Effects of higher-order deformations on in-plane vibration and stability of thick circular rings
To study the title problem, the author presents a one-dimensional higher-order theory based on the expansion of deformation into power series in normal coordinate. On the basis of this power series, a set of dynamic equations is derived through Hamilton's principle. Since the equations derived are very complex, approximate theories of various orders can be considered. For example, if the normal stress is zero we obtain the Timoshenko-type ring theory. Under the assumption of plane state of stresses in the depth direction, and assuming that the shear strain vanishes through the ring depth, the lowest-order approximate theory reduces to the classical ring theory. The one-dimensional higher-order theory developed by the author can predict natural frequencies and buckling stresses of a thick ring more accurately than the previously published ring theories.
expansion of deformation into power series in normal coordinate
scientific article; zbMATH DE number 1143330