Finite Element Analysis of Micro – Electro – Mechanical Systems: Towards the integration of MEMS in design and robust optimal control schemes of smart microstructures

Microelectromechanical Systems (MEMS) is the technology of the very small, and merges at the nano-scale into "Nanoelectromechanical" Systems (NEMS) and Nanotechnology. MEMS are also referred to as micro machines, or Micro Systems Technology (MST). MEMS are separate and distinct from the hypothetical vision of Molecular nanotechnology or Molecular Electronics. MEMS generally range in size from a micrometer (a millionth of a meter) to a millimeter (thousandth of a meter). At these size scales, the standard constructs of classical physics do not always hold true. Due to MEMS' large surface area to volume ratio, surface effects such as electrostatics and wetting dominate volume effects such as inertia or thermal mass. Finite element analysis is an important part of MEMS design. The paper presents the design of a vibration control mechanism for a beam with bonded piezoelectric sensors and actuators and an application of the arising smart structure for vibrations suppression too. The mechanical modelling of the structure and the subsequent finite element approximation are based on Hamilton’s principle and classical engineering theory for bending of beams in connection with simplified modelling of piezoelectric sensors and actuators. Two control schemes LQR and H2 are considered. The latter robust controller takes into account uncertainties of the dynamical system and moreover incompleteness of the measured information, it therefore leads to applicable design of smart structures. The numerical simulation shows that sufficient vibration suppression can be achieved by means of the proposed general methods. It is given as a perspective to the MEMS technology towards the direction of integrating MEMS in design and robust optimal control schemes. Key-Words: Finite Element Analysis, Micro – Electro – Mechanical Systems, ANSYS software, Coupled problems, Micro actuator, Bi stable electromagnetic actuation, UV-LIGA technology, Simulation, Active structural control, Smart beam, Composite structure, Piezoelectric layer.