The Detection of Impact Damage to the Edges of CFRP Plates Using Extensional Ultrasonic Edge Waves

Extensional edge waves propagate along the edges of plates, with low attenuation in the propagation direction and amplitude decreasing rapidly (within one or two wavelengths) in the direction perpendicular to the plate edge. This makes them an ideal candidate for inspecting the edges of plate-like structures. Here, finite-element models and experiments are used to investigate the propagation and scattering of extensional edge waves in composite plates and application to damage detection is demonstrated. Piezoceramic transducers attached to the edge of a 4-mm-thick carbon-fibre-reinforced polymer (CFRP) plate were used to excite 140-kHz edge waves and damage detection demonstrated using two experimental configurations: pitch-catch and two-transducer pulse-echo. Damage due to edge-on impacts of 5 J and 10 J were detected in both configurations. A mass-addition damage model was used to investigate the effect of damage location. Detection was specific to damage within 33 mm (1.5 wavelengths) of the plate edge with propagation unaffected by features beyond that distance. The time of arrival of reflected signals in pulse-echo mode was accurately predicted using the edge-wave group velocity indicating that this configuration can be used for locating damage on edges. The localisation of edge waves means that they can specifically detect damage at the edges of structures, and attenuation measurements indicate that their useful propagation distance is large (5.5 m).

The value of the plate mechanical properties in a case of thoracoplasty at the congenital pectus excavatum

Surgical treatment of a congenital pectus excavatum (CPE) includes using of a plate that holds the correct anatomical shape of the chest for a long time. Before implanting the plate behind a sternum, it is bent so that after correcting the deformation, it reproduces shape of the ribs on both sides and fits close to them. Displacement and rotation are the most frequent complications after plate implantation. Therefore, mechanical properties of the plate, such as: strength, ability to withstand the load during surgery and in the long term period — is one of the main guarantees to obtain the good result. Objective. To study the mechanical properties of the plate which is used for thoracoplasty at CPE under conditions comparable to real loads in order to gain maximal correction. Methods. Experimental bending tests were performed on 5 standard plates of 2.5 mm thick, 13 mm width and 200 mm length, made from titanium Ti6–AL4–V (according to ISO 5832-3). All plates were bent with a special surgical instrument according to the anatomical shape of a chest, using method of surgery by D. Nuss. All plates supports were placed on a distance from the fixing screws. The force of bending load was applied to the middle of the plate, gradually increasing from 150 to 600 H with a step 50 H. At each value of the loading we measured the height of the plate edge elevation. Results. Under load conditions of 600 H, the elevation of a plate edge did not exceed 3 mm and was equal to (2700 ± 177) μcm. In a case of twice lower loads (300 H), value of lifting edge of the plate decreased in three times and was (700 ± 85) μcm. Changes that happened under loading were the same for all five types of the plate. Conclusions. It is proved that the plates can fully withstand corrective loads with a minimal deformation after thoracoplasty. The discrepancy bet­ween the plate shape in the lateral parts to the restored thorax is caused by the changing of configuration of the last one and increasing in the anteroposterior size. Key words. Plate, mechanical pro­perties, thoracoplasty.

Developed liquid film passing a smoothed and wedge-shaped trailing edge: small-scale analysis and the ‘teapot effect’ at large Reynolds numbers

Recently, the authors considered a thin steady developed viscous free-surface flow passing the sharp trailing edge of a horizontally aligned flat plate under surface tension and the weak action of gravity, acting vertically, in the asymptotic slender-layer limit (J. Fluid Mech., vol. 850, 2018, pp. 924–953). We revisit the capillarity-driven short-scale viscous–inviscid interaction, on account of the inherent upstream influence, immediately downstream of the edge and scrutinise flow detachment on all smaller scales. We adhere to the assumption of a Froude number so large that choking at the plate edge is insignificant but envisage the variation of the relevant Weber number of $O(1)$ . The main focus, tackled essentially analytically, is the continuation of the structure of the flow towards scales much smaller than the interactive ones and where it no longer can be treated as slender. As a remarkable phenomenon, this analysis predicts harmonic capillary ripples of Rayleigh type, prevalent on the free surface upstream of the trailing edge. They exhibit an increase of both the wavelength and amplitude as the characteristic Weber number decreases. Finally, the theory clarifies the actual detachment process, within a rational description of flow separation. At this stage, the wetting properties of the fluid and the microscopically wedge-shaped edge, viewed as infinitely thin on the larger scales, come into play. As this geometry typically models the exit of a spout, the predicted wetting of the wedge is related to what in the literature is referred to as the teapot effect.

