For the plate described in Problem 8.23, find the equations for the plate natural frequencies and determine

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For the plate described in Problem 8.23, find the equations for the plate natural frequencies and determine the effects of positive (tensile) and negative (compressive) in-plane loads \(N_{x}\) and \(N_{y}\) on the natural frequencies.

Problem 8.23

Derive the equation of motion for free transverse vibration of a simply supported, specially orthotropic plate that is subjected to in-plane loads per unit length \(N_{x}\) and \(N_{y}\) as shown in Figure 8.53.

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