A dynamic non-linear theory for generally laminated shallow clidrical shallow eylindrical panels is developed with the aid of Hamilton's principle. The effects of transverse shear deformatin. Rotatory inertia and geometrically initial imperfectin are included in the analysis. A multi-mode solution is formulated for non-linear free vibratin of an anti-symmetric angle-ply cylindrical lamminate with its edges elastically restained against roataion. The resulting equoations for time functions are solved by the mehod of harmonic balance. The postbuckling behavior of the panel is treated as a special case. Numerical results in non-linear vibration and posbuckling are presented for different values of the amplitude of iaitial imperfection. side-to-thickness ratio rotaional edge stiffiness,aspect ratio, orientation angle,number of layrs and material properies. Present results are compared with available data.

This paper deals with the static large deflpetion and the large amplitude free flexural ibration of a symmetrically laminated orthotropic eliiptical plted with a simply equations of the plated in terms of the deflection and two inplane displacemets is presented by use of a modified Galerkin procedure. Two inplance equations of equilibrium and the associted inplance bonndary eonditions are satified axaotly. Numerical Comatations are performed for stsatic and dynamic responses of homogenceous and symmetric cross-plyelliptical plates with different axes rations, numbers of layers and high-modulus material properties. In the static and dynamic linear caasea, preent reaults are compared with avaliable data.

The chaotic motion of an elastic shaft-disk rotor system including the geometric nonlinearity of the shaft with a transverser crack is investigated. The critical condition for the system to enter chaotic state is given by the Melnikov method. Meanwhile, whether the chaos occurs is determined by the Poiacare map, phase portrait and time-displacement history diagram.

Based on Hamilton's principle and the Timoshenko-Mindlin hypotheses on moderately thiek plates, a set of non-linear governing equations of motion for truncated conical moderately thick shells is sen up in large overall motion. By using the Galerkin method and the harmonic balance method, the problem of non-linear vibration of the truncated conical moderately thick shelts is analzed. The present results are compared with the available data for speciat cases.

In this paper, the nonlinear dynamic stability of a rotating shaft-disk with a transverse crack is studied, The crack and the disk are located in arbitrary positions of the shaft respectively. Using the equivalent line-spring model, the deflections of the system with a crack are constructed by adding a deflection to the deflections of the uncracked system. The unstable regions are confirmed by Runge Kutta method and the Floquet theory. The effects of crack depth, crack position, disk position, disk thickness and rotating speed on the principal unstable regions are discussed. The numerical results are compared with available data.