Nonlocal wave propagation analysis of a rotating nanobeam on a Pasternak foundation

Abstract

In this paper, the wave propagation analysis of a cantilever rotating nanobeam modeled as a thin beam based on the Euler–Bernoulli theory on a Pasternak foundation has been investigated using the nonlocal theory of elasticity. The governing partial differential equation of motion for a uniform rotating nanobeam is derived using the Hamilton principle considering the nonlocal parameter of small scale effect. The Spectrum and dispersion relations of non-dimensional wave number are obtained analytically. The effect of changes of different parameters including nonlocal scale parameter, non-dimensional rotational speed, non-dimensional rotational wave frequency ratio, and shear stiffness of the Pasternak foundation on the wave dispersion behavior of the non-dimensional wave number and phase and group speeds dispersions for the rotating nanotube have been studied. It is observed that the wave dispersion characteristics of the rotating nanobeam are extremely influenced by rotational speed, wave number, nonlocal length scale parameter, and shear stiffness of the Pasternak foundation. Moreover, the propagated flexural wave has been shown to exhibit non-dispersive behavior at very high rotational speeds.

Keywords

cantilever rotating nanobeam wave propagation spectrum curve phase and group speeds dispersive behavior non-dispersive behavior

Get full access to this article

View all access options for this article.

References

Aranda-Ruiz

Loya

Fernandez-Saez

(2012) Bending vibrations of rotating nonuniform nanocantilevers using the Eringen nonlocal elasticity theory. Composite Structures 94(9): 2990–3001.

Das

Ray

Pohit

(2005) Large amplitude free vibration analysis of a rotating beam with non-linear spring and mass system. Journal of Vibration and Control 11(12): 1511–1533.

Gohari

Zarastvand

Talebitooti

, et al. (2020) Radiated sound control from a smart cylinder subjected to piezoelectric uncertainties based on sliding mode technique using self-adjusting boundary layer. Aerospace Science and Technology 106: 1–12.

Gunda

Singh

Chhabra

, et al. (2007) Free vibration analysis of rotating tapered blades using Fourier-p super element. Structural Engineering and Mechanics 27(2): 243–257.

Huang

Lin

Hsiao

(2010) Free vibration analysis of rotating Euler beams at high angular velocity. Computers and Structures 88: 991–1001.

Karami

Shahsavari

Janghorban

, et al. (2021) Wave dispersion of nanobeams incorporating stretching effect. Waves in Random and Complex Media 31(4): 639-659.

Lin

Hsiao

(2001) Vibration analysis of a rotation Timoshenko beam. Journal of Sound and Vibration 240(2): 303–322.

Lin

(2001) The probabilistic approach for rotating Timoshenko beams. International Journal of Solids and Structures 38(40–41): 7197–7213.

Lin

Lee

Wang

(2004) Dynamic analysis of rotating damped beams with an elastically restrained root. International Journal of Mechanical Sciences 46(5): 673–693.

10.

Lin

Mao

Lin

(2007) Vibration of a rotating smart beam. AIAA Journal 45(2): 382–390.

11.

(2007) Dynamic analysis of axially prestressed micro/nanobeam structures based on nonlocal beam theory. Journal of Applied Physics 101: 1–10.

12.

Narendar

Gopalakrishnan

(2011) Nonlocal wave propagation in rotating nanotube. Results in Physics 1(1): 17–25.

13.

Pradhan

Murmu

(2010) Application of nonlocal elasticity and DQM in the flapwise bending vibration of a rotating nanocantilever. Physica E: Low-dimensional Systems and Nanostructures 42(7): 1944–1949.

14.

Pesheck

Pierre

Shaw

(2002) Modal reduction of a nonlinear rotating beam through nonlinear normal modes. Journal of Vibration and Acoustics 124(2): 229–236.

15.

Rahmatnezhad

Zarastvand

Talebitooti

(2021) Mechanism study and power transmission feature of acoustically stimulated and thermally loaded composite shell structures with double curvature. Composite Structures 276: 1–14.

16.

Sinha

(2005) Non-linear dynamic response of a rotating radial Timoshenko beam with periodic pulse loading at the free-end. International Journal of Non-Linear Mechanics 40(1): 113–149.

17.

Seilsepour

Zarastvand

Talebitooti

(2022) Acoustic insulation characteristics of sandwich composite shell systems with double curvature: the effect of nature of viscoelastic core. Journal of Vibration and Control. online first. DOI: 10.1177/10775463211056758.

, et al. (2006) Vibration control of variable speed/acceleration rotating beams using smart materials. Journal of Sound and Vibration 298(4–5): 1150–1158.

(2004) Dynamic modelling and control of a rotating Euler–Bernoulli beam. Journal of Sound and Vibration 274(3–5): 863–875.

20.

Yang