چكيده به لاتين
In this thesis, nonlinear vibration suppression of a micro-beam covered by a piezoelectric layer is accomplished by a varying tensile force. The AFM micro-beam is a cantilever one, and a piezoelectric layer is located on its top surface in order to measure beam deflections. Base of the beam is subjected to a harmonic excitation. A micro-pump provides an axial time-varying tensile load into the micro-beam. The micro-pump which causes vibration suppression is the actuator. The micro-beam is an Euler-Bernoulli beam which abbeys Kelvin-Voigt model. Using such model supplies the comparison between elastic and viscoelastic beams; and one of the most important properties of viscoelastic materials, damping effect can readily be investigated. In this theory, shear stresses are neglected. The nonlinear equation and corresponding boundary condition are obtained based on energy or Hamiltonian method.
Here, first the Runge-Kutta method is used to compare elastic case with viscoelastic case and then the perturbation technique of Multiple Scales is employed as analytical method. The modulation equations of primary and secondary (sub-harmonic) harmonic resonances are derived for the dominant (vertical) frequency dimension, and the effects of different parameters on the amplitude of harmonic resonances are investigated.
In the following, design of micro-pump, with the purpose of vibration suppression, is considered. A new strategy for providing tensile force to suppress the transverse vibration of a micro-beam is introduced. This axial tensile force is supplied by a specific fluid flow called "magnetohydrodynamics" (MHD), which flows in a micro-pump, and then the fluid enters the micro-beam. The micro-beam is vibrated by an oscillating external force acting at its base. Therefore, a fluid structure interaction problem arises. The pressure of the fluid is increased due to the Lorentz force appears in the micro pump, and is directed by the channel towards the micro-beam and suppress the vibration of the micro-beam.
In this thesis, the effects of provided tensile force by the micro-pump on the amplitude of primary and second resonances are investigated; also, its effects on reducing unstable region and how the nonlinear system can be pushed towards the linear system are investigated. Additionally, the effect of magnetic as well as electric fields, the effect of applied force to the base of micro-beam, and the effects of Reynolds Number on flow parameters such as pressure, displacement and stress of micro-beam are studied.