Oscillations of elastic plate, located at the end of semi-infinite cylindrical acoustic waveguide

Получено точное аналитическое решение задачи о гармонических изгибных колебаниях тонкой круглой упругой пластины, расположенной в торце полубесконечного цилиндрического акустического волновода. Кромка пластины жестко заделана в стенку волновода. Волновод с жестким корпусом заполнен идеальной сжимаемой акустической средой. Колебания пластины возбуждаются набегающими на неё нормальными волнами волновода, распределение акустического давления для которых имеет цилиндрическую симметрию. Проведено численное исследование смещения пластины на разных частотах возбуждения. Показано, что наличие сжимаемой среды существенно влияет на форму колебаний пластины. Совместные колебания акустической среды и упругой пластины носят резонансный характер. На резонансных частотах имеет место значительное увеличение амплитуды колебаний пластины. На форму колебания пластины влияют как распространяющиеся, так и неоднородные нормальные волны в волноводе, что приводит к увеличению узловых линий в распределении смещения пластины. An exact analytical solution to the problem of harmonic bending oscillations of a thin round elastic plate located at the end of a semi-infinite cylindrical acoustic waveguide has been obtained. Plate edge is rigidly embedded in waveguide wall. The waveguide with rigid housing is filled with an ideal compressible acoustic medium. The plate oscillations are excited by the normal waveguide waves running to the plate. The distribution of acoustic pressure for waves has cylindrical symmetry. Numerical study of plate displacement at different excitation frequencies was carried out. It has been shown that the presence of a compressible medium significantly affects the waveform of the plate oscillation. Joint oscillations of acoustic medium and elastic plate are resonant. There is a significant increase in amplitude of plate oscillations at resonant frequencies. The waveform of the plate oscillation is influenced by both propagating and inhomogeneous normal waves in the waveguide, which leads to an increase in the nodal lines in the displacement distribution of the plate.

Effects of Plate Edge Thickness On Droplet Generation Caused by Water Film Breakup At the Plate Edge

Droplets generated at trailing edges of low-pressure steam turbines strike the leading edge of moving blades, resulting in severe damage by erosion. In this study, water film flows on a plate set in a parallel airflow and breakup patterns are observed and measured to investigate the breakup behavior of the water film at the plate edge and the effect of the plate edge thickness. Profiles of frequency distribution of the droplet diameters exhibit on approximately linear in a semilog graph. The gradient of those distributions becomes steeper when the air flow velocity increases. Coarse droplets are generated from the deformation of ligaments, as shown in the end stage of a sheet-type breakup, and will result in a secondary breakup. Meanwhile fine droplets whose diameters are similar to the critical diameter remain in the high airflow velocity region; they are assumed to contribute significantly to erosion damage. The plate edge thickness does not affect the frequency distributions of the droplet diameter and Sauter mean diameter. However, it affects the intermittency of discharge water. The discharged water period becomes longer when the plate edge thickness increases. This discharged water frequency is smaller than the wave frequency of the water film flow on the plate when the airflow velocity is high. Based on an experiment involving the highest airflow velocity, the discharged water frequency is similar to that generated by a general turbine rotation speed.

Measurement of the diffusion coefficient in liquids using Fresnel diffraction from a phase step

Fresnel diffraction from a phase step for measuring diffusion coefficient in transparent liquids is investigated. When a transparent glass plate immersed vertically in a cell containing two diffusing liquids is illuminated by a parallel beam of light, the diffraction pattern of the plate edge forms on a screen perpendicular to the beam direction and varies by diffusion. The gradient of the refractive index in the liquids is then obtained by analyzing the diffraction patterns at different times after the beginning of the diffusion process, from which the diffusion coefficient is determined. Using this method, we study the diffusion process of the sucrose-water solution and report the diffusion coefficient with a reliable accuracy.

Effect of Trapezoidal Shapes on the Thermal Buckling Behaviour of Perforated Composite Plates

Thermal buckling study on the symmetric laminated composite trapezoidal plate with a circular cutout subjected to a uniform increase in temperature for various boundary conditions is explored in this paper. In a mathematical model, the first-order shear deformation principle is employed in accordance with the variational energy system. For acquiring the thermal buckling temperature, a nine-node heterosis plate relation has been used in the finite element formulation. By correlating the present findings with accessible literature, the effectiveness of the present formulation is verified. The impact of different parameters, such as trapezoidal shape, cutout size, ply-orientation, plate edge conditions and plate width to thickness ratio have been considered to study the effect of each parameters on the buckling characteristics of plate under various temperatures. It is observed from the study that each parametric investigation significantly affect the thermal buckling behaviour of trapezoidal plates.

Effects of end-plate on the critical moment of I-section cantilever beam with free end restrained laterally

Effects of end-plate on the lateral buckling of doubly symmetrical I-section cantilever beam with free end restrained laterally are analyzed using the software COMSOL and linear shell finite elements. The torsional stiffness of the end-plate prevents the free warping of flanges and decreases the warping effective length of the cantilever beam. A parametric study is conducted on 3231 cantilever beams under uniform bending to propose an approximative formula to determine the warping effective length factor which depends on the ratio between the torsional constant of the end-plate and the warping stiffness of the beam. The small standard deviation and high coefficient of determination show a very good correlation between analytical formulas and numerical results. Numerical applications are applied to analyze some cantilever beams subjected to uniform bending to demonstrate the reliability of the proposed formula and the effects of the end-plate on the enhancement of the global stability of cantilever beams with free end restrained laterally. Keywords: cantilever lateral buckling; end-plate; edge stiffener; flexural-torsional buckling; warping effective length; warping effective length factor.

On non-axisymmetric buckling modes of inhomogeneous circular plates

Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The asymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value at which waves in the circumferential direction can appear. The effect of material heterogeneity and boundary on the buckling load is examined. For a plate with elastically restrained edge, the buckling pressure and mode number increase with a rise of spring stiffness. Increasing of the elasticity modulus to the plate edge leads to increasing of the buckling pressure, but the mode number does not change. If the translational flexibility coefficient is small, decreasing of the elasticity modulus to the shell (plate) edge leads to sufficient lowering of the buckling pressure.