Dynamics of A Single Elastic Bodies under Large Rigid Rotation

Abstract:

Article Preview

The generalized elasticity is presented where a modified constitutive relation for the couple stress is proposed. A rigid-flexible coupled model is set up where three types of additional inertia forces along with their increments are elucidated in the model. The finite element formulation is developed with the use of the constrained variational principle. As an example, a dynamic analysis on a rotating cantilever is numerically carried out. The dynamical responses of the displacement and rotational angle at the free end, the stress and couple stress at the fixed end of cantilever are presented. An idea of critical angular velocities is proposed to insure system stability. The displacement trajectory of the free end of cantilever is approached and the dynamic stiffening problem is discussed.

Info:

Periodical:

Edited by:

Chunliang Zhang and Paul P. Lin

Pages:

451-458

Citation:

Z. F. Liu and S. J. Yan, "Dynamics of A Single Elastic Bodies under Large Rigid Rotation", Applied Mechanics and Materials, Vols. 226-228, pp. 451-458, 2012

Online since:

November 2012

Export:

Price:

$41.00

[1] Kane TR, Ryan RR and Banerjee AK: Dynamics of a cantilever beam attached to a moving base. AIAA Journal of Guidance, Control, and Dynamics, 1987, 10(2): 139–151.

DOI: https://doi.org/10.2514/3.20195

[2] Berzeri M and Shabana AA: Study of the centrifugal stiffening effect using the Finite Element Absolute Nodal Coordinate Formulation. Multibody System Dynamics, 2002, 7(4): 357–387.

DOI: https://doi.org/10.1115/detc2005-84061

[3] Mindlin RD, Tiersten HF: Effects of couple-stresses in linear elasticity. Arch. Rational Mech. Anal, 1962, 11(1): 415–488.

DOI: https://doi.org/10.1007/bf00253946

[4] B Palais, R Palais: Euler's fixed point theorem: the axis of a rotation. J. Fixed Point Theory and Applications, 2007, 2(2): 215-220.

DOI: https://doi.org/10.1007/s11784-007-0042-5

[5] Eringen AC: Linear theory of micropolar elasticity. J. Math. Mech., 1966, 15(6): 909-923.