Judah Ari-Gur

Experimental and theoretical studies of columns under axial impact

Abstract The dynamic response of columns loaded by an impulsive axial compression was studied experimentally and theoretically. Approximate criteria for determination of dynamic buckling are discussed and applied. The investigation was carried out on clamped specimens, made of metals and composite materials, loaded impulsively by a striking mass. In the theoretical study Rayleigh-type beam equations are assumed for a geometrically imperfect column of a linear-elastic anisotropic material. A numerical solution, by a finite-difference approach, yields buckling behavior which correlates well with the experimental results. It is shown that initial geometrical imperfection, duration of impulse and effective slenderness have a major influence on the buckling loads whereas the effect of the material is secondary. The major effects are presented in a form that can guide the designer.

Dynamic pulse buckling of rectangular composite plates

Abstract The elastic dynamic buckling of geometrically imperfect rectangular composite plates under a longitudinal compressive pulse is investigated. Specifically, the effects of fiber orientations of angle-ply laminated panels are studied. Geometric nonlinearities due to large deflections, as well as wave propagation effects due to inplane inertia terms, are included in the analysis. The applied load is either a force or displacement pulse. A numerical solution, through an explicit finite-difference integration scheme, is then developed. Appropriate dynamic buckling criteria are defined for both loading types, and buckling loads are determined for various loading durations and material lay-up configurations. It is found that the dynamic buckling loads are not always higher than the static ones; in some cases there is a range of loading frequencies near the fundamental frequency of the plate where dynamic buckling occurs for lower loads. Buckling under a displacement pulse occurs at a load higher than that for a force pulse of similar duration. Also, the critical axial displacement is not sensitive to the material configuration. Comparisons with results obtained through a finite-element analysis support the conclusions of the present analysis.

Dynamic instability of a transversely isotropic column subjected to a compression pulse

Abstract A theoretical study of the dynamic instability of geometrically imperfect transversely isotropic columns under axial compressive pulse is presented. The analysis includes transverse shear deformation as well as translational and rotational inertia terms. The effect of transverse shear rigidity is investigated for various pulse frequencies, ranging from quasi-static to impulsive compressive loads. An appropriate dynamic instability criterion is defined and utilized and the corresponding buckling results are compared with those for isotropic columns, as well as with results obtained by the classical beam theory. The results show that for isotropic columns the classical theory predicts accurately the dynamic buckling strength. However, for columns with low transverse shear rigidity, buckling loads predicted by the refined theory may be as low as almost two thirds of those estimated via the classical theory.

Buckling of cylindrical shells under combined axial preload, nonuniform heating and torque

Thin aluminum-alloy cylinders were tested under different combinations of torque and circumferentially varying axial thermal stress. The methods of application of the required loads and the measuring techniques employed are discussed. The buckling process is described and interaction curves are presented.

On rotating polar-orthotropic circular disks

Abstract A closed-type solution is presented for a mathematical singularity which appears in Glushkovs solution of rotating polar orthotropic disks. It is further shown that optimization for stresses of such disks requires the establishment of a suitable criterion for each class of boundary conditions considered. The effect of angular acceleration on the design of rotating composite disks is indicated. Various examples are presented and discussed.

Pulse buckling of composite plates

The elastic dynamic buckling of geometrically imperfect rectangular composite plates under longitudinal compressive pulse is investigated. Specifically, effects of fiber orientations of angle-ply laminated panels are studied. Geometric nonlinearities due to large deflections, as well as wave propagation effects due to in-plane inertia terms, are included in the analysis. The loads are force or displacement pulses. A numerical solution, through an explicit finite-difference integration scheme, is then developed. Appropriate dynamic buckling criteria are defined for both loading types, and buckling loads are determined for various loading durations and layup configurations. It is found that the dynamic buckling loads are not always higher than the static ones; there is a range of loading frequencies near the fundamental frequency of the plate where dynamic buckling occurs for lower loads. Buckling under displacement pulses occurs at loads higher than those for force pulses of similar durations. Also, the critical axial displacements are not sensitive to the material configuration. Comparisons with results obtained through a finite-element analysis support the conclusions of the present analysis.

