Plate Of Uniform Thickness Research Articles

Flexural–gravity wave interaction with dual inverse Π-type breakwaters

ABSTRACT This study examines the interaction of flexural–gravity waves with dual inverse Π-type breakwaters, which consist of two thin vertical plates extending upward from the seafloor. The goal is to analyse how the addition of these vertical plates impacts wave scattering on an ice-covered surface. The ice cover is modelled as a thin, flexible plate of uniform thickness, based on the Euler–Bernoulli beam equation. To solve the boundary value problem, a system of integral equations (Fredholm-type) is derived using mode-coupling relations, and the multi-term Galerkin method is applied. Chebyshev polynomials, weighted appropriately, are used to handle the sharp edges of the plates. This study evaluates key physical quantities, such as the reflection coefficient, transmission coefficient and horizontal wave force, under various structural configurations. To validate the findings, present results are compared with existing studies for various limiting cases. The analysis shows that adding thin plates on both sides of a conventional rectangular breakwater improves wave scattering performance. Bragg resonance is observed with variations in ice sheet thickness and submergence gap from the ice-covered surface of the breakwater. Additionally, the thickness of the ice cover plays a significant role in enhancing breakwater effectiveness.

SH-wave based defect imaging method for CFRP plates with variable thickness

ABSTRACT Classical guided wave imaging methods find applicability in uniform-thickness plates or quasi-isotropic plates. To be compared with, the method presented in this paper advances damage imaging accuracy for both uniform-thickness and variable-thickness anisotropic plates by incorporating new compensation terms grounded in the theoretical excitation directivity of the quasi-SH0 mode in anisotropic material. Specifically, the nondispersive nature of the wave speed and skew angle of the quasi-SH0 mode in the low- fd states (frequency-thickness-product lower than the cut-off value of SH1 mode) is established through dispersion curves and wave structure calculations. Additionally, employing the elastic dynamics reciprocity theorem reveals that the directivity of this mode is also nondispersive in the low- fd states. Therefore, the quasi-SH0 mode is theoretically insensitive to thickness variation. Experiment validated these theoretical calculations. On this basis, this paper proposed an integrated imaging method that utilises transmitted and reflected wave information by incorporating matching pursuit algorithm, cross-correlation analysis, probabilistic reconstruction and delay-and-sum method that incorporates new compensation terms based on the quasi-SH0 mode theory. Experimental validation of uniform-thickness carbon fibre-reinforced polymer (CFRP) plates and variable-thickness CFRP plates shows the insensitivity of this method to structural thickness variation, enabling effective imaging of damage in such anisotropic structures.

Study on Nonlinear Behavior of Variable Thickness Plates

The analysis of variable-thickness plates is much more complicated than that of uniform-thickness plates because variable coefficients occur in the equations. In reality, this analysis is of great interest in various engineering disciplines, such as civil engineering, aerospace engineering, machine design, and so on. Although there is extensive literature on analyses of plates with constant thickness, a rather limited amount of technical literature is available on the solutions to problems dealing with plates with nonuniform thickness. The reason is that the analytical solutions meet insurmountable difficulties. Besides, the nonlinear analysis process also faces more difficulties than the linear analysis of structures. For these reasons, the nonlinear behavior of variable-thickness plates based on a finite element procedure is presented in this study. Although the topic is not special, it will help the engineer have a specific view of the nonlinear bending of the plate with variable thickness. This survey will be based on the change in geometrical parameters. Numerical solutions are then presented to verify the simplicity of this proposed procedure.

A wave model of high frequency vibrational energy transfer in a wedge-shaped combined plate structure

Wedge shaped combined plate structure (WCPS) is broadly applied in large-sized transport equipment such as aerospace and shipping. However, with the increase of equipment operating running, it is easy to cause high-frequency vibration of structure components. Therefore, studying the energy transfer and vibration response of high-frequency vibration in WCPS is significant for the structural design of aerospace and shipping. The promising method is energy finite element analysis (EFEA). However, the energy transfer coefficient at joint of WCPS is needed in EFEA. The current studies about the energy transfer coefficients are focus on the joint between two uniform thickness plate. But it is some different that getting the energy transfer coefficient for WCPS, because the near-field solve representation for wedge-shaped plate is complicated due to the non-uniform thickness of wedge-shaped plate member in WCPS. In this research, geometric acoustic approximation and an equilibrium equation on both ends of joints were used to derive the equation of the energy transfer coefficient for the WCPS. Then by setting coupling nodes, construction of a coupling matrix to characterize discontinuity of energy density at the coupling position of the WCPS and energy density governing equation of wedge-shaped plates were integrated. In doing so, the EFEA modeling of the WCPS was developed and the energy density distribution on each node of the WCPS could be obtained. Same-sized uniformly coupled structures is analyzed, the vibration energy distribution characteristics of two types of coupling structures were compared. The results show that the energy density value of the wedge plate member attenuate more slowly than that of the uniform plate member due to the acoustic black hole aggregation effect in the wedge plate part, and there is an abrupt change in the energy density value at the joint of WCPS. As a result, the factors influencing high-frequency vibration energy transfer were investigated.

