INTRODUCT1ON: In Alpine skiing, an effective damping of ski vibrations might improve the performance considerably. In the present study vibrations of a real ski are investigated both theoretically and experimentally. The ski was modeled as beam using exact geometric data for length, width, thickness, camber, the measured flexural stiffness, and a constant density [2]. Several situations were investigated: 1.) free vibrations of ski shovel and tail, ski center clamped 2.) vibrations of ski shovel and tail, ski loaded by a skier on an inelastic foundation 3.) vibrations caused by drop jumps of a skier from a height of 20-30 cm with an unedged ski. METHOD: The ski was modeled with the equation of motion for a vibrating Euler-Bernoulli beam with damping terms [1]: [...] Here, x denotes the length coordinate, t the time, w(x,t) the bending deflection of the ski, p the density, A(x) the cross section, and Ell(x) the flexural stiffness. The terms with a(x) and ß(x) characterize the external and the internal damping of the ski. The line load f(w,x,t) is the sum of the skier's weight and the ground reaction force. The partial differential equation was solved with finite differences using the method of lines. The vibrations of the ski were determined with a Lukotronic System which measured dynamically the space coordinates of infrared-markers fixed at the ski. The damping terms a(x) and ß(x) were determined in a least square sense from the measured data using the Nelder-Mead simplex algorithm in Matlab. RESULTS: Results will be presented for the various investigated situations. An example is given in Fig. 1. For the free vibrations of a marker at the ski tail the measured data and the computed solution are plotted. Further, results for different force laws describing the ski-snow interaction will be given. DISCUSSION/CONCLUSION: The simulation and the measurements agreed well. So, the presented damping model could be used for investigating vibrations of edged skis and chattering during skiing runs. REFERENCES [1] Magnus, K., Popp. K., Sextm, W. (2008). Schwingungen - Eine Einführung in die physikalischen Grundlagen und die theoretische Behandlung von Schwingungsproblemen. Vieweg + Teubner Verlag. Wiesbaden. [2] Mossner. M.. Heinrich. D., Kaps, P., Schretter, H., Nachbauer, W. (2008). Computer Simulation of Consecutive Ski Turns. Journal of ASTM International, Vol 5, Wo 8. ACKNOWLEDGEMENT The investigation was supported by the Austrian Science Foundation (FWF) under Project No. P20870.
© Copyright 2010 Book of Abstracts. 5th International Congress on Science and Skiing, Dec. 14 - 19, 2010, St. Christoph am Arlberg. Julkaistu Tekijä University of Salzburg, Interfakultärer Fachbereich Sport- und Bewegungswissenschaft/USI. Kaikki oikeudet pidätetään. / Kääntänyt https://www.DeepL.com/Translator