The vibration and stability behavior of freely supported FGM conical shells subjected to external pressure

The dynamic plastic behavior of fully clamped rectangular plates

This work presents a modified variational method for dynamic analysis of ring-stiffened conical–cylindrical shells subjected to different boundary conditions. The method involves partitioning of the stiffened shell into appropriate shell segments in order to accommodate the computing requirement of high-order vibration modes and responses. All essential continuity constraints on segment interfaces are imposed by means of a modified variational principle and least-squares weighted residual method. Reissner-Naghdi's thin shell theory combined with the discrete element stiffener theory to consider the ring-stiffening effect is employed to formulate the theoretical model. Double mixed series, i.e., the Fourier series and Chebyshev orthogonal polynomials, are adopted as admissible displacement functions for each shell segment. To test the convergence, efficiency and accuracy of the present method, both free and forced vibrations of non-stiffened and stiffened shells are examined under different combinations of edge support conditions. Two types of external excitation forces are considered for the forced vibration analysis, i.e., the axisymmetric line force and concentrated point force. The numerical results obtained from the present method show good agreement with previously published results and those from the finite element program ANSYS. Effects of structural damping on the harmonic vibration responses of the stiffened conical–cylindrical–conical shell are also presented.

A modified variational approach for vibration analysis of ring-stiffened conical–cylindrical shell combinations

Plastic deformation and perforation of thin plates resulting from projectile impact

A study on the free vibration of the joined cylindrical–spherical shell structures

A study was made of the free vibration frequencies and mode shapes for freely supported oval cylindrical shells. Cross section curvatures were expressed in terms of a single eccentricity parameter that allowed a wide range of doubly symmetric ovals to be studied. Kinematic equations employing both the Love and the Donnell assumptions from thin shell theory were used in this study and results of the two formulations were compared. Little difference was observed between the results obtained from the two theories for a wide range of shell configurations. Comparisons were also made between the results obtained from this study and those from two previous approximate analyses. It was found that one of the approximate analyses (a Rayleigh-Ritz technique) was quite accurate for all ranges of eccentricities studied. The other approximate analysis (a perturbation technique) was found to be reliable for ovals with eccentricities in the range ( — 0.5 < € < 0.5). A study was also made to determine the effects of eccentricity of oval cross sections. The frequencies and mode shapes were found to vary significantly with increasing eccentricities. Irregularities in the frequency vs wave-number curves and a localized "cupping" in the region near the minimum frequency were observed. In-plane inertias were retained yielding the expected three frequencies for each combination of longitudinal and circumferential wave numbers. However, unlike the unstiffened circular cylinder, more than one set of three natural frequencies and associated mode shapes were found for some combinations of longitudinal and circumferential wave numbers. However, although the wave numbers (i.e., number of crossings) were the same in these cases, the wave shapes were obviously different.

Free vibrations of freely supported oval cylinders

Free vibrations of circular cylinders with longitudinal, interior partitions

A method is developed to determine the natural frequencies and mode shapes of circular and noncircular cylindrical panels. The panels are assumed to be freely supported along their curved edges and to have arbitrary straight-edge boundary conditions. The Donnell equations of equilibrium for noncircular cylindrical shells are used. The displacement functions, assumed to be mixed power and trigonometric series, reduce the Donnell equations to a set of coupled, algebraic recurrence formulas. It is shown that this method yields the exact solution. A study was also made to investigate the effects of neglecting in-surface inertias. For each noncircular segment an equivalent circular panel, which vibrates at the same natural frequency as the corresponding noncircular panel, was found. A significant advantage of the power series method is that the natural frequencies of circular and noncircular panels can be obtained for all combinations of straight-edge boundary conditions without having to reformulate the problem for each set of boundary conditions.

Free vibrations of noncircular cylindrical shell segments

A numerical method is developed to determine the nonlinear dynamic responses of thin, elastic, rectangular plates subjected to pulse-type uniform pressure loads. The nonlinear plate theory used in this study may be identified as the dynamic von Karman theory. The numerical method is based on finite-difference approximations of the differential equations using central difference formulations. A special form of Gaussian elimination is used to solve the system of algebraic equation resulting from the finite-difference formulation. A stability criterion is developed and checked empirically. The convergence of the solution is examined. Four sets of boundary conditions are considered. The use of the method is demonstrated by specific example problems and the results are compared with other approximate solutions.

D. E. Boyd

Papers

Free vibrations of freely supported oval cylinders

Free vibrations of circular cylinders with longitudinal, interior partitions

Free vibrations of noncircular cylindrical shell segments

Nonlinear Vibrations of Rectangular Plates

A non-linear dynamic lumped-parameter model of a rectangular plate