Pulsating flow induced parametric instabilities of a smart embedded micro-shell based on nonlocal piezoelasticity theory

Abstract

In this study, the dynamical instabilities of an embedded smart micro-shell conveying pulsating fluid flow is investigated based on nonlocal piezoelasticity theory and nonlinear cylindrical shell model. The micro-shell is surrounded by an elastic foundation which is suitable for both Winkler spring and Pasternak shear modules. The internal fluid flow is considered to be purely harmonic, irrotational, isentropic, Newtonian and incompressible and it is mathematically modeled using linear potential flow theory, time mean Navier Stokes equations and Knudsen number. For more reality of the micro-scale problem the pulsating viscous effects as well as the slip boundary condition are also taken into accounts. Employing the modified Lagrange equations of motion for open systems, the nonlinear coupled governing equations are achieved and consequently the instability boundaries are obtained using the Bolotin’s method. In the numerical results section, a comprehensive discussion is made on the dynamical instabilities of the system (such as divergence; flutter and parametric resonance). It is found that applying positive electric potential field will improve the stability of the system as an actuator or as a vibration amplitude controller in the Micro Electro Mechanical Systems.