DYNAMICAL INSTABILITY ANALYSIS OF NANOTUBES USING NONLOCAL SHEAR BEAM THEORY

作者：Tylikowski Andrzej^*

来源：International Journal of Bifurcation and Chaos, 2011, 21(10): 3047-3052.

DOI：10.1142/S0218127411030350

• Nonlocal continuum mechanics
• shear beam theory
• stochastic parametric vibrations
• dynamic instability
• Liapunov method

The dynamics stability of distributed systems (continua) has been an object of considerable attention over the past half century. Numerous papers are available on isotropic and laminated beams, shafts, plates and shells under periodic and random forces. Most papers have applied finite dimensional or modal approximations in the analysis of vibration and stability. This paper focuses on the stochastic parametric vibrations of micro- and nanorods based on Eringens nonlocal elasticity theory and shear beam theory. The almost sure asymptotic instability criteria involving a damping coefficient, structure and loading parameters are derived using Liapunov's direct method. Using the appropriate energy-like Liapunov functional, sufficient conditions for the almost sure asymptotic instability of undeflected form of beam are derived. The nonlocal shear beam accounts for the scale effect, which becomes significant when dealing with short micro- and nanorods. From the obtained analytical formulas it is clearly seen that the small scale effect increases the dynamic instability region. Instability regions are functions of the axial force variance, the constant component of axial force and the damping coefficient.

• 出版日期2011-10