Free Edge Conditions Research Articles

Scale for the assessment of mucosal wave dynamics of the free edges during stroboscopic examination: clinical validation study and analysis of results.

Identifying the mucosal wave (MW) is essential when studying the voice; however, its characterization and perceived measurement during laryngeal stroboscopy (LS) are not well defined or standardized because of the subjectivity of its interpretation. This article proposed and validated a scale that characterized and approximated MW measurement during LS, applied it to participants divided into a healthy group and groups with free edge conditions, and identified differences between them. This is a descriptive and clinical validation study of the "VASQ (Vertical axis, Anteroposterior axis, Symmetry and Quantity) mucosal wave score" scale based on stroboscopy images of 137 adult men and women divided into a control group and functional and organic pathology groups. The images were analyzed by three evaluators according to an established protocol. Measurements dictating the reproducibility and validity criteria as well as the MW score in each group were obtained. The reliability of the scale was α = 0.90, internal consistency success rate was 91%, intra-observer reliability was 0.83, inter-observer reliability was 0.83, content validity coefficient was 0.92, and factor loading was 0.37-0.53. The MW total score values between 5 and 6 were established as a reference for normality (P < 0.05). Organic pathology showed lower MW score values (P < 0.05), and functional pathology to a lesser extent (P > 0.05). The proposed scale is a consistent, valid, and reliable tool. Its widespread application would favor commonly used terminology and facilitate quantitative comparisons in future studies.

Hydroelastic analysis of a forced circular elastic floating plate in the presence of porous barrier

The hydroelastic behavior of a forced circular elastic floating plate is analyzed, while considering the existence of vertical barrier. This study encompasses different edge conditions such as free, simply supported and built-in edge conditions. The eigenfunction matching method is employed with circular symmetry to obtain the solution in frequency-domain. The analysis in time-domain is performed by considering Gaussian forcing at different points on the plate, utilizing the Fourier transform for analysis. The study examines the vertical force acting on the plate and the time-dependent deflection at the point of force application, taking into account different permeable barriers and fluid depths. Additionally, the numerical findings are assessed and compared to the current ones for validation. The findings indicate that the plate encounters maximum force under a built-in edge condition. Furthermore, the time-dependent deflection of the point of forcing decreases with rising values of both the real and imaginary parts of the porous effect parameter G over the time. The outcomes arising from integrating a circular elastic plate with a porous barrier will provide valuable insights into how the plate responds to abrupt forces, similar to those experienced in seismic events or unforeseen disturbances and it also helps in the design of structures capable of enduring unexpected impacts or shocks, among other considerations.

TOPOGRAPHICAL EFFECTS ON WAVE SCATTERING BY AN ELASTIC PLATE FLOATING ON TWO-LAYER FLUID

This article illustrates the hydroelastic interactions between surface gravity waves and a floating elastic plate in a two-layer liquid with variable bottom topography under the assumptions of small amplitude waves and potential flow theory. In this study, semi-infinite and finite-length plates are considered. The eigenfunction expansion method is applied in the fluid region with uniform bottom topography. A system of differential equations (mild-slope equations) is solved in the fluid region with variable bottom topography. From the matching and jump conditions, the solution is expressed as a linear algebraic system from which all the unknown constants are computed. We explored the effects of density ratio, depth ratio, and bottom topography on the bending moment, shear force, and the deflection of the elastic plate. Results show that when the density ratio becomes closer to one, the occurred bending moment and shear forces to the elastic plates tend to diminish. The bending moment and shear forces to the pates are higher and lower at a smaller depth ratiofor the incident surface wave and interfacial waves, respectively. The variations in the bending moment, shear force, and plate deflection, caused by surface and interfacial waves, are observed to be in opposite trends, respectively. Bottom profiles similarly affect semi-infinite and finite-length plates when they undergo free-edge conditions. These effects, however, are substantial when the plate is simply supported at the edges. Elastic plate with free edges experiences lower deflection for concave-up and plane-sloping bottoms for incident surface and interfacial waves, respectively.

Study on the Effect of Free-edge Conditions on Bending Properties of Composite Materials

The glass fiber is selected as the reinforcement, and the structural design of the composite is carried out to enhance the continuity of the edge fiber of the laminate. The influence of the width of the edge fiber on the bending mechanical properties is discussed. It is found that when the edge fiber of the laminate is continuous, the failure mode of the laminate bending can be changed to a certain extent, and the strength of the reinforcement and the matrix bonding is strengthened. The width of the laminate is not the influence factor in improving the bending strength.

