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

Ming-Hung Hsu

doi:10.6180/jase.2009.12.2.02

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

Electrical Engineering

Ming-Hung Hsu This email address is being protected from spambots. You need JavaScript enabled to view it.¹

¹Department of Electrical Engineering, National Penghu University, Penghu, Taiwan 880, R.O.C.

Received: September 28, 2007
Accepted: January 20, 2009
Publication Date: June 1, 2009

Download Citation: ||https://doi.org/10.6180/jase.2009.12.2.02

ABSTRACT

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_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.

Keywords: Elastic Foundation, Vibration Analysis, Non-Uniform Beam, Spline Collocation Method, Taper Ratio

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