The purpose of this research is to establish the method of theoretically simulating the vibration spectrum which is very important to the performance of skis. For a uniform rigidity beam having a rectangular section and composed of N different materials, an equation of vibration which includes shear and rotatory inertia is solved for a natural frequency approximation under the condition of both ends free. To prove the approximation close enough, experiments are conducted on a monolithic material beam, a closed shell structure beam in which a reinforcement member encloses a core and a sandwich structure beam, with various materials. The results of the experiment indicate that very close approximation exists between the experimental values and theoretical values, and that the vibration spectrum of a beam composed of different materials can be estimated theoretically by using the modulus of longitudinal elasticity, modulus of transverse elasticity, density and size. Thus, more precise optimization can be established by employing the vibration spectrum in addition to the conventional material and structure design which has been determined by considering only the flexural and torsional rigidity.
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