Electromechanical Dynamics (Part 1).0098

Electromechanical Dynamics (Part 1).0098 - 3.1.2 A-PDF...

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Electromechanical Coupling the capacitance C(x) of plane parallel plates with area A and spacing x (Fig. 3.1.2). Then C(x) - A (3.1.54) and (3.1.51) gives f" - .A (3.1.55) 2x 2 The minus sign tells us that fO acts on the upper plate (node) in the (-x) direction. This we expect, for positive charges on the top plate are attracted by negative charges on the bottom plate. We can obtain the same result by using the energy and the translational form of (3.1.27). f = W(q, x) (3.1.56) ax From (3.1.53) and (3.1.54) f" = (3.1.57) 2Ae In view of (3.1.49) and (3.1.54) this result and (3.1.55) are identical. Suppose, however, that we blindly apply (3.1.56) to the energy of (3.1.53) with q replaced by Cv. The magnitude of the resulting force will be correct, but the sign will be wrong. For electrically nonlinear systems the magnitude of the force will also be wrong if the partial differentiation is not carried out correctly. The generalized force and coenergy equations are summarized in Table 3.1. This table is intended to illustrate the generality of
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  • Fall '11
  • Liu
  • Electric charge, plane parallel plates, A-PDF Split DEMO, Purchase Electromechanical Coupling, electrically nonlinear systems

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