Design and Fabrication of Shell Structures

Shell structures carry loads with their thin yet curved shapes. Being thin means shells require little material, which is desirable for minimizing embodied carbon footprints. However, the feature of being curved implies shells require immense effort to design and fabricate. To address the challenges, this dissertation consists of three parts: developing a design algorithm based on radial basis functions (RBFs), inventing a fabrication technique based on reconfigurable mechanisms, and producing prototypes based on the new algorithm and mechanism. The first part of this dissertation introduces a new algorithm based on RBFs for designing smooth membrane shells, which is more versatile than existing methods. The algorithm can generate membranes with both tensile and compressive stresses. It can also tweak an initial shape to meet free-edge conditions. It can also incorporate horizontal loads in the form-finding process. The second part of the dissertation presents a new system of flat-to-curved mechanisms, which allows a shell to be fabricated in a flat configuration and deployed into a double-curved state. Such a mechanism consists of panels connected by tilted hinges. The mechanism can contract non-homogeneously and change its Gaussian curvature. The last part of this dissertation demonstrates the integral application of the RBFs form-finding algorithm and the flat-to-curved mechanisms. The prototypes designed and produced deliver form-found shapes that have spans ranging from 0.2 to 4 meters. This dissertation contributes to the development and distribution of shell structures by developing computer algorithms and digital fabrication techniques to minimize the hurdles of designing and fabricating shell structures.

Geometrical Dimensional Effect on Natural Frequency of Single Layer Graphene in Armchair Configuration

Graphene has remarkable strength, such as yield strength and elasticconstant. The dynamic behaviour of graphene sheet is affected bygeometrical variation in atomic arrangement. This paper introducedgraphene with armchair atomic structure for estimating fundamental naturalfrequencies. The presented analysis can be useful for the possible highfrequency nanomechanical resonator systems. The analytical formulation,based on classical plate theory and continuum solid modelling based finiteelement method have been performed for estimation of fundamental naturalfrequencies of single layer graphene sheet (SGLS) with different boundaryconditions. The free edge and clamped edge boundary conditions have beenconsidered. For simplifying analytical formulations, Blevins approach fordynamic solution has been adopted and for validating analytical results.The finite element analysis of SLGS has been performed using ANSYSsoftware. The effect of variation in geometrical parameters in terms ofwidth and length of SLGS has been analysed for realization of ultra-highfrequency based nanomechanical resonator systems

Thin rectangular plates under axial point loading: Accuracy of the classical single Fourier series solution for stresses

The purpose of this article is to clarify certain ambiguities associated with commonly adopted solution strategies of the problem of thin rectangular plates subjected to equal and opposite colinear point loads. The problem is treated as a plane-stress problem where the boundary conditions are prescribed exclusively in terms of tractions. Both an elaborate exact solution and a simplified approximate Single Fourier Series (SFS) solution are employed, shedding light on the accuracy of the latter. This is accomplished, first, by showing that the error implicit in the sine single-Fourier series solution becomes significant for column plates, and, secondly, by re-evaluating the stress distribution at various cross-sections away from the compressed sides, through the application of a truly exact solution to the problem at hand, in which the free-edge conditions are precisely fulfilled. It is shown that the restrictions usually associated with the SFS technique may not be severe and that a wider range of plate shapes with free vertical sides could be amenable to analysis utilizing this simple approximate scheme.

Interaction of ocean wave with a harbor covered by an ice sheet

A domain decomposition method is developed to solve the problem of wave motion inside a harbor with its surface covered by an ice sheet. The shape of the horizontal plane of the harbor can be arbitrary while the sidewall is vertical. The entrance of the harbor is open to the sea with a free surface. The linearized velocity potential theory is adopted for fluid flow, and the thin elastic plate model is applied for the ice sheet. The domain is divided into two subdomains. Inside the harbor, the velocity potential is expanded into a series of eigenfunctions in the vertical direction. The orthogonal inner product is adopted to impose the impermeable condition on the harbor wall, together with the edge conditions on the intersection of the harbor wall and the ice sheet. In the open sea outside of the harbor, through the modified Green function, the velocity potential is written in terms of an integral equation over the surface of the harbor entrance, or the interface between the two subdomains. On the interface, the orthogonal inner product is also applied to impose the continuity conditions of velocity and pressure as well as the free ice edge conditions. Computations are first carried out for a rectangular harbor without the ice sheet to verify the methodology, and then extensive results and discussions are provided for a harbor of a more general shape covered by an ice sheet with different thicknesses and under different incident wave angles.

