David Hui

Influence of Geometric Imperfections and In-Plane Constraints on Nonlinear Vibrations of Simply Supported Cylindrical Panels

This papers deals with the effects of initial geometric imperfections on large-amplitude vibrations of cylindrical panels simply supported along all four edges. In-plane movable and in-plane immovable boundary conditions are considered for each pair of parallel edges. Depending on whether the number of axial and circumferential half waves are odd or even, the presence of geometric imperfections (taken to be of the same shape as the vibration mode) of the order of the shell thickness may significantly raise or lower the linear vibration frequencies. In general, an increase (decrease) in the linear vibration frequency corresponds to a more pronounced soft-spring (hard-spring) behavior in nonlinear vibration.

Effects of geometric imperfections on vibrations of biaxially compressed rectangular flat plates

This paper deals with the effects of geometric imperfections on the vibration frequencies of simply supported flat plates under in-plane uniaxial or biaxial compression. The analysis is based on a solution of the nonlinear von Kdrmdn equations for finite deflections, incorporating the influence of an initial geometric imperfection. It is found that significant increase in the vibration frequencies may occur for imperfection amplitude of the order of a fraction of the plate thickness, even in the absence of in-plane forces.

Effects of Geometric Imperfections on Frequency-Load Interaction of Biaxially Compressed Antisymmetric Angle Ply Rectangular Plates

The present paper deals with the influence of small geometric imperfections on the vibration frequencies of rectangular, simply supported, angle ply, thin composite plates subjected to inplane uniaxial or biaxial compressive preload. Depending on the amount of preload, the frequencies of laminated plates with different imperfection shapes may be significantly higher than those for perfect plates, especially in a certain range of fiber angles. Interaction curves between frequency and applied preload are plotted for various fiber angles and imperfection amplitudes for both the uniaxial and equal biaxial loading cases.

Postbuckling behavior of infinite beams on elastic foundations using Koiter's improved theory

Abstract This study deals with the postbuckling behavior of infinite beams on non-linear elastic foundations subjected to axial compression. The analysis utilizes an improved Koiters postbuckling theory such that the postbuckling coefficients are evaluated at the actual applied load rather than at the classical buckling load. The improved postbuckling paths are found to agree well with the non-linear large deflection solution using the Ritz procedure. This paper substantiates Koiters conjecture that the general theory of elastic stability may be improved. The implications of various lower-bound buckling loads are examined.

Asymmetric postbuckling of symmetrically laminated cross ply, short cylindrical panels under compression

Abstract Buckling and initial postbuckling behavior of symmetrically laminated, thin cross ply cylindrical panels under axial compression are investigated. The panels are simply supported at all four edges. Closed form solutions are obtained for the buckling loads. The initial asymmetric postbuckling behavior is demonstrated by computing the postbuckling coefficients within the context of Koiters theory of elastic stability. Parameter studies involving the flatness parameter, the length-to-width ratio, number of layers and Youngs moduli ratio are presented for typical cross ply cylindrical panels likely to be encountered in practice.

Soft-spring nonlinear vibrations of antisymmetrically laminated rectangular plates☆

Abstract This paper deals with the effects of initial geometric imperfections and in-plane boundary conditions on the large-amplitude vibration behavior of angle- and cross-ply rectangular thin plates. It is found that the presence of imperfection amplitudes of the order of only half the total laminated-plate thickness may significantly raise the vibration frequencies and change the large-amplitude vibration behavior from the well-known hard-spring to soft-spring behavior. The effects of fibre angles and bending-stretching coupling for angle-ply plates and Youngs moduli ratios and number of layers for antisymmetric cross-ply plates are examined.

Initial Postbuckling Behavior of Imperfect, Antisymmetric Cross-Ply Cylindrical Shells Under Torsion

This paper deals with the initial postbuckling of antisymmetric cross-ply closed cylindrical shells under torsion. Under the assumptions employed in Koiter’s theory of elastic stability, the structure is imperfection-sensitive in certain intermediate ranges of the reduced-Batdorf parameter (approx. 4 ≤ ZH ≤ 20.0). Due to different material bending-stretching coupling behavior, the (0 deg inside, 90 deg outside) two-layer clamped cylinder is less imperfection sensitive than the (90 deg inside, 0 deg outside) configuration. The increase in torsional buckling load due to a higher value of Young’s moduli ratio is not necessarily accompanied by a higher degree of imperfection-sensitivity. The paper is the first to consider imperfection shape to be identical to the torsional buckling mode and presents concise parameter variations involving the reduced-Batdorf paramter and Young’s moduli ratio.

DESIGN OF BENEFICIAL GEOMETRIC IMPERFECTIONS FOR ELASTIC COLLAPSE OF THIN-WALLED BOX COLUMNS

Abstract This paper deals with the design of beneficial geometric imperfections for elastic collapse of thin-walled box columns of square cross-section under axial compression. From the point of view of high elastic post-collapse stiffness, it is desirable to force the column to collapse with a larger number of axial half-waves than with the preferred wave number which is approximately equal to the aspect ratio. By introducing a beneficial geometric imperfection with such a larger wave number and if the magnitude of such imperfection exceeds the transitional value, it is found that the column will collapse in the beneficial mode in the initial postbuckling (assume to be elastic) finite-deflection regime. Equilibrium paths of typical box columns are plotted and analyzed. The two-mode potential energy is found to fall into the category of a double-cusp catastrophe.

Shear Buckling of Anti-Symmetric Cross Ply Rectangular Plates

Abstract This paper deals with buckling of anti-symmetric cross ply, simply supported rectangular flat plates under shear loads. The effects of the Youngs moduli ratios and the number of layers for these plates which exhibit bending-stretching coupling are examined. The linearized equilibrium and compatibility differential equations for buckling are solved, using the Galerkin procedure, by assuming a double sine series for the out-of-plane displacement. Both the symmetric and anti-symmetric buckling modes are considered. The asymmetric nature of the initial post buckling problem is demonstrated by the existence of a non-zero cubic term of the potential energy within the context of Koiters theory of elastic stability.

Effects of uni-directional geometric imperfections on vibrations of pressurized shallow spherical shells

Abstract This paper deals with the effects of initial geometric uni-directional imperfections on vibrations of a pressurized spherical shell or spherical cap. The analysis is based upon shallow shell theory. Frequency vs applied pressure interaction curves are plotted for various values of the imperfection amplitude. Imperfections are shown to have a severe effect in reducing the natural frequencies similar to that demonstrated in the buckling behavior of spherical shells.