Finite Plate Research Articles

Breakdown of laminar regime in flat plate boundary layer seen in numerical solutions of the Navier–Stokes equations obtained with 16th-order scheme

Numerical solutions of the Navier–Stokes equations describing the onset and the development of the boundary layer instability of a subsonic flow about a finite width flat plate are described. They were obtained via exciters-free calculations with the 16th-order multioperators-based scheme optimized to resolve very small solutions scales. Some relevant details of the scheme are briefly outlined. The occurrence of the Tollmien–Schlichting waves near the leading edge, their downstream propagation and breakdowns some distance away are displayed. The role of the oblique waves seen in the solutions is emphasized. The nonlinear stage in the form of structured vortices followed by the solutions randomization are described.

Sound transmission through an unbaffled plate

Commonly occurring complex structures can often be modelled as simple finite plates mounted without baffles. Thus, the objective here is to study the sound transmission loss of a simply-supported rectangular finite unbaffled plate impinged upon by an acoustic plane wave. The total pressure jump across the plate surface is expressed as the sum of the pressure jump due to pure diffraction, where the plate normal displacement is zero and the pressure jump due to plate radiation. These pressure jumps are computed using the definition of the free-space Green's function in the wavenumber domain and the Euler equation. Then, the coupled equation of motion is solved for the plate displacement. The method of stationary phase is used to derive the closed-form expression for the improper double integral that appears in the far-field acoustic pressure. Finally, the far-field transmitted power is numerically computed and the sound transmission loss of the unbaffled plate is compared with that of the baffled one.

Wave interaction with a floating finite elastic plate of arbitrary shape

Wave interaction with a floating finite elastic plate of arbitrary shape

A novel hybrid boundary element for polygonal holes with rounded corners in two-dimensional anisotropic elastic solids

A novel hybrid boundary element is developed for polygonal holes in finite anisotropic elastic plates based on two different special fundamental solutions for holes. Since these special fundamental solutions satisfy traction-free condition along the hole's boundary, there is no mesh required on the boundary of polygonal holes. Various types of polygonal holes with rounded corners, such as triangles, rhombuses, ovals, pentagons, are considered by adding proper perturbation to an elliptical hole. The developed hybrid element is a mixture of two special boundary elements: one is based on the special fundamental solution derived through nonconformal mapping and the other is based on the solution derived through perturbation technique with conformal mapping. The special boundary element methods are combined through submodeling technique. First, the global model is solved using the perturbation solution. Then, using the displacements obtained from global model, an auxiliary submodel is set up and the results are evaluated with the nonconformal solution. The present method is compared and validated with conventional boundary element method and finite element method. The effect of hole curvature, material anisotropy, and loading condition on the stress distribution around the hole is presented.

Prediction of Coefficient of Restitution for Impact Elastoplastic Spheres Considering Finite Plate Thickness

Collisions between objects are a relatively common phenomenon in nature. Analyses of collision processes can greatly contribute to solving problems such as impact-rub faults and particle impacts. The coefficient of restitution is a critical parameter in the analysis of collision processes. Many experiments have shown that the coefficient of restitution is closely related to the plate thickness, and the smaller the plate thickness, the more inaccurate the coefficient of restitution predicted by the existing model, which seriously affects the process of collision analysis. To remedy this shortcoming, this paper proposes a plate thickness influence factor with the ratio of sphere diameter to plate thickness as the variable. The plate thickness influence factor can optimize the coefficient of restitution model to effectively predict the coefficient of restitution of impacting elastoplastic spheres with finite plate thickness. Finally, the validity of the new model is verified using a large amount of experimental data.

Measurement of sound scattering from a finite flat plate using a three-dimensional spatial method

The sound scattering from a finite flat plate is crucial in the scatter analysis in the water. Due to the reverberations and difficulty of determining the attitude of the finite flat plate in the water, the reflection or absorption coefficient is often used for the evaluation of the scattering properties, indirectly. A three-dimensional spatial method is proposed for directly measuring the sound scattering of a finite flat plate. The ultrasonic ranging method is utilized to determine the attitude of a finite flat plate in real-time. The complex cepstrum method is modified to extract the sound scattering from the reverberations. Using a three-dimensional spatial measurement method, a measurement system is established for measuring sound scattering from a finite stainless-steel flat plate, with a length of 1.6 m, a width of 1.2 m, and a thickness of 5 mm. The measurement results are consistent with the calculated results by a finite-element model.