Analysis of damping characteristics in carbon fiber sheet embedded with an Acoustic Black Hole structure

Acoustic Black Hole (ABH) is a newly developed passive control method. It commonly uses the gradual change of the vertical thickness of the structure to control the propagation and aggregation of bending waves, which has excellent performance in structural vibration suppression and other aspects. Carbon fiber is the most famous composite material, the structure of low density, high strength and stiffness. The dynamic characteristics of carbon fiber sheet with ABH structure were analyzed by finite element method, and the vibration suppression performance was further verified by experiments. The results show that in the frequency range of 180~3000 Hz, the vibration level of the CFRP-ABH structure is reduced by 6~20 dB compared with the uniform thickness plate, showing excellent broadband vibration reduction performance.

Comparative Pharmacognostical Evaluation and HPTLC Analysis of Stem Bark of Kanchnar (Bauhinia Variegata Linn.) and Kovidar (Bauhinia Purpurea Linn.)

The current study was carried out to provide comparative macroscopy, microscopy, physicochemical parameters and HPTLC analysis of stem bark of Kanchnar (Bauhinia variegata L.) and Kovidar (Bauhinia purpurea L.) T.S. of stem bark of Bauhinia variegata L. shows a wide stratified cork have thin-walled yellow brown cells followed by brown colored cells; inner cork layer has transversely elongated orange brown cells. T.S. of Bauhinia purpurea L of shows presence of few layers of cork, Outer layers contains reddish brown content and inner layers are colourless. Its cortex is composed of 10 to 12 layers of parenchyma cell. Total Ash value found in sample of Kanchnar was 5.67% and in Kovidar was 15.2%. The Alcohol soluble extractive value of Kanchnar was found 29.8 % and of Kovidar was found 4.8%. Water soluble extractive value in sample of Kanchnar was found 20.68% and in Kovidar it was found 13.83%. Reference marker betasitosterol and lupeol was applied on a pre-coated silica gel GF254 plate of uniform thickness (0.2mm). The mobile phase consisting Toluene: Ethyl acetate: formic acid (9:1:0.1). Presence of marker betasitosterol and lupeol in sample of Bauhinia variegata L. were 85.19µg/ml and146.4µg/ml respectively. Presence of marker betasitosterol and lupeol in sample of Bauhinia purpurea L. were 244.6µg/ml and 305µg/ml respectively.

A method for improving wave suppression ability of acoustic black hole plate in low-frequency range

The acoustic black holes (ABH) with the power-law profile are applied in many fields, such as vibration control, energy collection, etc. It is widely known that the ABH only works above the cut-on frequency. However, few studies improve the vibration suppression performance of acoustic black hole structures below the cut-on frequency. This paper proposes shunt damping to improve the wave suppression ability of an ABH plate in the low-frequency range. The ABH plate with shunt damping obeys the Kirchhoff–Love plate theory. Based on the Hamiltonian principle, the modified Fourier series is selected as the shape function, and the natural frequency of the ABH plate is calculated by the energy method. Compared with the finite element method results, the correctness of this method is verified. Further, comparing the vibration characteristics of the ABH plate with those of the uniform thickness plate, it can be obtained that the ABH plate has excellent vibration damping performance in high frequency but a poor effect in low frequency. Therefore, a shunt damping with blocking circuits is pasted on one side of the central area of the ABH and successfully suppresses four resonate formants in the low-frequency band. Finally, the high-frequency vibration characteristics of the ABH plate with shunt damping are improved by increasing the thickness of the ordinary damping layer. This paper proposes a shunt damping ABH plate composite structure with excellent vibration suppression performance in both the high-frequency and low-frequency range, providing a new idea for the application of two-dimensional ABH plate structures in vibration control. • A semi-analytical method is employed to solve the vibration of ABH plate with shunt damping. • Piezoelectric patch with an external circuit is equivalent to homogeneous material. • Shunt damping can suppress multiple resonate formants at specified frequencies. • An ABH plate with the shunt and ordinary damping can achieve vibration suppression in low and high-frequency bands.

