Stability of cylindrical ribbed shells affected by compound loading

Methods of stability analysis for unsupported shells affected by compound loading have been expounded quite thoroughly in the literature [1, 2, 5–7]. In this case both the homogeneous, membrane subcritical state [1, 2, 5] as well as the inhomogeneous moment state [6] are considered. The homogeneous membrane subcritical state assumption [5, 6] is employed in the analysis of ribbed shells. The critical loads are found from equations of mixed-type.Timoshenko Institute of Mechanics, Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika, Vol. 30, No. 1, pp. 33–37, January, 1994.     

Nonlinear free vibration of spinning cylindrical shells with arbitrary boundary conditions

The aim of the present study is to investigate the nonlinear free vibration of spinning cylindrical shells under spinning and arbitrary boundary conditions. Artificial springs are used to simulate arbitrary boundary conditions. Sanders' shell theory is employed, and von Kármán nonlinear terms are considered in the theoretical modeling. By using Chebyshev polynomials as admissible functions, motion equations are derived with the Ritz method. Then, a direct iteration method is used to obtain the nonlinear vibration frequencies. The effects of the circumferential wave number, the boundary spring stiffness, and the spinning speed on the nonlinear vibration characteristics of the shells are highlighted. It is found that there exist sensitive intervals for the boundary spring stiffness, which makes the variation of the nonlinear frequency ratio more evident. The decline of the frequency ratio caused by the spinning speed is more significant for the higher vibration amplitude and the smaller boundary spring stiffness.     

Geometrically nonlinear vibration of laminated composite cylindrical thin shells with non-continuous elastic boundary conditions

The geometrically nonlinear forced vibration response of non-continuous elastic-supported laminated composite thin cylindrical shells is investigated in this paper. Two kinds of non-continuous elastic supports are simulated by using artificial springs, which are point and arc constraints, respectively. By using a set of Chebyshev polynomials as the admissible displacement function, the nonlinear differential equation of motion of the shell subjected to periodic radial point loading is obtained through the Lagrange equations, in which the geometric nonlinearity is considered by using Donnell’s nonlinear shell theory. Then, these equations are solved by using the numerical method to obtain nonlinear amplitude–frequency response curves. The numerical results illustrate the effects of spring stiffness and constraint range on the nonlinear forced vibration of points-supported and arcs-supported laminated composite cylindrical shells. The results reveal that the geometric nonlinearity of the shell can be changed by adjusting the values of support stiffness and distribution areas of support, and the values of circumferential and radial stiffness have a more significant influence on amplitude–frequency response than the axial and torsional stiffness.

     

A boundary layer theory for the buckling of thin cylindrical shells under external pressure

Based on the boundary layer theory for the buckling of thin elastic shells suggested in ref. [14]. the buckling and postbuckling behavior of clamped circular cylindrical shells under lateral or hydrostatic pressure is studied applying singular perturbation method by taking deflection as perturbation parameter. The effects of initial geometric imperfection are also considered. Some numerical results for perfect and imperfect cylindrical shells are given. The analytical results obtained are compared with some experimental data in detail, which shows that both are rather coincident.     

Influence of boundary conditions on dynamics and stability of thin cylindrical shells conveying fluid

This paper is concerned with the effect of boundary constraints of thin cylindrical shells containing flowing fluid, and investigates the quantitative relation between the fundamental natural frequency and mode shape and the geometric parameters and the flow velocity in detail. The results show that although axial displacements are smaller than radical displacements, the effect of axial constraints is significant for simply supported systems. It makes the lowest critical velocity of instability increase by 40%, and the minimum frequencies by 50%, even for long shells (L/a=20.0). On the contrary, the influence of rotation constraint (w/x=O) is much smaller.     

Longitudinal impact of cylindrical shells

The transient response due to longitudinal impact of three aluminum cylindrical shells of different thickness-to-radius ratios is studied both analytically and experimentally. The analyses were obtained from method of characteristics' solutions of two sets of equations: one which includes the transverse shear, radial inertia and rotary inertial effects; and the other set is from a modified membrane theory. Experimentally, longitudinal and circumferential strains are monitored along the length of each of the shells; the velocity of the impacter ring is also measured. The experimental results of this study indicate that the wavefront, after traveling three diameters from the impacted end, propagates at essentially the plate velocity, in agreement with the theory. In addition, the longitudinal and circumferential strains calculated from the two theories are in good agreement with the experimental results.     

Stability of oval cylindrical shells

Elastic buckling under aial compression of finite, oval cylindrical shells with clamped boundaries was investigated experimentally. The determination of the buckling strength was made on a series of oval shells made of Mylar A. The test results indicated that the discrepancy between theoretical and experimental initial buckling loads for the ovals is similar to that of the circular cylindrical shells. However, in contrast to the circular case, a collapse load significantly exceeding the initial buckling load is observed in the case of ovals with moderate-to-large eccentricity.