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The method of riveting by forming the closing head under increasing pressure or by a series of hammer blows is investigated. The question as to the best edge distance, i.e. that distance from the rivet center to the plate edge below which it is unadvisable to go and, at the same time useless to go beyond, was examined. The slippage of plates which occurs under the effect of a certain stress, does not completely disappear on unloading. The elastic form change is essentially a function of the elasticity modulus, the slip modulus, the supporting moment, the rivet spacing, etc.
In one scenario of a crack in an airplane fuselage, the crack is subjected to cyclic tensile and out of plane shearing loads. To predict the fatigue crack growth in such a situation, experiments are being performed to measure the crack growth rate in laboratory specimens subjected to similar loadings. The mechanics of this problem are reviewed, the energy release rate is calculated and designs for an experiment are discussed along with some preliminary experimental observations.
The near and very near wake of a flat plate with a circular trailing edge is investigated with data from direct numerical simulations. Computations were performed for six different combinations of the Reynolds numbers based on plate thickness (D) and boundary layer momentum thickness upstream of the trailing edge (theta). Unlike the case of the cylinder, these Reynolds numbers are independent parameters for the flat plate. The separating boundary layers are turbulent in all the cases investigated. One objective of the study is to understand the changes in the wake vortex shedding process as the plate thickness is reduced (increasing theta/D). The value of D varies by a factor of 16 and that of theta by approximately 5 in the computations. Vortex shedding is vigorous in the low theta/D cases with a substantial decrease in shedding intensity in the large theta/D cases. Other shedding characteristics are also significantly altered with increasing theta/D. A visualization of the shedding process in the different cases is provided and discussed. The basic shedding mechanism is explored in depth. The effect of changing theta/D on the time-averaged, near-wake velocity statistics is also discussed. A functional relationship between the shedding frequency and the Reynolds numbers mentioned above is obtained.
Acoustic emission was interpreted as modes of vibration in plates. Classical plate theory was used to predict dispersion curves for the two fundamental modes and to calculate the shapes of flexural waveforms produced by vertical step function loading. There was good agreement between theoretical and experimental results for aluminum. Composite materials required the use of a higher order plate theory (Reissner-Mindlin) to get good agreement with the measured velocities. Four composite plates with different laminate stacking sequences were studied. The dispersion curves were determined from phase spectra of the time dependent waveforms. Plate modes were shown to be useful for determining the direction of source motion. Aluminum plates were loaded by breaking a pencil lead against their surface. By machining slots at angles to the plane of a plate, the direction in which the force acted was varied. Changing the source motion direction produced regular variations in the waveforms. To demonstrate applicability beyond simple plates, waveforms produced by lead breaks on a thin walled composite tube were also shown to be interpretable as plate modes. The tube design was based on the type of struts proposed for Space Station Freedom's trussed structures.
The intermediate wakes of thin flat plates with circular trailing edges (TEs) are investigated here with direct numerical simulations (DNSs). The separating boundary layers are turbulent in all cases. The near wake in two thin-plate cases (IN & NS), with a focus on the vortex shedding process, was explored in a recent article. Intermittent shedding was observed in Case IN. Case NS, with half the TE diameter of Case IN, was an essentially non-shedding case. A third case (ST) with a sharp trailing edge was also investigated and found to exhibit an intermittent wake instability. The objectives of the present study are twofold. The first is to determine if the wake instability found in Case ST exists in Cases IN and NS as well. The second is to provide the distributions of the turbulent normal intensities and shear stress in the wake and to understand these distributions via the budget terms in the corresponding transport equations. The results show that both Cases IN & NS exhibit a wake instability in the intermediate wake region, that is similar to that found earlier in Case ST. We note that in Case IN, the presence of an intermediate-wake instability results in the co-existence of two different types of instability within a single wake. The distributions of the turbulent normal intensities and shear stress, and the budget terms for the streamwise intensity are included and discussed here. All the budget terms contribute appreciably to the overall budget in the transport equation for streamwise normal intensity.
