Vibration Analysis of Non-Uniform Beams Resting on Elastic Foundations Using the Spline Collocation Method

10.6180/jase.2009.12.2.02

Ming-Hung Hsu

Elastic Foundation ； Vibration Analysis ； Non-Uniform Beam ； Spline Collocation Method ； Taper Ratio

淡江理工學刊

12卷2期（2009 / 06 / 01）

113 - 122

英文

The natural frequencies of non-uniform beams resting on elastic foundations are numerically obtained using the spline collocation procedure. The spline collocation method is a numerical approach effective at solving partial differential equations. The boundary conditions that accompanied the spline collocation procedure were used to convert the partial differential equations of non-uniform beam vibration problems into a discrete eigenvalue problem. The beam model considers the taper ratios α, β, the boundary conditions, and the elastic foundation stiffness, k(subscript f), all of which impact the dynamic behavior of non-uniform beams resting on elastic foundations. This work developed the continuum mechanics and combined with the spline collocation method to simulate the dynamic properties of non-uniform beams resting on elastic foundations.