Vibration Correlation Technique Research Articles

Applicability of the Vibration Correlation Technique for Estimation of the Buckling Load in Axial Compression of Cylindrical Isotropic Shells with and without Circular Cutouts

Applicability of the vibration correlation technique (VCT) for nondestructive evaluation of the axial buckling load is considered. Thin-walled cylindrical shells with and without circular cutouts have been produced by adhesive overlap bonding from a sheet of aluminium alloy. Both mid-surface and bond-line imperfections of initial shell geometry have been characterized by a laser scanner. Vibration response of shells under axial compression has been monitored to experimentally determine the variation of the first eigenfrequency as a function of applied load. It is demonstrated that VCT provides reliable estimate of buckling load when structure has been loaded up to at least 60% of the critical load. This applies to uncut structures where global failure mode is governing collapse of the structure. By contrast, a local buckling in the vicinity of a cutout could not be predicted by VCT means. Nevertheless, it has been demonstrated that certain reinforcement around cutout may enable the global failure mode and corresponding reliability of VCT estimation.

Buckling prediction of panels using the vibration correlation technique

The Vibration Correlation Technique (VCT) for experimentally nondestructive determination of buckling loads of thin-walled structures is applied to stringer stiffened curved panels manufactured both from aluminum and laminated composite material. The modal behavior of the panels is investigated by exciting the structures using the modal hammer method. Natural frequencies of the panels are recorded as a function of the applied axial compression load. Unlike shell structures which present a non-stable post-buckling behavior, the stringer stiffened panels show a stable post-buckling behavior, enabling the measurement of the natural frequencies up to the actual experimental buckling load. The modal behavior of compressed panels is compared for reference to shells, yielding areas of applicability for VCT to predict efficiently the buckling loads of thin-walled structures. Guidelines are then formulated for the application of the VCT.

Experimental and numerical estimation of buckling load on unstiffened cylindrical shells using a vibration correlation technique

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells.This paper presents and discusses an experimental and numerical validation of a novel approach, using the vibration correlation technique, for the prediction of realistic buckling loads on unstiffened cylindrical shells loaded in compression. From the experimental point of view, a batch of three composite laminated cylindrical shells are fabricated and loaded in compression up to buckling. An unsymmetric laminate is adopted in order to increase the sensitivity of the test structure to initial geometric imperfections. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation, without actually reaching the instability point. Furthermore, a series of numerical models, including non-linear effects such as initial geometric and thickness imperfection, are carried-out in order to characterize the variation of the natural frequencies of vibration with the applied load and compare the results with the experiment findings. Additional experimental tests are currently under development to further validate the proposed approach for metallic and balanced composite structures.

Experimental Nondestructive Test for Estimation of Buckling Load on Unstiffened Cylindrical Shells Using Vibration Correlation Technique

Nondestructive methods, to calculate the buckling load of imperfection sensitive thin-walled structures, such as large-scale aerospace structures, are one of the most important techniques for the evaluation of new structures and validation of numerical models. The vibration correlation technique (VCT) allows determining the buckling load for several types of structures without reaching the instability point, but this technique is still under development for thin-walled plates and shells. This paper presents and discusses an experimental verification of a novel approach using vibration correlation technique for the prediction of realistic buckling loads of unstiffened cylindrical shells loaded under axial compression. Four different test structures were manufactured and loaded up to buckling: two composite laminated cylindrical shells and two stainless steel cylinders. In order to characterize a relationship with the applied load, the first natural frequency of vibration and mode shape is measured during testing using a 3D laser scanner. The proposed vibration correlation technique allows one to predict the experimental buckling load with a very good approximation without actually reaching the instability point. Additional experimental tests and numerical models are currently under development to further validate the proposed approach for composite and metallic conical structures.