Free vibration analysis of uniform thickness and stepped P-FGM plates: A FSDT-based dynamic stiffness approach

In this article, the dynamic stiffness method (DSM) is implemented to analyze the out-of-plane free vibration behavior of uniform thickness and stepped functionally graded plates with power-law material property variation (P-FGM) along the thickness direction. The P-FGM plate is discretized suitably in a number of segments, and for each segment the dynamic stiffness (DS) matrix is formulated. The displacement field is defined with respect to the physical neutral surface of the plate based on the first-order shear deformation theory (FSDT). Assuming Levy-type plate boundary conditions, the governing differential equations are solved exactly to obtain the DS matrix pertaining to a plate segment. Finally, the eigenvalues and eigenvectors of the assembled global DS matrix are computed using the Wittrick–Williams algorithm to obtain the natural frequencies and mode shapes of various P-FGM plate configurations. It is shown that the frequency results obtained using DSM are very accurate as the method utilizes the exact solution of the governing differential equations. It is emphasized that FSDT-based frequency results for stepped P-FGM plates are reported, for the first time, in this article, and these results can be used as benchmark solutions for comparison purposes.

Buckling shape control in metal plates via material distribution

The aim of this study is to explain from a fundamental perspective, how distributing the material thickness of a metal plate in different ways can be used to control the shape of the elastic buckling mode. The Evolutionary Structural Optimisation (ESO) method is modified to control the buckled shape of plates simply supported on three sides with the remaining longitudinal edge free. The bucking objectives are considered both from a fundamental perspective, and for the application of kinetic façade design, that is, façade panels that undergo shape changes to facilitate ventilation or shading control. A series of buckling experiments of optimised aluminium plates validates the optimised designs. It is shown that in order to achieve a maximum opening in a buckled plate, the buckled shape should be controlled in such a manner as to create a relatively flat zone of maximum transverse displacement over much of the displaced free edge, a shape that differs from the fundamental mode of a uniform thickness plate. Notably, such a shape may be achieved via optimisation with objectives that relate either to the shape itself, or to the objective of maximising the opening. The design methods and experiments demonstrate that redistribution of plate material can efficiently control the buckling characteristics of metal plates for desired functions, and provide significant performance enhancements over uniform thickness plates. • Buckling shape of metal plates is controlled via material distribution of the plate thickness. • ESO method is used to optimise the plate material distribution. • Experiments validate the optimised plates. • Optimised plates have substantially larger buckled openings than uniform thickness plates. • Optimised plates are suitable for kinetic façade applications.

Vibro-Acoustic Analysis of Rectangular Plate-Cavity Parallelepiped Coupling System Embedded with 2D Acoustic Black Holes

An acoustic black hole (ABH) has the ability to concentrate and manipulate flexural waves, which can be used for structural vibration suppression and noise attenuation. In this paper, a 2D ABH rectangular plate is designed and a 2D ABH plate-cavity coupling system is constructed using the 2D ABH plate and five rectangular elastic plates of uniform thickness. Series of vibro-acoustic FEM models of the plate-cavity parallelepiped coupling system embedded with 2D ABHs are established, and the vibro-acoustic coupling simulation is conducted to analyze the effects of ABHs on the coupling modes, vibro-acoustic coupling characteristics, and mechanism of ABHs and the damping layer. It is shown that at most frequencies in the range of 3600~5000 Hz, the damping 2D ABH plate-cavity parallelepiped coupling system can significantly suppress the sound pressure and greatly reduce the peak values. It is also found that the significant reduction of the participation factor of the acoustic modes within the 100th order is the main mechanism for the obvious suppression of the sound pressure in the damping ABH plate-cavity coupling system at 3701 Hz. Finally, an experimental platform of vibro-acoustic measurement of the 2D ABH coupling system is constructed, and the accuracy of the vibro-acoustic FEM models of the 2D ABH coupling systems established in this paper and the numerical simulation calculation are verified by the vibro-acoustic measurement experiment.

Free vibration analysis of annular sector sandwich plates using first-order shear deformation theory

The present paper is concerned with the analysis of free transverse vibration of moderately thick annular sandwich sector plates of uniform thickness consisting of isotropic facings and core based on first-order shear deformation theory. The radial edges of the plate are taken as simply-supported (S) while the other two edges are considered to be under three combinations of clamped (C), and free (F) boundary conditions. The effects of transverse shear and rotatory inertia are included in the governing equations which are derived from Hamilton's principle. The differential quadrature method is used to discretise these equations and compute the lowest three eigenvalues of frequency parameter reported as the first three modes of vibration. The influence of boundary conditions, core thickness, facing thickness, inner-to-outer radii ratio, and sector angle on the frequency parameter of the plate is presented. Convergence of the results is also presented. Results are compared in special cases. Three-dimensional mode shapes for the first three modes are plotted.