Study on vibration bandgap characteristics of a cantilever beam type local resonance unit

This article proposes a novel phononic crystal configuration consisting of a through-hole cantilever beam and a mass block, and conducts numerical analysis and experimental verification on the bandgap characteristics of a two-dimensional periodic array plate containing this configuration. The results indicate that there are multiple bending wave band gaps in the proposed structure, and the formation of the bandgap is due to the coupling between elastic waves in the matrix and the resonance characteristics of the local resonant structure. The width of the bandgap is related to the coupling strength. Further research has also found that the proportion of effective mass of the mode is a criterion for determining whether the mode generates a bandgap. At the same time, the regulation of band gaps by the cell constants and geometric parameters of local resonance units was studied. Based on the above research, by improving the original local resonance structure, more abundant bandgap features were obtained, providing a feasible approach for the design of broadband bandgaps. Finally, the vibration transmission rate of the finite period structural plate was obtained through simulation calculations and experiments, and its attenuation frequency band was basically consistent with the bandgap range, indicating that the structure has good low-frequency vibration reduction performance, which has broad engineering application prospects in the field of vibration and noise reduction.

Calibrating the Discrete Boundary Conditions of a Dynamic Simulation: A Combinatorial Approximate Bayesian Computation Sequential Monte Carlo (ABC-SMC) Approach.

This paper presents a novel adaptation of the conventional approximate Bayesian computation sequential Monte Carlo (ABC-SMC) sampling algorithm for parameter estimation in the presence of uncertainties, coined combinatorial ABC-SMC. Inference of this type is used in situations where there does not exist a closed form of the associated likelihood function, which is replaced by a simulating model capable of producing artificial data. In the literature, conventional ABC-SMC is utilised to perform inference on continuous parameters. The novel scheme presented here has been developed to perform inference on parameters that are high-dimensional binary, rather than continuous. By altering the form of the proposal distribution from which to sample candidates in subsequent iterations (referred to as waves), high-dimensional binary variables may be targeted and inferred by the scheme. The efficacy of the proposed scheme is demonstrated through application to vibration data obtained in a structural dynamics experiment on a fibre-optic sensor simulated as a finite plate with uncertain boundary conditions at its edges. Results indicate that the method provides sound inference on the plate boundary conditions, which is validated through subsequent application of the method to multiple vibration datasets. Comparisons between appropriate forms of the metric function used in the scheme are also developed to highlight the effect of this element in the schemes convergence.

Finite Element Analysis based Stress Intensity Factor Solutions for Surface Cracks

The stress intensity concept is important in termsof crack extension as critical values of the stress intensityfactors govern crack initiation. Therefore, the present workdetermines stress intensity factors for semielliptical shallowand deep surface cracks as a function of parametric angle,crack depth, and aspect ratio for tension and bending loads.The stress intensity factors are obtained from a threedimensional finite-element analysis of semielliptical surfacecracks in finite plates subjected independently to tensionand bending loads under elastic conditions. The obtainedstress intensity factor is used to predict the crack growthunder linear elastic conditions. Results show that the stressintensity factor varies along the crack front for shallow anddeep cracks. At the deepest point in bending and tension thestress intensity factor increases as the ratio of the crackdepth to the crack length at surface decreases. However, atthe free surface the stress intensity factor becomesmaximum when the crack depth equals crack length. Asurface crack in tension loading is predicted to break thewall thickness with a relatively small amount of crackgrowth at surface. While in bending the crack breaksthrough with large amount of crack growth in the widthdirection.

Determination and analysis of stress concentration factor in finite plate with different polygonal discontinuities under uniaxial compression using finite element analysis (FEA)

Stress concentration is the accumulation of stress in a body due to a sudden change in its geometry. Stresses and stress concentrations are created at the nearer area of the structural discontinuities. Any structural discontinuity compromises the strength of the structure. Numerical approaches can be used to determine the maximum stress concentration for various complex geometries without regard to time or cost constraints. The current study gives a thorough finite element analysis of stress concentration in a structural steel plate with a polygonal cutout. In contrast to orientation and area, this study looks at an isotropic finite plate for the stress concentration factor (SCF) with central polygonal cutouts (triangular, square, pentagonal, and hexagonal). ANSYS, a finite element program, calculates the von Mises stresses, and based on the results, stress concentrations are calculated. The orientation of polygonal cutouts in a square plate and the constant area of polygonal cutouts in a square plate are two parameters considered in the calculation. These results are verified by literature for the orientation of the hole, which concludes that a square hole position parallels the loading direction showing a 50% reduction in stress concentration factor.

