Studying continuum dynamic behaviour through rigid multibody dynamics

Abstract

Studying the dynamic behaviour of continuum using discretization through Finite Element is common place. This paper attempts to apply the concept of rigid multibodies connected with proper kinematic pairs to approximate the kinematic behaviour of a flexible body; the system of interconnected rigid multibodies is then used to simulate the deformation pattern of a flexible body under dynamic loading. With this aim, this paper simulates, to begin with, the dynamic behaviour of a simple Cantilevered beam by considering several bar-like rigid multibodies connected by revolute pairs having properly design torsional stiffness to simulate the static deformation pattern under different loading conditions. Later this system is used to find out the dynamic deformation pattern with the help of the software, called ReDySim (Shah et al. in CSTAM Theor Appl Mech Lett 2:063011, 2012 [2]), a multibody dynamic simulation package based on Decoupled Natural Orthogonal Complement (DeNOC) (Saha et al. in Mech Sci 4:1–20, 2013 [1]) concept, in the form of mode shapes and natural frequencies of the system. Next the same model is extended to simulate the dynamic behaviour of a Cantilevered overhung rotor-shaft. The results obtained from ReDySim are compared with those obtained from a MATLAB code written for simulating a formulation based on FEM; a close match between these two dynamics behaviors is obtained to prove the validity of the approach. Thus the rigid multi-body equivalent of a continuum (a structure or a rotor) is built and this is supposed to be useful in simulating dynamic behaviour of continua under generic dynamic conditions.