Then, as in previously published papers selleck inhibitor [9, 11, 12], MEM (NEM) actuators can be simplified into a 1DOF for these two models. The 1DOF is the displacement, kinase inhibitor Trichostatin A u, of the upper movable beam for the parallel-plate model, and is the torsional angle, ��, for the torsional model. Here, two intermolecular forces, the non-retarded vdW and retarded Casimir, are considered. For convenience, the dimensionless equations are introduced.2.1. Parallel-plate modelFor the parallel-plate model with damping, the system can be simplified to a 1DOF as shown in Figure 1. The 1DOF is the displacement, u, of the upper movable beam, or the gap distance, r. They satisfy the simple geometrical relation: u=g?r where g is the initial gap distance between the upper movable beam and the ground plate.
Figure 1.
1DLM for the parallel-plate actuator.The system is a typical mass-spring-damping one. For the different intermolecular Inhibitors,Modulators,Libraries forces, the applied forces on the same model are the electrostatic, Inhibitors,Modulators,Libraries vdW, or Casimir forces. Then the equation of motion ismd2udt2+��dudt+ku=Felec+FvdW,(1)when the vdW force Inhibitors,Modulators,Libraries is considered, ormd2udt2+��dudt+ku=Felec+FC,(2)when the Casimir force is considered. Here, m is the mass of the upper movable beam, �� is the damping coefficient for the parallel-plate model, and k is the spring constant [9, 11].The electrostatic Inhibitors,Modulators,Libraries force Felec (neglecting the fringing force) acting between the planes with potential difference V, the vdW force FvdW and the retarded Casimir force, respectively, areFelec=��0wLV22(g?u)2,FvdW=AwL6��1(g?u)3,FC=��2?cwL240(g?u)4,where Inhibitors,Modulators,Libraries ��0 is the Inhibitors,Modulators,Libraries permittivity of vacuum within the gap, A= ��2C��2 is the Hamaker constant which lies in the range (0.
4�C4)10?19 Inhibitors,Modulators,Libraries J, �� is the volume density of graphite, C is a constant Batimastat charactering the interactions between the two atoms, ? is Planck’s constant divided by 2��, and is equal to 1.055��10?34 Js, c Inhibitors,Modulators,Libraries is the speed of light and is equal to 2.988��108ms-1. L and w are the length and width of the upper movable beam, respectively.Introducing dimensionless variables: �� =u/g, �� =t/T, =��/kT, a= ��0wLV2/2kg3, bvdW =AwL/6��kg4, bc= Brefeldin_A ��2?cwL/240kg5, and characteristic time T=m/k.
Equations (1) and (2) can be transformed into a dimensionless form:d2��d��2+�̡�d��d��+��=a(1?��)2+bvdW(1?��)3,(3)when the vdW force is considered, ord2��d��2+�̡�d��d��+��=a(1?��)2+bC(1?��)4,(4)when the Casimir force is considered.According to the definition of these parameters, physically meaningful solutions exist in the region 0 < �� < 1. The dimensionless parameter a denotes the order www.selleckchem.com/products/Cisplatin.html of magnitude of ratio between the electrostatic and elastic forces, bvdW denotes the order of magnitude of ratio between the vdW and elastic forces, bC denotes the order of magnitude http://www.selleckchem.com/products/crenolanib-cp-868596.html of ratio between the Casimir and elastic forces.2.2.