Refined theories may be needed for vibration analysis of structures with overhang

Abstract The effect of shear deformation and rotary inertia terms on the free vibration of a beam with overhang was investigated. A recently proposed modified Timoshenko-type equations of motion were used to analyze the vibration of the structure. Two different sets of boundary conditions, with either a fixed or hinged end support, were studied. The results were compared with those obtained for the classical Bernoulli–Euler beam theory. The comparison shows that for a hinged end beam with very long overhang, where the span between the supports is less than one tenth of the overall beam length, the classical theory significantly overestimates the values of the fundamental natural frequencies, even for isotropic shear rigidity. On the other hand, the span effect is reversed for the clamped end beam, for which a relatively significant difference between the classical theory and shear theory results may occur only for a long span. For transversely isotropic beams, the refined theory predictions of the fundamental natural frequencies may be much smaller than those obtained through the rigid shear theory, especially for short span hinged end beams and long span clamped end beams.

Effects of anisotropy on the pulse response of composite panels

Abstract The effects of fiber orientation on the dynamic deflection of shallow composite shells under lateral pressure pulse were investigated. Symmetrically-laminated angle-ply composite cylindrical panels were subjected to various frequencies of pulse loads, and the magnitude and shape of the resulting deflections were studied. It was found that the optimal fiber orientation depends not only on the shell curvature but also on the frequency of the applied load. The largest deflections occur when the ratio of the pulse frequency to the fundamental natural frequency of the structure is about 0.65. Around this range the stiffest fiber orientation is θ = ±45°, as for a flat plate. In the range of impulsive loads, however, the optimal fiber orientation shifts towards the longitudinal direction, just as under static loads, due to the curvature-stiffening effects. It was also observed that different transient deflection patterns occur for various fiber orientations and pulse frequencies, and the peak deflection is not always at the center of the panel. The primary conclusion is that the static optimal layup configuration is not valid for time-dependent loading.

Lightweight Mitigating Materials for Structures Under Close-in Blast Loading

This study investigated the effects of lightweight blast mitigating materials to protect commercial aircraft structures against internal blast loading. Thin clamped aluminum test panels with rivet-attached frame and stringer stiffeners were used to represent a portion of the fuselage structure of a commercial aircraft. These reinforced test panels were prepressurized before blast loading to simulate typical in-flight loads experienced by a commercial aircraft due to cabin pressurization. Bare spherical explosive charges of C4 were then detonated at a fixed distance from the outer surface of these pre-pressurized plates. A high-speed camera was used to determine the mechanism and time scale of failure propagation in the reinforced panels. Eleven unique combinations of blast mitigating linings were used in the testing. The specific explosive charge mass and standoff distance selected for this study was found to produce massive damage in unprotected test panels. Several tests with blast mitigating liners also showed complete destruction of the test panel, indicating the inadequacy of these protective compositions. In the end, it was determined that a blast liner comprised of a rigid outer layer, such as aluminum, in combination with an elastomeric backing layer was successful in preventing the rupture of the reinforced test panel. This material combination was found to be effective over several tests and with slight variations of the specific rigid and flexible materials used.

Non-Linear Dynamic Pulse Response of Plates and Cylindrical Panels

The dynamic response of plates and cylindrical panels with various curvatures under external lateral pressure pulse was studied. Nonlinearities due to large deflections were included and the dynamic response was analyzed using a finite element code. Effects of shell curvatures, pulse durations and load intensities were investigated. The observed dynamic behavior included also non-linear shell buckling due to the compressive stresses under the external pressure on the cylindrical panels. The results, when compared to the linear response, show the effects of the increased load intensity and the resulting non-linear behavior on the response to various pulse durations. Also, the differences between the static and the dynamic behaviors for similar load intensities were studied. Non-dimensional processing of the results, including in the large deflection range, highlights the effects of high load intensities on the structural stiffness and in turn on the changing characteristics of the response under a given pulse duration.Copyright