A New Analytical Method for Spherical Thin Shells’ Axisymmetric Vibrations

In order to improve the spherical thin shells’ vibrations analysis, we introduce a new analytical method. In this method, we take into consideration the terms of the inertial couples in the stress couples’ differential equations of motion. These inertial couples are omitted in the theories provided by Naghdi–Kalnins and Kunieda. The results show that the current method can solve the axisymmetric vibrations’ equations of elastic thin spherical shells. In this paper, we focus on verifying the current method, particularly for free vibrations with free edge and clamped edge boundary conditions. To check the validity and accuracy of the current analytical method, the natural frequencies determined by this method are compared with those available in the literature and those obtained by a finite element calculation.

On the symplectic superposition method for new analytic free vibration solutions of side-cracked rectangular thin plates

In this study, a first attempt is made to develop an up-to-date symplectic superposition method for some new analytic free vibration solutions of side-cracked rectangular thin plates that were not obtained by conventional semi-inverse methods. In contrast with the classical Lagrangian system and Euclidean space, the present method is implemented within the Hamiltonian-system framework and symplectic space. The solution procedure involves expressing the problems in the Hamiltonian system and dividing a side-cracked plate into several sub-plates that are analytically solved by the symplectic superposition method, where the imposed quantities are determined by the plate boundary conditions, free edge conditions along the crack, and interfacial continuity conditions between the sub-plates. In the analytic solution of a sub-plate, specifically, the symplectic eigenvalue problems are formulated, followed by the symplectic eigen expansion. The integration of the solutions of the sub-plates yields the final solution of a side-cracked plate. The rigorous mathematical techniques, without predetermination of solution forms, qualify the present method as an unusual approach for exploring more analytic solutions. Comprehensive natural frequency and mode shape solutions of the side-cracked plates under three representative boundary constraints are provided and well validated by other methods. The new analytic solutions obtained may serve as benchmarks for other potential solution methods.

An efficient three-dimensional method for the prediction of building vibrations from underground railway networks

This paper proposes a new efficient three-dimensional (3D) method to predict the vertical building vibration generated by trains running in tunnels in a multi-layered half-space. The tunnel-ground-building dynamic interaction involving in the proposed method is handled using the sub-structuring approach. The multi-story building is considered as rectangular floors supported by a distribution of columns. Each building floor is divided into several sub-plates. The dynamic stiffness matrix of a single sub-plate derived by the dynamic stiffness method is assembled to obtain the global one of each building floor. The free edge condition of the building floor is satisfied in this solution. The train-track-tunnel-ground dynamic interaction is modelled by a fully-coupled analytical method. The proposed method shows sufficient efficiency and accuracy, making it a suitable tool for predicting large-scale vibrations and performing parametric studies. The responses of a four-story building generated by the passage of trains in a tunnel are analyzed. The building vibrations are significantly affected by the dynamic properties of the building and the building-ground dynamic interaction. The dynamic interaction between the shallow foundations of buildings has a considerable influence on the building vibrations in the low-frequency range. The isolation effectiveness of the floating slab track and the base-isolation of buildings is highly dependent on the isolation frequency.

New analytic buckling solutions of side-cracked rectangular thin plates by the symplectic superposition method

Exploring new analytic buckling solutions of cracked plates is of much importance for providing benchmark results and implementing preliminary structural designs based on explicit parametric analysis and optimization. However, the governing higher-order partial differential equations as well as the geometric discontinuity across a crack essentially complicate the problems, make it more intractable to seeking analytic solutions. This paper presents a first attempt to extend an up-to-date symplectic superposition method to linear buckling of side-cracked rectangular thin plates. The problems are introduced into the Hamiltonian system, and a side-cracked plate is then divided into several sub-plates that are analytically solved by the symplectic superposition method, where the symplectic eigenvalue problems are formulated, followed by the symplectic eigen expansion. Some elaborated mechanical quantities are imposed on the edges of each sub-plate, with multiple sets of constants determined by the actual boundary conditions of the cracked plate, free edge conditions along the crack, and interfacial continuity conditions among the sub-plates. The final analytic solution of a side-cracked plate is obtained by integration of the solutions of the sub-plates. Comprehensive benchmark results are tabulated and plotted for buckling loads and mode shapes of typical plates with a side crack from a simply supported edge, a clamped edge, or a free edge. The crack length effect is also investigated by the analytic solutions obtained. Due to the rigorous mathematical derivations without predetermination of solution forms, the present method provides a rational approach to exploring more analytic solutions.

