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Structural Health Monitoring with Piezoelectric Wafer Active Sensors, 2nd Edition by Victor Giurgiutiu

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Chapter 4

Vibration of Plates

This chapter analyzes the vibration of thin plates. After reviewing the general plate equations, two situations are considered separately: (a) axial in-plane vibration of plates; and (b) flexural out-of-plane vibration of plates. Both rectangular coordinates and cylindrical coordinates are used, as appropriate. For rectangular plates, simplified solutions are derived for straight-crested axial and flexural vibrations and compared with the corresponding 1-D cases discussed in Chapter 3. General solutions for the 2-D flexural vibration of rectangular plates are given from the literature. The vibration of circular plates is treated in terms of Bessel functions. Closed-form solutions are derived for axisymmetric vibration ...

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