Vibrations of the Mass Variable Systems
Livija Cveticanin and Dragan Cveticanin
Abstract There are a significant number of systems with time-variable mass. The
mass variation may be continual or discontinual. During discontinual mass change,
a body with certain mass is added to or separated from an initial body. During
this process, the position of acting parts is assumed to be unmovable, while their
velocities have the jump-like variation. The effect of discontinual mass variation is
evident during fracture of the body. The result of dynamic analysis of mass variation
gives the prediction of kinematic properties of the separating and remaining bodies. It
is concluded that the discontinual separation is the opposite process to the impact of
bodies. Theoretical results are supported with an example of a windmill with bended
or broken blades. If the separation or addition of mass is continual and slow, during
mass variation a reactive force and a reactive torque occur, which are the product of
mass time derivative and of the velocity change and the product of the time derivative
of the moment of inertia moment and angular velocity, respectively. This force and
torque excite vibration in the system. It is of interest to investigate the influence of
the reactive force and torque on the oscillatory behavior of the system. Mathematical
model of the system is formed, and methods for solving equations with slow timevariable parameters are developed. The obtained results are convenient for dynamic
analysis. In this paper, the vibrations of the rotor, as a two-degree-of-freedom system,
are considered. The effect of reactive force on the motion of the sieve for particle
separation is also discussed.
L. Cveticanin (B)
University of Novi Sad, Trg D. Obracovica 6, Novi Sad, Serbia
e-mail: cveticanin@uns.ac.rs
Obuda University, Nepszinhaz uU. 7, Budapest, Hungary
D. Cveticanin
Remming, B. Nusica 15, Novi Sad, Serbia
e-mail: dragan.cveticanin@remming.co.rs
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_3
25
Livija Cveticanin and Dragan Cveticanin
Abstract There are a significant number of systems with time-variable mass. The
mass variation may be continual or discontinual. During discontinual mass change,
a body with certain mass is added to or separated from an initial body. During
this process, the position of acting parts is assumed to be unmovable, while their
velocities have the jump-like variation. The effect of discontinual mass variation is
evident during fracture of the body. The result of dynamic analysis of mass variation
gives the prediction of kinematic properties of the separating and remaining bodies. It
is concluded that the discontinual separation is the opposite process to the impact of
bodies. Theoretical results are supported with an example of a windmill with bended
or broken blades. If the separation or addition of mass is continual and slow, during
mass variation a reactive force and a reactive torque occur, which are the product of
mass time derivative and of the velocity change and the product of the time derivative
of the moment of inertia moment and angular velocity, respectively. This force and
torque excite vibration in the system. It is of interest to investigate the influence of
the reactive force and torque on the oscillatory behavior of the system. Mathematical
model of the system is formed, and methods for solving equations with slow timevariable parameters are developed. The obtained results are convenient for dynamic
analysis. In this paper, the vibrations of the rotor, as a two-degree-of-freedom system,
are considered. The effect of reactive force on the motion of the sieve for particle
separation is also discussed.
L. Cveticanin (B)
University of Novi Sad, Trg D. Obracovica 6, Novi Sad, Serbia
e-mail: cveticanin@uns.ac.rs
Obuda University, Nepszinhaz uU. 7, Budapest, Hungary
D. Cveticanin
Remming, B. Nusica 15, Novi Sad, Serbia
e-mail: dragan.cveticanin@remming.co.rs
© Springer Nature Switzerland AG 2021
N. Herisanu and V. Marinca (eds.), Acoustics and Vibration of Mechanical
Structures—AVMS 2019, Springer Proceedings in Physics 251,
https://doi.org/10.1007/978-3-030-54136-1_3
25