The governing equations of the free vibrations of spherical and cylindrical shellswith a regular singularity. are solved by Frobenius Series Method in the form ofmatrix. Considering the relationship of the roots of th...The governing equations of the free vibrations of spherical and cylindrical shellswith a regular singularity. are solved by Frobenius Series Method in the form ofmatrix. Considering the relationship of the roots of the indicial equation, we get somevarious expressions of solutions according to different cases. This work lays afoundation of solving certain elastic problems by analytical method.展开更多
A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compressio...A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.展开更多
文摘The governing equations of the free vibrations of spherical and cylindrical shellswith a regular singularity. are solved by Frobenius Series Method in the form ofmatrix. Considering the relationship of the roots of the indicial equation, we get somevarious expressions of solutions according to different cases. This work lays afoundation of solving certain elastic problems by analytical method.
基金Project supported by the the Natural Science Foundation of China (Nos. 10132010 and 50135030).
文摘A system of Mathieu–Hill equations have been obtained for the dynamic stability analysis of electrical graded piezoelectric circular cylindrical shells subjected to the combined loading of periodic axial compression and radial pressure and electric ?eld. Bolotin’s method is then employed to obtain the dynamic instability regions. It is revealed that the piezoelectric e?ect, the piezoelectric graded e?ect and the electric ?eld only have minor e?ect on the unstable region. In contrast, the geometric parameters, the rigidity of constituent materials and the external loading play a dominant role in determining the unstable region.
