Tapered Beam Axial Vibration Frequency: Linear Cross-area Variation Case

Abstract

The expression describing a cross-area linear variation for a tapered beam vibrating axially is considered. It is utilized to formulate the first axial vibration mode shape. The later, results from the normalization of the displacement function obtained by solving the exact solution of the second order differential equation with none constant coefficients. This function is governing the non uniform bar element equilibrium. After this first step, the well known Rayleigh quotient is used for calculating the fundamental natural frequency. The obtained results are comparable to those issued from numerical and theoretical methods. These findings suggest a simply useable handle tool expressed by a curve which allows a quick fundamental frequency evaluation for various taper degrees.