Barun Pratiher

Nonlinear Vibration of a Magneto-Elastic Cantilever Beam With Tip Mass

In this work the effect of the application of an alternating magnetic field on the large transverse vibration of a cantilever beam with tip mass is investigated. The governing equation of motion is derived using DAlemberts principle, which is reduced to its nondimensional temporal form by using the generalized Galerkin method. The temporal equation of motion of the system contains nonlinearities of geometric and inertial types along with parametric excitation and nonlinear damping terms. Method of multiple scales is used to determine the instability region and frequency response curves of the system. The influences of the damping, tip mass, amplitude of magnetic field strength, permeability, and conductivity of the beam material on the frequency response curves are investigated. These perturbation results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion and experimental results. This work will find extensive applications for controlling vibration inflexible structures using a magnetic field.

Nonlinear Vibrations and Frequency Response Analysis of a Cantilever Beam Under Periodically Varying Magnetic Field

In this paper, nonlinear vibration of a cantilever beam with tip mass subjected to periodically varying axial load and magnetic field has been studied. The temporal equation of motion of the system containing linear and nonlinear parametric excitation terms along with nonlinear damping, geometric and inertial types of nonlinear terms has been derived and solved using method of multiple scales. The stability and bifurcation analysis for three different resonance conditions were investigated. The numerical results demonstrate that while in simple resonance case with increase in magnetic field strength, the system becomes unstable, in principal parametric or simultaneous resonance cases, the vibration can be reduced significantly by increasing the magnetic field strength. The present work will be very useful for feed forward vibration control of magnetoelastic beams which are used nowadays in many industrial applications.

Nonlinear response of a soft magneto elastic cantilever beam with end mass under static and dynamics magnetic field

In this work, the nonlinear vibration of a cantilever beam with end mass subjected to both static and alternating transverse magnetic field has been studied. The governing temporal equation of motion of the system which contains nonlinearities of geometric and inertial type along with parametric excitation and non-linear damping terms due to the body force and couple generated by the magnetic field has been derived. Method of multiple scales (MMS) is used to determine the instability region and frequency response curves of the system. The influences of the damping, amplitude of static and dynamic magnetic field strength, and tip mass on the instability regions and frequency response curves for simple and principal parametric resonance conditions have been investigated. These results are found to be in good agreement with those obtained by numerically solving the temporal equation of motion.