Wave diffraction by multiple arbitrary shaped cracks in an infinitely extended ice sheet of finite water depth

Flexural-gravity wave interactions with multiple cracks in an ice sheet of infinite extent are considered, based on the linearized velocity potential theory for fluid flow and thin elastic plate model for an ice sheet. Both the shape and location of the cracks can be arbitrary, while an individual crack can be either open or closed. Free edge conditions are imposed at the crack. For open cracks, zero corner force conditions are further applied at the crack tips. The solution procedure starts from series expansion in the vertical direction based on separation of variables, which decomposes the three-dimensional problem into an infinite number of coupled two-dimensional problems in the horizontal plane. For each two-dimensional problem, an integral equation is derived along the cracks, with the jumps of displacement and slope of the ice sheet as unknowns in the integrand. By extending the crack in the vertical direction into the fluid domain, an artificial vertical surface is formed, on which an orthogonal inner product is adopted for the vertical modes. Through this, the edge conditions at the cracks are satisfied, together with continuous conditions of pressure and velocity on the vertical surface. The integral differential equations are solved numerically through the boundary element method together with the finite difference scheme for the derivatives along the crack. Extensive results are provided and analysed for cracks with various shapes and locations, including the jumps of displacement and slope, diffraction wave coefficient, and the scattered cross-section.

Wave energy dissipation by a floating circular flexible porous membrane in single and two-layer fluids

In this study, the impact of gravity wave on a circular elastic floating permeable membrane is investigated using linear water wave theory in both homogeneous and two-layer fluids. The matched eigenfunction expansion technique is employed to obtain an analytic solution of the boundary value problem. Further, the plane wave integral representation of Bessel and Hankel functions are applied to study the influence of porous structure in damping the far-field wave energy. In order to examine the effect of various physical parameters, heave force exerted on the membrane, deflection of the membrane, reflected and transmitted wave amplitudes, flow distribution around the structure and far-field energy dissipation are computed and analyzed for three different edge conditions such as (i) free edge, (ii) moored edge and (iii) clamped edge. The study reveals that the surface wave amplitude on the lee side of the structure decreases significantly in the presence of floating porous elastic membrane. Moreover, the membrane having clamped edge dissipates more wave energy as compared to that for moored and free edge conditions.

Mesh-adapted stress analysis of multilayered plates using a layerwise model

This paper proposes a new finite-element modelling of a recent layerwise model for multilayered plates. This layerwise model is built from a specific 3D stress-field expansion along the thickness direction and involves, in particular, interlaminar transverse shear and out-of-plane stresses as generalized stresses. Its main feature is that 3D equilibrium equations and free-edge boundary conditions are directly taken into account into the stress-based construction of the model. A dual displacement-based finite-element discretization is implemented using the FEniCS software package and a remeshing strategy is proposed based on a novel error indicator. The error indicator is built based on the 3D stress field directly deduced from the layerwise generalized stresses and compared to a reconstructed stress field based on the model generalized displacements. The proposed error indicator is shown to identify the most critical parts of a laminate structure associated with complex 3D stress fields such as boundaries or stress concentration/singularity regions (near free-edges or delamination fronts). Through the combination of thickness discretization and in-plane mesh refinement in regions of interest, the proposed framework therefore offers an attractive alternative to 3D solid finite elements for an accurate prediction of stress states in composite laminates.

Axisymmetric bending and free vibration of symmetrically laminated circular and annular plates having elastic edge constraints

Abstract To fill the gap noticed in the literature, this paper presents free vibration results of symmetrically laminated circular and annular plates having elastic edge constraints. Some static bending results have also been presented. Each layer is having cylindrical/polar orthotropy. A Differential Quadrature Method (DQM) based methodology is utilized for spatial discretization. The problem of shear-deformable laminated circular/annular plates having translational as well as rotational edge constraints is studied. By varying the edge stiffnesses, several combinations of free, simply supported, clamped and free edge conditions have been simulated. The results have been verified with the help of convergence study in terms of the number of discretization nodes and by comparison with the results of isotropic circular plates and of laminated circular/annular plates available in the literature. Some parametric studies in terms of material and geometrical variables are also reported.