Thin plates and thin walled cylinders aeroelastic stability in fluid flow, analyzing panel flutter
The near and very near wake of a thin flat plate with a circular trailing edge are investigated with direct numerical simulations (DNS). Data obtained for two different Reynolds numbers (based on plate thickness, D) are the main focus of this study. The separating boundary layers are turbulent in both cases. An earlier investigation of one of the cases (Case F) showed shed vortices in the wake that were about 1.0 D to 4.0 D in spanwise length. Considerable variation in both the strength and frequency of these shed vortices was observed. One objective of the present investigation is to determine the important contributors to this variability in strength and frequency of shed vortices and their finite spanwise extent. Analysis of the data shows that streamwise vortices in the separating boundary layer play an important role in strengthening/weakening of the shed vortices and that high/low-speed streaks in the boundary layer are important contributors to variability in shedding frequency. Both these features of the boundary layer contribute to the finite extent of the vortices in the spanwise direction. The second plate DNS (Case G, with 40 percent of the plate thickness of Case F) shows that while shedding intensity is weaker than obtained in Case F, many of the wake features are similar to that of Case F. This is important in understanding the path to the wake of the thin plate with a sharp trailing edge where shedding is absent. Here we also test the efficacy of a functional relationship between the shedding frequency and the Reynolds numbers based on the boundary layer momentum thickness (Re (sub theta) and D (Re (sub D)); data for developing this behavioral model is from Cases F & G and five earlier DNSs of the flat plate wake.
Strain-energy release rates are often used to predict when delamination growth will occur in laminates under compression. Because of the inherently high computational cost of performing such analyses, less rigorous analyses such as thin-film plate analysis were used. The assumptions imposed by plate theory restrict the analysis to the calculation of total strain energy, G(sub t). The objective is to determine the accuracy of thin-film plate analysis by comparing the distribution of G(sub t) calculated using fully three dimensional (3D), thin-film 3D, and thin-film plate analyses. Thin-film 3D analysis is the same as thin-film plate analysis, except 3D analysis is used to model the sublaminate. The 3D stress analyses were performed using the finite element program NONLIN3D. The plate analysis results were obtained from published data, which used STAGS. Strain-energy release rates were calculated using variations of the virtual crack closure technique. The results demonstrate that thin-film plate analysis can predict the distribution of G(sub t) quite well, at least for the configurations considered. Also, these results verify the accuracy of the strain-energy release rate procedure for plate analysis.
The problem of electromagnetic (EM) scattering from irregularly shaped, thin, metallic flat plates in free space is solved using the electric field integral equation (EFIE) approach in conjunction with the method of moments (MoM) with quadrilateral meshing. An irregularly shaped thin plate is discretized into quadrilateral patches and the unknown electric surface current over the plate is expressed in terms of proper basis functions over these patches. The basis functions for the electric surface current density that satisfy the proper boundary conditions on these quadrilateral patches are derived. The unknown surface current density on these quadrilateral patches is determined by setting up and solving the electric field integral equation by the application of the MoM. From the knowledge of the surface current density, the EM scattering from various irregularly shaped plates is determined and compared with the earlier published results. The novelty in the present approach is the use of quadrilateral patches instead of well known and often used triangular patches. The numerical results obtained using the quadrilateral patches compare favorably with measured results.
Steady stress state and temperature field in thin thermoelastic plate weakened by circular hole
A finite element formulation is presented for determining the large-amplitude free and steady-state forced vibration response of arbitrarily laminated anisotropic composite rectangular thin plates. The nonlinear stiffness and harmonic force matrices of an arbitrarily laminated composite rectangular plate element are developed for nonlinear free and forced vibration analyses. The linearized updated-mode method with nonlinear time function approximation is employed for the solution of the system nonlinear eigenvalue equations. The amplitude-frequency relations for convergence with gridwork refinement, different boundary conditions, aspect ratios, lamination angles and number of plies are presented. The finite element results are compared with available approximate continuum solutions.
