Supersonic flutter and free vibration features of functionally graded material nanobeams incorporating surface effects

Abstract

In the present work, a numerical investigation is provided for free vibrational and aeroelastic stability features of nanobeams made of Functionally Graded Material (FGM) resting on an elastic Pasternak foundation. The FGM nanobeam's mechanical properties are considered to differ based on power-law and exponential functions in the thickness direction. The effect of size is modeled in terms of the Gurtin-Murdoch surface elasticity theory and the Nonlocal Strain Gradient Theory (NSGT) is employed for incorporating the surface effects. Mathematical modeling of the FGM nanobeam is oriented by three various beam theories including Reddy's third-order Shear Deformation Beam Theory (TSDBT), Timoshenko beam theory (TBT), and Euler-Bernoulli Beam Theory (EBT), moreover, the aerodynamic pressure is determined in terms of the linear supersonic piston theory. It is concluded that when the surface effects are incorporated, the width-to-length ratio of the FGM nanobeam plays a sensible role in determining the natural frequencies; but it has no sensible effect on the flutter boundaries. Numerical results reveal that the importance of the surface effects increases as the values of thickness-to-length and width-to-length ratios decrease.

KEYWORDS:

• Free vibration
• flutter
• surface effects
• nanobeam
• nonlocal strain gradient theory

Disclosure statement

No potential conflict of interest was reported by the author(s).