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

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 alpha, beta, the boundary conditions, and the elastic foundation stiffness, kf, 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.