Acoustic waves propagate in thin plates as guided or Lamb modes. The velocities of these modes are dispersive in that they depend not only on the material elastic properties and density, but also on the frequency. Accurate characterization of Lamb wave dispersion is important in many acoustic based nondestructive evaluation techniques. It is necessary for ultrasonic measurements in thin plates to determine elastic properties and for flaw detection and localization. In acoustic emission (AE) testing, if not taken into account, highly dispersive Lamb mode propagation can lead to large errors in source location. In this study, the pseudo Wigner-Ville distribution (PWVD) was used for measurement of group velocity dispersion of Lamb waves in a unidirectional graphite/epoxy (AS4/3502) laminate. The PWVD is one of a number of transforms which provide a time-frequency representation of a digitized time series. Broad band acoustic waves were generated by a pencil lead fracture (Hsu-Neilsen source) and were detected with broad band ultrasonic transducers. The arrival times for the lowest order symmetric (S(sub 0)) and antisymmetric (A(sub 0)) Lamb modes were determined from measurements of the time at which the respective peak amplitudes occurred in the PWVD. Measurements were made at several source-to-detector distances and a least squares fit used to calculate the velocity. Results are presented for propagation along, and perpendicular to, the fiber direction. Theoretical dispersion curves were also calculated and a comparison between theory and experiment demonstrates good agreement.
Thin elastic plates dynamic stability under random distribution edge loading using theory of linear stochastic systems
Elastic state determination of thermal stress in thin, flat plate of finite dimensions
The near and very near wake of thin flat plates with both sharp and circular trailing edges (TEs) are investigated with direct numerical simulations (DNSs). The TE is circular in two of the cases (IN & NS) and sharp in one of them (ST). The separating boundary layers are turbulent in all cases. The objectives of this study are twofold. The first is to explore the effect of significantly reducing Re(sub D) (Reynolds number based on circular TE diameter, D) on the flow in the TE region, and the shedding process (Cases IN and NS). The second is to better understand the reasons underlying the findings of an earlier experimental wake investigation (sharp TE) where (1) the center-line values in normal intensity, and the peak in shear stress profiles in the cross-stream direction, were found to first increase in the streamwise direction (x), from that obtained at the TE, before diminishing further downstream, and (2) a broadband peak was observed in centerline cross-stream velocity (v) spectra (indicating quasi-periodicity, possibly due to vortices or wave-like motions). Case ST from the present study showed a near wake instability resulting in spanwise vortices (with a streamwise component). The instability is intermittent and contributes to both the broadband peak in the v spectrum and the initial increases in normal intensity and shear stress (as in the experiment). Case NS, with the lower value of ReD is an "essentially" non-shedding case where the flow in the TE region continually changes direction (upward/downward) because of turbulence. Case IN, with twice the value of ReD as Case NS, also exhibits a swaying motion in the TE region. In addition, vortex shedding is initiated during periods when the flow direction changes rapidly. Shedding in this case is intermittent. It results in a peak in the v spectrum obtained at the centerline (x/D = 1.0).
Rarefied gas dynamics - surface pressure & pitot pressure distribution in neighborhood of leading edge of thin flat plate
Low-frequency resonant model analysis, a technique for the detection and characterization of fatigue cracks in thin metal plates, which could be adapted to rapid scan or large area testing, is considered. Experimental data displaying a direct correlation between fatigue crack geometry and resonance frequency for the second vibrational plate mode are presented. FEM is used to calculate the mechanical behavior of the plates, and provides a comparison basis for the experimentally determined resonance frequency values. The waveform of the acoustic emission generated at the resonant frequency is examined; it provides the basis for a model of the interaction of fatigue crack faces during plate vibration.