| Summary: | 碩士 === 國立臺灣科技大學 === 機械工程系 === 94 === Following the Wittrick’s differential equations modified with including the temperature effect, the present study uses the Rayleigh-Ritz method to develop the one-dimensional finite element equations of motion for the cylindrical helical springs. For the static problems of cylindrical helical springs, the modified Wittrick’s differential equations can be solved for the exact solutions. The displacement functions in the exact solutions are used to derive the interpolation functions which are used in the computation of the mass, stiffness matrices and thermal load of the present spring element. The present finite element model is applied in the static problems and free vibration analyses of cylindrical helical springs, respectively. In the present static analysis, the cylindrical helical springs subjected to uniform temperature change are also considered. The present model performance is compared with that of exact solutions and other finite elements. The accuracy and efficiency of the present spring element are demonstrated through the numerical results.
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