Dispersion by submerged pinned/sliding finite elastic plate

Submerged structures are quite important in ocean and marine sciences. In this article, we have presented the solution of finite submerged elastic plate of negligible thickness. Solution is obtained using the method of mode matching with two different edge conditions: (i) pinned edge condition and (ii) sliding edge condition. Reflection coefficient at both edges for different values of physical parameters: submergence depth, length and stiffness of elastic plate is analyzed. Surface and plate displacement for both edge conditions is also presented. Since the gradient of velocity potential gives insight about the velocity of particles, therefore, the way it behaves in different regions around elastic plate is also discussed. Furthermore energy balance relation for the finite submerged elastic plate is also given.

Data-based adaptive refinement of finite element thin plate spline

The thin plate spline, as introduced by Duchon, interpolates a smooth surface through scattered data. It is computationally expensive when there are many data points. The finite element thin plate spline (TPSFEM) possesses similar smoothing properties and is efficient for large data sets. Its efficiency is further improved by adaptive refinement that adapts the precision of the finite element grid. Adaptive refinement processes and error indicators developed for partial differential equations may not apply to the TPSFEM as it incorporates information about the scattered data. This additional information results in features not evident in partial differential equations. An iterative adaptive refinement process and five error indicators were adapted for the TPSFEM. We give comprehensive depictions of the process in this article and evaluate the error indicators through a numerical experiment with a model problem and two bathymetric surveys in square and L-shaped domains.

Damping performance of finite microperforated plates using multi-size and spatial distributions of perforations

In the context of structural dynamics, recent works by the authors showed that microperforations can be used to mitigate vibration. Microperforated plates (MPP) have been shown to exhibit substantial added damping arising from fluid-structure interactions and visco-thermal effects in the boundary layers of the perforations during relative motion between the solid and the fluid contained in the perforations. The added damping reaches a maximum for a characteristic frequency, depending only on the diameter of the perforation. Choosing the diameter of the perforation so that the characteristic frequency coincides with a given natural frequency of the plate reduces the contribution of the associated plate mode. However, the MPP studied had a single set of perforations homogeneously distributed throughout the structure. In this work, it is proposed to extend the added damping to several modes of the plate by using MPP with multi-size perforations and an optimized spatial distribution of these perforations. As an extension of the previous vibratory model of the authors, the dynamics of MPP with perforations of multiple sizes based on a homogenization model is established. In addition, the effect of the spatial distribution of perforations on the additional damping is captured by including a spatially dependent perforation ratio in the model. Experimental measurements on MPP validate the proposed analytical models. The results show that (i) MPP with multiple-size perforations feature a wider effective damping frequency band, and (ii) the added damping is accentuated when the perforations are distributed in the zone of the antinodes of the considered modes. Thus, by combining the two effects, it is possible to achieve MPP that effectively reduce the vibratory responses on several modes.

Mixed convection flow over a horizontal plate and the horizontal wake far downstream

The laminar mixed convection flow over a heated or cooled horizontal plate of finite length is a surprisingly intriguing problem. The hydrostatic pressure jump at the trailing edge and across the wake is to be compensated by induced circulation in the outer potential flow, similar to a plate at a non-zero angle of attack. The mixed convection flows over semi-infinite and finite horizontal plates, respectively, are thus substantially different. As the hydrostatic pressure jump remains finite along the infinitely extended wake, the induced outer potential flow around the plate would grow beyond bounds in a domain extending to infinity. Thus, boundary conditions must be imposed at the boundaries of a finite domain. However, the numerical solution of the Navier-Stokes equations remains a challenging problem due to the lack of appropriate outflow conditions. The traditional outflow condition cannot comply with the finite hydrostatic pressure jump across the wake. Thus, an asymptotic expansion for the wake far downstream from the plate is performed. Remarkably, the perturbation of the flow does not decay with increasing distance from the plate as in a classical wake. The asymptotic solution is implemented as an outflow boundary condition for the numerical solution of the Navier-Stokes equations. The results are compared with a boundary-layer solution obtained in previous work for the limiting case of vanishing Prandtl number.

