NON-LINEAR FORCED VIBRATION OF A TAPERED CANTILEVER BEAM

Document Type : Original Article

Authors

1 Department of Mechanical Engineering, Faculty of Engineering and Technology, University, of Jordan, Amman, Jordan.

2 Department of Civil Engineering, Faculty of Engineering and Technology, University of Jordan, Amman, Jordan.

Abstract

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.

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