Dynamic properties of a body with discontinual mass variation

Abstract

In this paper the procedure for the dynamic analysis of body separation is introduced. Based on the general laws of classical dynamics, the method for obtaining the velocity and the angular velocity of the remainder body during separation is developed. Due to the discontinual mass variation, the jump-like change of the velocity and the angular velocity of the body is evident. Various types of motion of the separated body are considered. Depending on the type of motion of the separated body the dynamic properties of the remainder body are obtained. As a special case the in-plane motion of the body before and after separation is considered. The theoretical considerations are applied for the separation analysis of a rotor (a shaft-disc system). The transient motion of the body after separation is investigated. To prove the correctness of the procedure suggested in the paper, the case when the mass and the moment of inertia of the separated body are infinitesimal is analyzed. The obtained differential equations are the same as those previously obtained.

Dynamics of body separation—analytical procedure

“…The dynamics of body separation, as it was suggested in the paper [28], represents an inverse process of the perfectly plastic impact of the two perfectly inelastic bodies. During the separation, which lasts for a very short time interval τ , the body undergoes a relaxation which causes the energy of deformation (potential energy) to be transformed into kinetic energies of the separated and the remainder bodies.…”

“…Using the aforementioned assumptions and the principles of dynamics, the velocity and angular velocity of the remainder body after the separation are obtained (see [28]). Namely, the body with mass M and velocity of mass center v S has the linear momentum K 1 = Mv S .…”

“…Taking into account (21) and using the relations (22), (25), (28), and (29), the following system of equations is obtained…”

“…The kinematic and dynamic properties of the system during separation are investigated. Cveticanin and Djukic [28] extended the investigations for a body in general motion. The principles of momentum and angular momentum conservation were modified to obtain the velocity and angular velocity values during body separation.…”

Geometry of motion and nutation stability of free axisymmetric variable mass systems

“…The second generation of studies was more expansive. Apart from revisiting the derivation of the equations of motion of continuous mass varying systems [5][6][7], attention has also been paid to algorithm development for simulating rigid [8] and flexible systems with mass variation [9,10], as well as analyses of systems with discontinuous mass variation [11,12].…”