Vibration analysis of irregular-shaped plates on simple supports

In this work, we propose a general perturbative approach for modal analysis of irregular-shaped plates of uniform thickness with uniform boundary conditions. Given a plate of irregular boundary, first, a uniform circular plate of identical thickness and area, centred at the centroid, is determined. The irregular boundary is then treated as a perturbation with a suitable smallness parameter, and is expressed as a generalized Fourier series. The frequency parameter, shape function and boundary conditions are then perturbed in terms of the smallness parameter. The homogeneous zeroth-order equation corresponds to the circular plate, which is exactly solvable. We show that the inhomogeneous equations in the higher orders can also be solved exactly using a particular solution structure. We can then construct the exact perturbative solution up to any order. The proposed method is demonstrated through the modal analysis of simply supported super-circular plates. The results are validated using the numerical results obtained from ANSYS ® , which are an excellent match. Interestingly, the supposedly degenerate modes with an even number of nodal diameters of super-circular plates are found to split naturally.

Analysis of semiconducting plate under photothermal theory bordered with inviscid liquid half-spaces

The present investigation is concerned with the study of two-dimensional deformation in an infinite semiconducting plate of uniform thickness bordered with inviscid liquid half-spaces. The plate is under the influence of the mechanical force of constant magnitude. The analytical expressions of displacement components, stress components, temperature distribution, and carrier density are obtained by normal mode analysis. The numerical results are presented graphically to show the effect of the thermoelectric coupling parameter and plate thickness on the physical components.

Determination of elastic thickness of the lithosphere using gravity and topography data: a case study for the Golpayegan, Arak, and the Qom Blocks

The elastic thickness, Te, is a measure of the strength of the lithosphere under loading and its elastic behavior. While there have been previous investigations on the nature of the lithosphere of Iran using satellite gravity and topography data, here, for the first time, using high-resolution gravity data we determine the elastic thickness for the Iranian lithosphere on a small scale, focusing on a region including Golpayegan, Arak, and Qom Blocks. The lithospheric elastic thickness is calculated using a wavelet transform method. The technique uses a superposition of two-dimensional Morlet wavelets that yields isotropic yet complex wavelet coefficients for the auto- and cross-spectra of gravity and topography data. These are subsequently applied to compute a spatially varying, isostatic coherence, from which both global and local estimates may be obtained. We applied the method to synthetic gravity and topography data generated for a thin elastic plate of uniform elastic thickness. After testing the validity of the technique on synthetic data, it was applied on real terrestrial gravity and topography data obtained from the National Cartographic Center (NCC) with grid spacing of 5 km. The average value calculated for the elastic thickness in the study area is 28 km which is in good accordance with the geological/tectonic structure of the region and previous interpretations for lithospheric strength based on geophysics and geodynamic studies.

On maximum forces exerted by floating ice on a structure due to constrained thermal expansion of ice

Abstract The problem of interaction between a floating ice cover and an engineering structure is considered, in which the ice–structure contact forces are caused by an increase in ice temperature due to solar radiation in situations, when the lateral thermal expansion of ice is constrained. The focus is on the determination of the maximum thermally-induced horizontal force exerted on a structure wall, assuming that the magnitude of this force is bound by the smallest force capable of fracturing the ice cover due to its buckling. The ice cover is modelled as a rectangular plate of uniform thickness, with its four edges being constrained by vertical rigid walls, and it is assumed that ice deforms, and eventually fails, by the mechanism of viscous creep buckling. The plate is subjected to in-plane axial compressive stresses developing in ice to prevent its thermal expansion due to solar heating, and is transversely (vertically) bent by the forces caused by the reaction of underlying water. The floating ice is treated as a material whose elastic and viscous properties depend on temperature and the ice porosity, and therefore they vary with time and the depth of ice. The results of numerical simulations, conducted for a variety of the ice plate horizontal dimensions, thicknesses and daytime temperature-change scenarios, illustrate the evolution of the plate deflection surface prior to its failure, and show the time variation of the maximum forces exerted by ice on a structure wall as functions of the ice thickness and maximum daytime temperature rise at the top surface of ice.

Generation of optical orbital angular momentum light by an azimuthally-graded refractive index plate

We propose and numerically demonstrate a method to generate orbital angular momentum (OAM) light by using an azimuthally graded index (AGI) plate of uniform subwavelength thickness. We illustrate, theoretically, through numerical simulations, how a plane polarized fundamental gaussian beam incident onto such an AGI plate acquires a nonzero orbital angular momentum, and exhibits an annular far-field intensity profile with a phase singularity line along its axis. We further confirm the OAM property of the output beam by calculations of the overlap integral between its far-field and the paraxial Laguerre Gaussian modes of nonzero OAM. We also highlight the advantages of the proposed AGI plate over existing methods to generate OAM light.

