Electromechanical Dynamics (Part 1).0055

Electromechanical Dynamics (Part 1).0055 - vlV + ,+ dt dt...

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Lumped Electromechanical Elements magnitudes in the three regions; consequently, our definition of voltage applied in the three regions yields V 1 v 2 E 2 = - -V Em V2 - V 1 X 1 We now use (1.1.25) with a rectangular surface enclosing the top plate to obtain ql = -- IwEE 1 - (I,. - x 2 )weOE, and with a rectangular box enclosing the right-hand movable plate to obtain q 2 = -l1 2 •wE 2 + (I, - X 2 )w•OEm. These two expressions are electrically linear and can be written in the forms q, = Cjv 1 - CmV 2 , (a) q2 = -CmV1 + C 2 v 2 , (b) where Sow[Ill + (1, - x)J C = (c) x 1 C2 = CEO + ,X 2 ) (d) CoW(V, - X2) c, X (e) x 1 With vj, v 2 , x 1 , and x 2 given as specified functions of time, we can write the terminal currents as dv 1 dv 2 + 8C = dV x 1 C, CC X acd, d Cm dx, 2 il = C, Cm x' + _-_ t) dt dt a8z dt ar, dt v x( dt X dt' VdC d+ v (Cm dX 1 8Cm dC• 2 •2 1C2 dx1 C 2 dx 2 \ is = -C, + C, -
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Unformatted text preview: vlV + ,+ dt dt ax, dt x 2 dt ) x dt ax 2 dt A comparison of these results with those of the preceding example illustrates how quickly the expressions become longer and more complex as the numbers of electrical terminal pairs and mechanical displacements are increased. 2.1.3 Discussion In the last two sections we specified the process by which we can obtain the electrical terminal properties of lumped-parameter, magnetic field and electric field systems. The general forms of the principal equations are summarized in Table 2.1. The primary purpose of obtaining terminal relations is to be able to include electromechanical coupling terms when writing circuit A-PDF Split DEMO : Purchase from www.A-PDF.com to remove the watermark...
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This note was uploaded on 02/10/2012 for the course MECE 4371 taught by Professor Liu during the Fall '11 term at University of Houston.

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