Study on the inertia effect of helical spring of the absorber on suppressing the dynamic responses of a beam subjected to a moving load

Abstract

In the dynamic analysis of the classical absorber composed of a spring, a damper and a lumped mass, the mass of its helical spring (or spring mass) is usually neglected. The purpose of this paper is to present a modified absorber with inertia effect of the spring mass considered. In order to evaluate the vibration–reduction efficiency of the presented modified absorber, the forced vibration analyses of a single degree-of-freedom (dof) and a multiple dof structural systems are performed. The first analysis is to determine the dynamic magnification factor of a single dof spring–mass system, respectively, attached by a classical absorber and a modified absorber and subjected to a harmonic excitation. The second analysis is to determine the maximum dynamic responses of a multiple dof pinned–pinned beam, respectively, attached by the last two kinds of absorbers and subjected to a moving concentrated load. Because the second analysis is conducted using the conventional finite element method (FEM), in additional to the mass matrix, damping matrix and stiffness matrix of the classical and modified absorbers, the expressions for calculating the optimum parameters of the last two absorbers associated with any order of vibration mode of the pinned–pinned beam are also derived based on the modal data obtained from the mode superposition methodology and the orthogonal property between the normal mode shapes. Numerical results reveal that the spring mass of the absorber has the effect of suppressing the maximum dynamic responses of the main structural system and should be considered in the formulation to agree with the practical situation.