Parametric modal analysis of an induced-strain actuated wing-like plate for pitch and heave coupling response

This article investigates the feasibility of a plate-like flapping wing with varying geometric and boundary conditions actuated by surface-bonded piezoelectric material devices. The most influential structural parameters that vary dynamic response and heave–pitch mode coupling are investigated. An analytically and experimentally validated dynamic finite element model is developed to analyze the structure. A parametric analysis is conducted by varying critical geometric parameters and boundary conditions, such as aspect ratio, actuator position, actuator angle, clamp size, and position; substrate thickness variation; and substrate-to-actuator-thickness ratio. Response metrics representing heave and pitch motions are taken as longitudinal curvature and lateral slope, respectively—the surface regression analysis and results leading to these choices are presented. Maximum longitudinal curvature and lateral slope amplitudes and phase shifts are reported for key parameter choices. Longitudinal curvature to lateral slope coupling is achieved with the introduction of a leading edge stiffener to the otherwise uniform thickness plate. Conditions and parameters that lead to and influence heave–pitch coupling are presented and discussed in detail. This article presents a unique approach to flapping mode of flight compared to the literature. The article proposes a purely induced-strain actuation approach rather than the typical “mechanisms” based approach.

ВЛИЯНИЕ ЛЕДЯНОГО ПОКРОВА НА ВОЛНЫ КЕЛЬВИНА И ПУАНКАРЕ

This work presents theoretical foundations of Kelvin and Poincare waves in the homogeneous ocean under an ice cover. The ice is considered as thin elastic plate of uniform thickness, with constant values of Young’s modulus, Poisson’s ratio, density, and compressive stress. The boundary conditions are such that the normal velocity at the bottom is zero, and at the undersurface of the ice the linearized kinematic and dynamic boundary conditions are satisfied. We present and analyze explicit solutions for the Kelvin and Poincare waves and the dispersion equations. The problem is examined in the context of a unified theory and without the hydrostatic assumption.

Vibration Characteristics of Plate Structures Embedded with Acoustic Black Holes and Distributed Dynamic Vibration Absorbers

This study discusses a method of combining the acoustic black hole (ABH) concept and dynamic vibration absorbers (DVAs) together as a lightweight passive control approach for structural vibration and noise attenuation. Finite element (FE) simulations and experiments are used to compare vibration response levels of plate structures. The plate structures have been integrated with various vibration attenuation treatments including damping layers, DVAs, ABHs and ABH-DVA pairs. It is demonstrated experimentally that the plate structure integrated with two ABH-DVA pairs has the lowest overall vibration response level in the frequency range below 800 Hz. More interestingly, the total structural mass of the plate structure integrated with ABH-DVA pairs is 8.24% less than that of the uniform thickness plate. The experimental observations are further verified with simulation results. With the help of the FE model, plate structures integrated with more than two ABH–DVA pairs targeted at the simultaneous attenuation of multiple resonances are studied and compared with traditional uniform thickness plates. Under the design constraint of the total structural mass being equal, it is shown that plates integrated with DVA-ABH pairs always have lower vibration response levels in the low-mid frequency range where mechanical vibration commonly occurs.

Nonlinear interaction of co-directional shear horizontal waves in a two-layered elastic medium

The nonlinear interaction of co-directional shear horizontal (SH) waves propagating in a two-layered plate of uniform thickness is considered. It is assumed that the constituent materials of both layers are nonlinear, homogeneous, isotropic and incompressible elastic and having different mechanical properties. It is also assumed that between the linear shear velocities of the top layer, $$c_1$$ , and the bottom layer, $$c_2$$ , the inequality $$c_1<c_2$$ is valid. For the existence of a SH wave, the phase velocity of the wave, c, must satisfy either the inequality $$c_1<c_2 \le c$$ or the one $$c_1< c\le c_2 $$ and here the problem is examined under the second condition. By employing an asymptotic perturbation method and balancing the weak nonlinearity and dispersion in the analysis, it is shown that the first order slowly varying amplitudes of interacting waves are governed asymptotically by a coupled nonlinear Schrodinger (CNLS) equations. Then the effects of nonlinearity of the materials and the ratio of layers’ thickness on the linear instabilities of solutions of the CNLS equations and the existence of solitary wave solutions of the CNLS are examined.