Vibration and damping analysis of a scarf-jointed beam in flexure

Abstract

In this paper, an analysis for the determination of resonance frequencies, modal loss factors, and complex mode shapes of a simply supported beam with a scarf joint is presented. The system consists of a pair of isotropic or orthotropic beams that are scarf-jointed with a certain angle by a viscoelastic adhesive. The governing equations of motion of the system, for a general case of forced vibration under transverse distribution load, are first derived using the energy method and Hamilton’s principle. The adhesive material is modeled using the complex modulus approach. By using a finite-difference method, the numerical solutions of the governing equations for free vibration are obtained. A parametric study has been conducted to study the effects of various material and geometric parameters on the system’s dynamic stiffness and modal loss factors. It has been shown that there exists an optimum scarf angle for a given configuration that maximizes the system damping.