Nano - and Micro Eelectromechanical Systems - S.E. Lyshevski Part 4

Tham khảo tài liệu 'nano - and micro eelectromechanical systems - . lyshevski part 4', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | The magnetic energy density is r r r r wm 2 A-J 2B H. Using Newton s second law and the stored magnetic energy we have nine highly coupled nonlinear differential equations for the xyz translational motion of microactuator. In particular dF xyz dt fF Fxyz vxyz Xxyz H dv xyz dt fv Fxyz Vxyz Xxyz FLxyz dxxyz dt fx vxyz xxyz x xyz xyz where F yz are the forces developed vxyz and xxyz are the linear velocities and positions FLxyz are the load forces. The expressions for energies stored in electrostatic and magnetic fields in terms of field quantities should be derived. The total potential energy stored in the electrostatic field is obtained using the potential difference V as We 2 ò pvVdv where the volume charge density is found as pv V D v V is the curl operator. In the Gauss form using pv V D and making use ofE -VV one obtains the following expression for the energy stored in the electrostatic field We ị ò D Edv and the electrostatic volume energy density v is 2 D E. For a linear isotropic medium one finds f I ri2 1 r 1 Iri2 W 2 ò s - 2 ò 1 DK vv The electric field E x y z is found using the scalar electrostatic potential function V x y z as r E x y z -Vv x y z . In the cylindrical and spherical coordinate systems we have E r f z -VV r f z and E r d f -VV r d f . Using the principle of virtual work for the lossless conservative nano-and microelectromechanical systems the differential change of the electrostatic energy dWe is equal to the differential change of mechanical 2001 by CRC Press LLC energy dWmec dWe dWmec. For translational motion dWmec Fe dl where dl is the differential displacement. One obtains dWe VWe dl . Hence the force is the gradient of the stored electrostatic energy Fe VWe . In the Cartesian coordinates we have F d and F W ex ey 1 ez 1 . ơx dy dz Energy conversion takes place in nano- and microscale electromechanical motion devices actuators and sensors smart structures antennas and ICs. We study electromechanical motion devices that convert .