After substitution, the differential equation of the bending is d2w F q (i2 , M0
• Loaded plate without edge force in x-direction (F = 0): Let us consider a uninform load q applied all over the plate and bending moments ±M0 applied to the long edges. If no force acts in the x-direction at the long edges, then the first corresponding boundary at those edges is a freedom to move in the x-direction. Various boundary cases are shown in Fig. 1.52. The successive integrations of (1.146) with F = 0 leads to w = dfex" + (MD-T^V + C1x + C2. ,,147a)
14 Many authors prefer using an opposite sign convention for the bending moment M in (1.143) (cf. for instance Timoshenko and Woinowsky-Krieger ); this leads to an opposite sign in the representation of the flexure. For the applications of active optics methods, we always use here the more natural sign convention of a positive flexure for a positive curvature i.e. a positive second derivative.
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