Vibration correlation technique for the estimation of real boundary conditions and buckling load of unstiffened plates and cylindrical shells

Nondestructive experimental methods to calculate the buckling load of imperfection sensitive thin-walled structures are one of the most important techniques for the validation of new structures and numerical models of large scale aerospace structures. Vibration correlation technique (VCT) allows determining equivalent boundary conditions and buckling load for several types of structures without reaching the instability point. VCT is already widely used for beam structures, but the technique is still under development for thin-walled plates and shells. This paper intends to explain the capabilities and current limitations of this technique applied to two types of structures under buckling conditions: flat plates and cylindrical shells prone to buckling. Experimental results for a flat plate and a cylindrical shell are presented together with reliable finite element models for both cases. Preliminary results showed that the VCT can be used to determine the realistic boundary conditions of a given test setup, providing valuable data for the estimation of the buckling load by finite element models. Also numerical results herein presented show that VCT can be used as a nondestructive tool to estimate the buckling load of unstiffened cylindrical shells. Experimental tests are currently under development to further validate the approach proposed herein.

Experimental determination of the buckling load of rectangular plates using vibration correlation technique

This study investigates the use of a vibration correlation technique (VCT) to identify the buckling load of a rectangular thin plate. It is proposed that the buckling load can be determined experimentally using the natural frequencies of plates under tensile loading. A set of rectangular plates was tested for natural frequencies using an impact test method. Aluminum and stainless steel specimens with CCCC, CCCF and CFCF boundary conditions were included in the experiment. The measured buckling load was determined from the plot of the square of a measured natural frequency versus an in-plane load. The buckling loads from the measured vibration data match the numerical solutions very well. For specimens with well-defined boundary conditions, the average percentage difference between buckling loads from VCT and numerical solutions is -0.18% with a standard deviation of 5.05%. The proposed technique using vibration data in the tensile loading region has proven to be an accurate and reliable method which might be used to identify the buckling load of plates. Unlike other static methods, this correlation approach does not require drawing lines in the pre-buckling and post-buckling regions; thus, bias in data interpretation is avoided.

Repeated buckling and its influence on the geometrical imperfections of stiffened cylindrical shells under combined loading

The present experimental study aims at providing better inputs for improvement of the buckling load predictions of stiffened cylindrical shells subjected to combined loading. The work focuses on two main factors which considerably affect the combined buckling load of stiffened shells, namely geometric imperfections and boundary conditions. Six shells with nominal simple supports were tested under various combinations of axial compression and external pressure. The vibration correlation technique is employed to define the real boundary conditions. The geometric imperfections of the integrally stiffened shells are measured in the present experiments in situ and are used as inputs to a multimode analysis which yields the corresponding “knockdown” factor for various combinations of loading. Thus, when employing the repeated buckling procedure for obtaining interaction curves, each point on the curve is adjusted (using the multimode analysis) for the measured “new” surface of the shell and this results in more realistic interaction curves. The geometrical imperfections of the preloaded shells can also serve as an input to the International Imperfection Data Bank for future studies on the correlation between the manufacturing method of the shell and their geometric imperfections.

Effect of sequence of combined loading on buckling of stiffened shells

The vibration-correlation technique, VCT for definition of real boundary conditions, and the method of repeated buckling were employed for nondestructive generation of improved interaction curves for buckling of stringer-stiffened circular-cylindrical shells subjected to a combined axial compression and external-pressure state of loading. Thirteen shells were tested, five on clamped boundary conditions and eight on norminal simple supports. The study also included an assessment of the influence of the order of loading on the behavior of the shells before and at buckling as a result of the nonlinear interaction. It has been shown that the VCT and repeated buckling approach are feasible for closely stiffened shells and are adequate tools for the derivation of more realistic buckling interaction curves. It appears that the sequence of loading, constant axial compression first and then increasing the external pressure until buckling occurs, or the reverse order of loading, does not influence the buckling loads.

Vibration Techniques for Definition of Practical Boundary Conditions in Stiffened Shells

A vibration correlation technique, consisting essentially of experimental determination of the frequencies under load and assessment of equivalent elastic restraints, developed earlier for stringer-stiffened shells on laboratory-type end rings, has been extended to realistic boundary conditions. Six shells with end conditions, simulating typical missile joints, have been tested and analyzed. Lumping' of end effects has been studied and results have been compared with tests of similar shells on laboratory-type end rings with prescribed load eccentricity. A method for detection of load eccentricity from vibration tests and assessment of equivalent end restraints has been developed.