Stress intensity factor and T-stress around hypocycloidal-shaped holes in finite sheets

Hypocycloidal-shaped holes are seen in sheet structures in special designs or because of the crack growth in particular fatigue loadings. The study focused on the determination of stress intensity factor (SIF) and T-stress around these holes’ cusps. Three-cusp and four-cusp hypocycloid holes with various lengths in various plate sizes were simulated in ANSYS. Results showed both SIF and T-stress decrease with the increase in the plate size. The SIF in a finite plate gets close to the infinite plate SIF where the fraction of plate length to hole length is around 10. For the T-stress, a considerable difference was seen between finite and infinite plates. Finally, the numerical results were experimentally validated using the DIC technique.

Vibrational analysis of finite plate on elastic foundation subjected to oblique impact

Vibrational analysis of finite plate on elastic foundation subjected to oblique impact

Comparison of approximation methods for bending of finite and infinite elastic plates: The traction boundary value problem

A generalized Fourier series method is designed to approximate the solution of the Neumann problem in a finite domain and in an infinite domain with a hole, for the mathematical model of bending of elastic plates with transverse shear deformation. The results in the two cases are compared and contrasted, and the analysis is illustrated by examples with specific boundary conditions.

Stress distributions around the interference fit between a round pin and a perforated finite plate

Interference fit couplings between a perforated finite plate and a round pin are widely used mechanical systems in several industrial applications. Only a few works in the literature investigate the coupling contact pressure due to interference in the absence of an external load, and these works are limited to a few specific configurations. To overcome this limitation, this work performs a numerical systematic investigation of the pin-plate coupling for a wide range of configurations that can be encountered in practice. Three are the variables investigated: the pin diameter, the plate length, and the pin offset in the longitudinal direction, all of them normalized over plate width, for a total of 18 configurations. The work provides a detailed prediction of the contact pressure and equivalent von Mises stress along the contact surface and compares the results with photoelastic investigations retrieved from the literature. For design purposes, the results are synthesized through two stress concentration factors, one referring to the peak contact pressure, and the second one to the peak von Mises stress.

Research on the factors influencing the process of prefabricated fragments penetrating finite thickness concrete

The damage to the back of the target plate is a phenomenon that occurs when concrete is subjected to high-speed impact. In order to study the motion parameters of prefabricated spherical fragments penetrating finite thickness concrete targets at high speeds and the occurrence rules of concrete damage, as well as the impact of target back damage on the motion of fragments, experiments were conducted on 100 mm finite thickness concrete targets with prefabricated spherical fragments. The concrete model parameters in LS-DYNA were modified based on the residual velocity of fragments, and numerical simulations were conducted on the penetration of prefabricated fragments with different impact velocities and concrete target plates with different thicknesses. By analyzing the location of concrete target plate damage, the relationship between concrete thickness and concrete damage was obtained; Combining the motion parameters of fragment penetration process, the phenomenon of concrete collapse was linked to fragment motion, and the influence of concrete thickness on fragment motion parameters was analyzed. The results indicate that the thickness of the finite thickness concrete target plate and the penetration speed of fragments have a significant impact on the damage state of the target back, and further affect the motion change response stage during the penetration process of prefabricated fragments.

Robust transport and topological valley refraction of fundamental symmetric lamb waves in perforated phononic crystal plates

Lamb waves can be divided into antisymmetric Lamb waves (type A) and symmetric Lamb waves (type S), which are widely used in health monitoring of engineering structures and nondestructive evaluation of materials. However, due to the fact that each mode of Lamb wave has the setting group velocity in a certain bandwidth range, it is easy to cause the aliasing of multi-mode Lamb waves, partly limiting the application scenarios of Lamb wave. In this paper, a hexagonal lattice meta-structure is designed and the zero-order symmetric (S0) Lamb wave in a finite thickness plate is successfully separated. By breaking the spatial C 3v symmetry, a valley topological phononic crystal (PnC) plate for the pure S0 mode is constructed, and its robust topological transports are demonstrated. Firstly, the valley topological phase transition of S0 mode is realized by changing the angle of scatterer in PnC plate and the valley edge state of S0 mode is obtained. Furthermore, by introducing structural mismatch, it is verified that the edge state of S0 mode is robust to various bends and defect. Finally, by changing the material property of the terminal, the valley refraction with different directionality is realized. The results offer a route to individually study the symmetric modes of Lamb waves, and have potential application prospects in rapid and accurate ultrasonic nondestructive testing based on Lamb waves.