This chapter considers the nonlinear vibration of plates and shallow cylindrical shells. It starts with a description of the classical analysis of flat-plate vibration. Following on from flat plates, the vibration of a shallow curved shell is considered. Due to its curvature, this type of shell (or curved plate) naturally leads to a coupled set of nonlinear ordinary differential equations. We consider an example in which the quadratic nonlinear terms are most significant, leading to 1/2 subharmonic resonances.
The final part of this chapter considers cylindrical shells which are bi-stable. This means that they have two statically stable states, both of which are in the form of a shallow cylindrical shell. To change (or morph) from one state to the other, the plate must be deflected past the unstable flat position via a process know as snap-through. The possible applications of this type of bi-stable shell to morphing structures are briefly discussed at the end of this chapter.
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(2010). Plates and Shells. In: Wagg, D., Neild, S. (eds) Nonlinear Vibration with Control. Solid Mechanics and Its Applications, vol 170. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-2837-2_8
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