of environmental exposure.

Resonances of skis can be attenuated via TMD, but often multiple bending modes of the skis can be problematic. A Constrained Layer Damping System (CLDS) may therefore be a good countermeasure choice for attenuation of the response of the skis due to those bending resonances. It is possible to integrate the CLDS into the build-up of the ski via lamination. As always, the VEM selection and the geometry of the CLDS must be designed based on the flexural rigidity of the ski, the frequency content of the resonance response, and the operating temperature range. Typically, an FEA model is required to optimized the CLDS.

The TMD would be located within the hollow aluminum bat, but again, location is critical and depends on the mode shape of the troublesome resonance. Attenuation of resonance response of the bat will make you a better hitter!

The TMD is located typically within the handle and frame in a tennis racket application. Local resonances of tennis racket strings can often be attenuated via Damping Links applied locally to the strings near the frame. Attenuation of resonance response of your tennis racket will improve your tennis game!

Bending resonances of skis can be attenuated via surface-coverage Constrained Layer Damping System (CLDS). This is particularly appropriate where multiple bending resonances aggravate stable performance of the ski. Tuned Mass Dampers can also be a countermeasure option if a single resonance is the target. Attenuation of resonance response of your skis will make you a better skier!