Non-Linear Forced Vibration of a Tapered Cantilever Beam

Abstract

This paper presents a study on the nonlinear frequency response of a tapered cantilever beam. The mathematical model is developed based on the large deformation theory, nonlinear curvature and with the constraint of inextensible beam. The Lagrangian dynamics with the assumed mode method is utilized in deriving the nonlinear, uni-modal temporal equation of motion. The non-linear equation of motion is solved analytically using the harmonic balance method (HB). Results were obtained for tapered beams with different values of taper ratio. The effect of taper ratio and excitation level on the qualitative behaviour of the forced response of the beam were studied and presented the first three modes of vibration.