The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω...The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω lies at a certain interval and the waves in the circumferential direction are not too many. All of their asymptotic solutions are developed, which are valid for the whole range of the shell surface and satisfy the required accuraracy of the theory of thin shells. Three categories of the generalized function Z_h (h=1, 2, 3, 4), R and J are defined, of which a singular membrane solution and four bending solutions can be expressed. Particularly, the second category of the generalized function R is first obtained which is a generalization of a new solution to the related equation. This new solution is found by modifying the Laplace transform method. The frequency equation of the truncated shells of revolution clamped at their two boundaries is finally given.展开更多
文摘The equations representing the free vibration of any thin shells of revolution, except the shells with constant curvature (cylindrical and spherical shell), have a simple turning point, when the frequency parameter Ω lies at a certain interval and the waves in the circumferential direction are not too many. All of their asymptotic solutions are developed, which are valid for the whole range of the shell surface and satisfy the required accuraracy of the theory of thin shells. Three categories of the generalized function Z_h (h=1, 2, 3, 4), R and J are defined, of which a singular membrane solution and four bending solutions can be expressed. Particularly, the second category of the generalized function R is first obtained which is a generalization of a new solution to the related equation. This new solution is found by modifying the Laplace transform method. The frequency equation of the truncated shells of revolution clamped at their two boundaries is finally given.
