Skip to main content
SpringerLink
Log in

Dynamics of plane motion of a body with a system of flexible inextensible rods connected in series by elastoviscous joints at large angles of rotation

  • Published:
Mechanics of Solids Aims and scope Submit manuscript

Abstract

The principle of virtual displacements is used to obtain the equations of plane motion, in generalized coordinates, of a free rigid body with a system of flexible inextensible rods connected in series by elastoviscous joints at large angles of rotation. Each rod rotates as a line connecting its ends and bends according to two given shapes. The imposition of the kinematic conditions of inextensibility of the rods ensures that the mathematical model of the system does not contain oscillations caused by longitudinal vibrations of the rods. This fact improves the computational stability of the system.

As an example, the dynamic analysis of unfolding of a system consisting of five identical rigid rods connected by elastic joints is carried out. The system is initially in vertical position and is folded up. To allow the system to come to a given state, highly rigid clamps with viscous damping are used, which are switched on under certain restrictions on the rotation angles.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. V. A. Svetlitsky, Mechanics of Rods, Vol. 2: Dynamics (Vysshaya Shkola, Moscow, 1987) [in Russian].

    Google Scholar 

  2. V. A. Svetlitsky, Mechanics of Absolutely Flexible Rods (Izd-vo MAI, Moscow, 2001) [in Russian].

    Google Scholar 

  3. L. V. Dokuchaev, Nonlinear Dynamics of Aircraft with Deformable Elements (Mashinostroenie, Moscow, 1987) [in Russian].

    Google Scholar 

  4. F. N. Shklyarchuk, “Nonlinear and Linearized Equations of Motion for Elastic Space Structures,” Izv. Akad. Nauk. Mekh. Tverd. Tela, No. 1, 161–175 (1996) [Mech. Solids (Engl. Transl.) 31 (1), 141–153 (1996)].

  5. A. N. Danilin, T. V. Grishanina, F. N. Shklyarchuk, and D. V. Buzlaev, “Dynamics of a Space Vehicle with Elastic Deploying Tether,” Computer and Struct., No. 72, 141–147 (1999).

  6. T. V. Grishanina and F. N. Shklyarchuk, Dynamics of Elastic Controllable Structures (Izd-vo MAI, Moscow, 2007) [in Russian].

    Google Scholar 

  7. T. V. Grishanina and F. N. Shklyarchuk, “Dynamics of Deployment of Multielement Plane Rod and Cable Systems,” in Proc. 2nd Intern. Conf. “Problems of Nonlinear Mechanics of Solids” (Izd-vo Kazan. Gos. Univ., Kazan, 2009), pp. 142–144 [in Russian].

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Aviation Institute (State University of Aerospace Technologies), Volokolamskoe sh. 4, GSP-3, A-80, Moscow, 125993, Russia

    T. V. Grishanina & F. N. Shklyarchuk

Authors
  1. T. V. Grishanina
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. F. N. Shklyarchuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. V. Grishanina.

Additional information

Original Russian Text © T.V. Grishanina, F.N. Shklyarchuk, 2011, published in Izvestiya Akademii Nauk. Mekhanika Tverdogo Tela, 2011, No. 2, pp. 109–117.

About this article

Cite this article

Grishanina, T.V., Shklyarchuk, F.N. Dynamics of plane motion of a body with a system of flexible inextensible rods connected in series by elastoviscous joints at large angles of rotation. Mech. Solids 46, 248–255 (2011). https://doi.org/10.3103/S0025654411020130

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.3103/S0025654411020130

Keywords

Search

Navigation