Free edge stress prediction in thick laminated cylindrical shell panel subjected to bending moment

• A Galerkin based Layer-wise formulation is presented for thick composite panel subjected to bending moment. • An analytical solution is presented for governing equations of the panel considering free edge conditions. • Free edge stresses in bending of thick panel with general layer stacking is studied for the first time. • The predictions satisfy the free edge and free surface conditions. • The effect of geometrical parameters and layer stacking are investigated. A thick composite cylindrical shell panel with general layer stacking is studied to investigate the free edge and 3D stresses in the panel which is subjected to pure bending moment. To this aim, a Galerkin based layerwise formulation is presented to discretize the governing equation of the panel to ordinary differential equations. Employing a reduced displacement field for the cylindrical panel, the governing equations for thick panel are developed in terms of displacements and a set of coupled ordinary differential equations is obtained. The governing equations are solved analytically for free edge boundary conditions and applied pure bending moment. The accuracy of numerical results is examined and the distribution of interlaminar and in-plane stresses is studied. The free edge stresses are studied and the effect of radius to thickness ratio, width to thickness ratio and layer stacking on the distribution of stresses is investigated. The focus of numerical results is on the prediction of boundary layer and free edge stress distribution.

Free vibration of thin functionally graded viscoelastic open-cell foam plates on orthotropic visco-Pasternak medium

The present study deals with vibration of functionally graded viscoelastic open-cell foam plates resting on three parameters orthotropic visco-Pasternak foundation. The kinematic and constitutive relations are described by classical plate theory and separable kernels framework, respectively. Viscoelastic treatment of bulk and shear moduli of plates are modeled by standard solid and Kelvin-Voigt models. Also, nonlinear non-symmetric porosity distribution through thickness is obtained using power law and neutral surface decoupling. The integro-PDE of motion with frequency-dependent coefficients is figured out by weighted residual method and iterative numerical algorithm to obtain natural frequencies and modal loss factors. In elastic domain, frequencies are compared with those reported for thin functionally graded plates resting on isotropic Pasternak foundation while in the viscoelastic domain, complex frequencies are compared for standard solid and Kelvin-Voigt viscoelastic plates where acceptable correlation is observed. Influences of various boundary conditions including fully clamped and fully free edge conditions, aspect ratio, coefficients and orthotropy angle of medium on dynamic characteristics are scrutinized via a comprehensive parametric study which could be used as benchmark results in future studies.

Three-dimensional and free-edge hygrothermal stresses in general long sandwich plates

The hygrothermal stresses in sandwich plate with composite faces due to through the thickness gradient temperature and (or) moisture content are investigated. The layer-wise theory is employed for formulation of the problem. The formulation is derived for sandwich plate with general layer stacking, subjected to uniform and non-uniform temperature and moisture content through the thickness of the plate. The governing equations are solved for free edge conditions and 3D stresses are investigated. The out of plane stresses are obtained by equilibrium equations of elasticity and by the constitutive law and the results for especial case are compared with the predictions of a 3D finite element solution in order to study the accuracy of results. The three-dimensional stresses especially the free edge effect on the distribution of the stresses is studied in various sandwich plates and the effect of uniform and non-uniform thermal and hygroscopic loading is investigated.

AWJ machinability performance of CS/UPR composites with the effect of chemical treatment

ABSTRACTThis work focuses on the effect of chemical treatment of coconut sheath/unsaturated polyester (CS/UPR) composite on the performance of abrasive waterjet machining (AWJM). Two different chemical treatments, namely alkali (NaOH) and trichlorovinylsilane, were imposed on the CS fiber. Further, the induced compressive strength arising as a result of AWJM was studied along the radial and depth directions of the composite. Experimental results revealed significantly lower induced stress at all points compared to the ultimate stress of CS/UPR composites except the free-edge loading condition. The chemically treated composites also exhibited inconsistent results in the machining characteristics such as kerf taper angle (Ta) and surface roughness (Ra) under varying cutting conditions. However, no direct correlation was seen between interfacial adhesion and Ta and Ra of the cutting zone. The maximum decrease of 12% of Ta and 22% of Ra was found for silane-treated composites compared to the untreated ones. In addition, the composite failure mechanisms such as fiber pullout, fiber breakage, interfacial debonding, matrix failure, and voids were identified in the cutting surfaces through scanning electron microscopy analysis.