Coupled Flexural–Longitudinal Vibrations of Timoshenko Double-Beam Systems Induced by Mass Eccentricities

Abstract

In many instances, marine vessel may suffer unexpected flexural–longitudinal vibrations as the consequences of the unevenly distribution of the inner structures and equipment. In order to study the dynamic behaviors of the marine vessel with the involvement of the mass unevenness, the whole vessel is modeled as a discretely connected double-beam system in this paper. In this model, the misalignment between geometric and gravitational center are considered as the simplification of the mass unevenness. The governing equations of coupled flexural–longitudinal vibrations of Timoshenko beam due to mass eccentricity are derived. Extending to the double-beam model, the natural frequencies, modal shapes and forced response of the system are obtained analytically by using the modified transfer matrix method. The comparison between the present method and the conventional finite element method shows a great match. The result indicates that the existence of mass eccentricity can cause significant coupled flexural–longitudinal vibrations, thus, even only vertical force is applied, the vibration in longitudinal direction can be excited and controlled by the natural frequencies of the flexural vibration.