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The deformation of a thin shell can be described completely by the deformation of its middle (neutral) surface. The undeformed middle surface of a thin shell can be described conveniently by two independent coordinates. The distance between two arbitrary points after deformation can also be used to define the components of strain in the shell. This chapter derives the expressions for strain energy, kinetic energy, and work done by the external forces, to derive the equations of motion of the shell using Hamilton's principle. The equations of motion of a cylindrical shell can be simplified using the Donnell‐Mushtari‐Vlasov (DMV) theory. In the vibration of thick shells, the effects of shear deformation and rotary inertia play an important role. The chapter derives the equations of motion of a shell by including the effects of shear deformation and rotary inertia using an approach similar to that of Timoshenko beams and Mindlin plates.
The deformation of a thin shell can be described completely by the deformation of its middle (neutral) surface. The undeformed middle surface of a thin shell can be described conveniently by two independent coordinates. The distance between two arbitrary points after deformation can also be used to define the components of strain in the shell. This chapter derives the expressions for strain energy, kinetic energy, and work done by the external forces, to derive the equations of motion of the shell using Hamilton's principle. The equations of motion of a cylindrical shell can be simplified using the Donnell‐Mushtari‐Vlasov (DMV) theory. In the vibration of thick shells, the effects of shear deformation and rotary inertia play an important role. The chapter derives the equations of motion of a shell by including the effects of shear deformation and rotary inertia using an approach similar to that of Timoshenko beams and Mindlin plates.
Vibration of Shells
Rao, Singiresu S. (author)
Vibration of Continuous Systems ; 549-615
2019-03-06
67 pages
Article/Chapter (Book)
Electronic Resource
English
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