Loading...

Vibration Control of Nonclassical Microbeams Using Boundary Control Theory of Partial Differential Equations

Vatankhah, Ramin | 2012

2210 Viewed
  1. Type of Document: Ph.D. Dissertation
  2. Language: Farsi
  3. Document No: 45155 (08)
  4. University: Sharif University
  5. Department: Mechanical Engineering
  6. Advisor(s): Alasty, Aria
  7. Abstract:
  8. Nowadays, continuous systems such as strings, bars, beams and plates have become widespread in science and engineering applications. To achieve the control purposes of continuous systems, most of engineers use discretization techniques to reduce the governing partial differential equation (PDE) into a set of ordinary differential equations (ODEs). From practical point of view, this model reduction can cause many problems such as in-domain measurement and actuation and control spillover. This thesis attempts to investigate the problem of vibration control of nonclassical microscale beams using the partial differential equation control theory which eliminates spillover instabilities. To this end, mathematical tools and preliminaries such as functional analysis, operator theory and semigroup technique are required to employ. Stability and well-posedness analysis of the closed loop system are accomplished using these mathematical tools.In non-classical micro-beams, the stress-strain relations and the governing partial differential equation of motion are obtained based on the non-classical continuum mechanics. In this investigation, asymptotic and exponential stabilization and exact controllability of nonclassical microbeams have been studied without reducing the PDE model of the system. These control objectives have been achieved using the boundary control laws in which the actuators and sensors are aligned on the boundaries of the microbeam. Furthermore, the effectiveness and performance of the proposed boundary controllers have been investigated in the presence of prevalent nonlinear forces in microscale structures such as electrostatic, casimir and van der waals forces
  9. Keywords:
  10. Vibration Control ; Partial Differential Equations ; Boundary Control ; Exponential Stability ; Nonclassical Microbeams ; Asymptotic Stabilization ; Exact Controllability

 Digital Object List