Response of a micro-capillary system exposed to a moving mass in magnetic field using nonlocal strain gradient theory

Abstract

In this study, the dynamic behaviour of the micro dimensional Timoshenko beam (micro capillary system) exposed to a moving mass in a magnetic field is modelled using the non-local strain gradient theory. The motion equations of the Timoshenko micro-beam, which interacts with the moving mass, are obtained by considering the effects of strain gradient elasticity that provides stiffening and non-local elasticity that provide softening. The transverse Lorentz force acting on the beam in the magnetic field is obtained by Maxwell's equations and combined with the motion equations of the beam. These equations are converted into a weak form finite element equation by applying the exact shape functions of the two-node Timoshenko beam element in the Galerkin's method. Along with the effects of the magnetic field, the effects of the amount of different non-local parameters and the mass ratio and speed of the moving mass on the dynamics of the micro beam are presented. Experimental and theoretical studies have shown that the dynamic behaviour of the capillary structural systems is negatively affected by the effect of moving mass except for the non-local properties. Depending on the velocity and quantity of the mass and the nonlocal elasticity, the natural frequencies of the system drop excessively. When the mass ratio (moving mass/mass of the beam) is around 0.5, the frequencies have been observed to drop by as much as 60%, and the non-local elasticity and velocity of the mass are also effective in this. It has been shown that these disadvantages can be eliminated by the effect of the force obtained using the directed magnetic field. In fact, a desired system stiffness can be obtained by adjusting the magnitude of the magnetic field at the level required by the application.