Dynamical Response of a Beam
in a Centrifugal Field Using the Finite
Element Method
Eliza Chircan , Maria Luminit , a Scutaru , and Ana Toderi¸ t˘ a
Abstract In this chapter, we propose a method of analyzing the motion equations in
the case of a beam in rotation in plane, in order to determine the domain of instability
without actually calculating the eigenvalues or to integrate the obtained equations
of motion. This can ease the computational effort needed to solve such a problem.
Some examples are studied in the paper.
1 Introduction
The first research in the field of elastic elements with a general rigid motion using
numerical methods (especially Finite Element Method) has begun in the 1970s. The
first studies were made for a single-beam one-dimensional finite element, using
third-degree-shape functions. The complexity of the studied cases increased, and the
method was developed for fifth-degree-shape polynomials. The method was used
for a plane motion and for the three-dimensional rigid motion of a beam. In all
these cases, a one-dimensional finite element was used [1–5]. The first model was a
Bernoulli model. Other models, such as the Rayleigh model or Timoshenko model,
were studied in [6–11]. Thereafter, the researchers developed two-dimensional and
three-dimensional finite elements [12–14]. The developed models created new theoretical problems related to the methods of solving and qualitative analysis of such
equations [15, 16]. To study a mechanical system with elastic elements which also
involve a previous dynamical analysis, so we use of MBS (multibody models) models.
In this paper, we propose to make a study, for a set of geometrical parameters, if the
mechanical system is stable or not, in the case of a beam with a rotation around one
of the ends. More elaborated models are made in [17–19].
E. Chircan (B) · M. L. Scutaru · A. Toderi¸ t˘ a
Transilvania University, Str. Politehniciii nr. 1, 500024 Bras , ov, Romania
e-mail: chircan.eliza@unitbv.ro
M. L. Scutaru
e-mail: lscutaru@unitbv.ro
© 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_11
101
in a Centrifugal Field Using the Finite
Element Method
Eliza Chircan , Maria Luminit , a Scutaru , and Ana Toderi¸ t˘ a
Abstract In this chapter, we propose a method of analyzing the motion equations in
the case of a beam in rotation in plane, in order to determine the domain of instability
without actually calculating the eigenvalues or to integrate the obtained equations
of motion. This can ease the computational effort needed to solve such a problem.
Some examples are studied in the paper.
1 Introduction
The first research in the field of elastic elements with a general rigid motion using
numerical methods (especially Finite Element Method) has begun in the 1970s. The
first studies were made for a single-beam one-dimensional finite element, using
third-degree-shape functions. The complexity of the studied cases increased, and the
method was developed for fifth-degree-shape polynomials. The method was used
for a plane motion and for the three-dimensional rigid motion of a beam. In all
these cases, a one-dimensional finite element was used [1–5]. The first model was a
Bernoulli model. Other models, such as the Rayleigh model or Timoshenko model,
were studied in [6–11]. Thereafter, the researchers developed two-dimensional and
three-dimensional finite elements [12–14]. The developed models created new theoretical problems related to the methods of solving and qualitative analysis of such
equations [15, 16]. To study a mechanical system with elastic elements which also
involve a previous dynamical analysis, so we use of MBS (multibody models) models.
In this paper, we propose to make a study, for a set of geometrical parameters, if the
mechanical system is stable or not, in the case of a beam with a rotation around one
of the ends. More elaborated models are made in [17–19].
E. Chircan (B) · M. L. Scutaru · A. Toderi¸ t˘ a
Transilvania University, Str. Politehniciii nr. 1, 500024 Bras , ov, Romania
e-mail: chircan.eliza@unitbv.ro
M. L. Scutaru
e-mail: lscutaru@unitbv.ro
© 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_11
101