Eur. Phys. J. Plus (2021) 136: 1109
https://doi.org/10.1140/epjp/s13360-021-02117-0

Regular Article

Vibration and stability analysis of fluid-conveying sandwich micro-pipe with magnetorheological elastomer core, considering modified couple stress theory and geometrical nonlinearity

¹ Noise and Vibration Control Research Laboratory, School of Mechanical Engineering, Iran University of Science and Technology, Tehran, Iran
² School of Mechanical Engineering, Iran University of Science and Technology, Narmak, Tehran, Iran

^b rtalebi@iust.ac.ir

Received: 21 August 2021
Accepted: 26 October 2021
Published online: 5 November 2021

Abstract

The main goal of this paper is to investigate the size-dependent nonlinear vibration and stability response of fluid-conveying sandwich micro-pipes exploiting magnetorheological elastomer (MRE) as a smart core. Considering the geometrical nonlinearity, based on von-Karman assumption, Euler–Bernoulli theory is employed for mathematical formulation of the problem. Additionally, modified couple stress theory (MCST) is utilized as a size-dependent theory to reach an accurate model. Kerwin assumption is taken into account, and Hamiltonian’s approach is hired to derive the coupled and nonlinear governing equations and boundary conditions of the system. For solution procedure, differential quadrature method (DQM) is used to discretize the governing equations and corresponding boundary conditions. Thereafter, the obtained algebraic nonlinear equations and boundary conditions are solved numerically to acquire the nonlinear eigenvalues of the system which could be analyzed to discuss the stability and critical flow velocity of the system. In numerical analysis, a detailed examination is conducted to elucidate the exact influences of the main intrinsic characteristics of MRE core (i.e., magnetic intensity and MRE core thickness) on vibrational response of the system. Accordingly, the main effects of the MRE layer on vibrational properties including frequency, loss factor, critical flow velocity and stability region for both cantilever and clamped–clamped pipes are investigated. The results reveal the substantial effect of the MRE core on the vibrational characteristics and stability of the system. The boosting effect of the MRE core layer on the stability of the system was disclosed. The results declare that, in addition to the magnetic intensity as a controlling parameter, the MRE core thickness is another important factor in vibration and stability characteristics of the system. Totally, the research reveals that the fabulous properties of the MRE layers could be considered and exploited in designing the fluid-conveying micro-pipes to obtain an efficient, smart and adaptive system response.