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Introduction: 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. Methods: 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. Results: 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). Conclusions: 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. [ABSTRACT FROM AUTHOR]

In the past few decades, plates made of laminated composite materials have attracted the attention of many engineers and designers due to their favorable properties of high strength to weight ratio and stiffness. The behavior of thin laminated plates having a general stacking sequence is governed by three coupled partial differential equations, derived based on the "Kirchhoff plate theory". Analytical solutions of these equations have been obtained for cases involving simple geometries and boundary conditions. One of the important and practical boundary conditions which is not fully addressed yet is the corner supported plate. The purpose of this study is to propose a Ritz method-based approach for obtaining an accurate solution for a uniformly loaded corner supported thin laminated composite plate having a general stacking sequence. In the proposed approach, Ritz method is cast in a matrix form and an automated symbolic integration procedure is used to allow the use of as many approximating polynomial terms as required for convergence. The accuracy of the proposed method is validated by comparing the obtained results against those of finite element method solutions generated using the commercial software ABAQUS. [ABSTRACT FROM AUTHOR]

Background: The simple shear experiment is widely used for the calibration of plasticity models due to straightforward post processing. The specimen can be as simple as a rectangular strip of sheet metal, but the maximum strain is limited by early initiation of fractures from the free edges. Avoiding this drawback has been a major motivation for the development of new specimens with optimized edge geometries or the in-plane torsion test, but at the cost of a more complex analysis of the test and often a reduction of the gauge section. Objective: The objective of the present work is to overcome the initiation of fracture from the free edges during simple shear experiments. Our goal is to double the achievable maximum strain, while keeping the size of the specimen and the post processing simplicity of a standard simple shear test. Methods: A sequential single shear test is proposed, consisting of several two steps sequences on a notched geometry. First, an interrupted shear test is performed up to a specified displacement value. Then, the damaged free edges of the specimen are removed through milling. The specimen is then ready for the following sequence of shear and re-machining. Results: Experiments are performed on three engineering materials, with up to five loading-machining sequences. The maximum attained effective strain is up to two times the one reached during a monotonic experiment. Numerical simulations are used to validate the shear stress and strain calculations from experimental measurements. Practical recommendations are derived for the choice of the displacement step size and Digital Image Correlation analysis. Conclusion: It is found that the maximum strain attained before the undesired failure of the specimen during simple shear test can be substantially extended through repeated re-machining of the specimen boundaries, enabling behavior identification at larger strains. [ABSTRACT FROM AUTHOR]

A new method for calculating the actuator influence functions of a rectangular deformable mirror with free edges in a model of concentrated loads is presented. The deflection function of the mirror is sought in the form of the Fourier series as an expansion into modes of natural vibrations of a thin rectangular plate with free edges. The vibration modes are calculated numerically using the finite element method. The resulting modes are substituted into the expressions for calculating the coefficients of the terms of the series used (partial sum). This solution is verified by comparing with the calculation of the influence functions fully based on the finite element method in ANSYS software. The result can be used for selection and optimization of the scheme for the actuator layout of rectangular and square deformable mirrors used in of adaptive optics problems. [ABSTRACT FROM AUTHOR]

This paper investigates the classical buckling problem of rectangular thin plates with two opposite edges free and others rotationally restrained by the finite Fourier integral transform method. The rotationally restrained edges are typically practical boundary conditions in many engineering structures, such as bridge decks. However, these non‐classic edges bring mathematical difficulties in solving boundary value problems of governing partial differential equations of plate. Based on the integral transform theory, the title problem is transformed into solving regular linear algebraic simultaneous equations, which provides a more rational and theoretical solution process than traditional inverse/semi‐inverse approaches. The acquired comprehensive results of critical buckling load factors and mode shapes are in excellent agreement with the ones obtained by finite element method, which verifies the validity and accuracy of the present approach. In addition, classical boundary conditions, such as simply supported and clamped edges, can be investigated by choosing different rotational fixity factors. Furthermore, the features of the employed method that no preselection of trial function and the generality for various boundary conditions enable one to analytically solve static problems for moderately thick plates and thick plates. [ABSTRACT FROM AUTHOR]

This paper develops a Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered monoclinic angle-ply laminates under the combined action of extension, bending, and torsion. The present solution satisfies the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the four edge surfaces of the rectangular section, and the interfacial continuity conditions in multilayered laminates. The proposed method only requires the solutions of matrix and eigen equations, regardless of the number or lamination of the layers. The finite element analyses are used to validate the accuracy of the analysis. The analytical solution and the numerical solutions are in excellent agreement. [ABSTRACT FROM AUTHOR]

In this paper, the Ritz method is developed for the analysis of thin rectangular orthotropic plates undergoing large deflection. The trial functions approximating the plate lateral and in-plane displacements are represented by simple polynomials. The nonlinear algebraic equations resulting from the application of the concept of minimum potential energy of the orthotropic plate are cast in a matrix form. The developed matrix form equations are then implemented in a Mathematica code that allows for the automation of the solution for an arbitrary number of the trial polynomials. The developed code is tested through several numerical examples involving rectangular plates with different aspect ratios and boundary conditions. The results of all examples demonstrate the efficiency and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

In this study, a Ritz method-based solution of the corner supported thin rectangular plate under different symmetrical loading is presented. The load can be uniformly distributed, symmetrically applied point, patched, or line loads or any type of load applied symmetrically about the plate axes. A two-dimensional polynomial that satisfies the essential boundary conditions (zero deflection at the corners) is proposed to approximate the deflection of the plate. The results are found to be in an excellent agreement with the literature and finite element results. For cases of point loads, however, the proposed polynomial as well as the previously proposed methods in the literature are not capable of capturing the singularity under the point loads. As a remedy to this problem, the proposed polynomial expression is strengthened with the fundamental solution. The strengthened polynomial is found to be able to capture the singularity as well as to accurately satisfy the natural boundary conditions at the free edges. [ABSTRACT FROM AUTHOR]

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications. [ABSTRACT FROM AUTHOR]

The problem of flexural characteristics of rectangular orthotropic thin plates with opposite rotationally restrained and free edges subjected to arbitrary transverse loads is investigated in present study. By introducing a rotational fixity factor to simulate the elastic rotation restraint at plate edges, the finite integral transform method is employed to obtain exact analytical solution of the problem. Numerical solutions for rectangular plates with various aspect ratios and edge flexibility are investigated and compared to the results reported in previous research. The accuracy and convergence of the present formulation are assessed by comparing with previously reported results. The excellent agreement on the results between the proposed method and previous studies indicates that the proposed method is accurate and effective. [ABSTRACT FROM AUTHOR]

Many types of engineering structures can be effectively modelled as orthotropic plates with opposite free edges such as bridge decks. The other two edges, however, are usually treated as simply supported or fully clamped in current design practice, although the practical boundary conditions are intermediate between these two limiting cases. Frequent applications of orthotropic plates in structures have generated the need for a better understanding of the dynamic behaviour of orthotropic plates with non-classical boundary conditions. In the present study, the transverse vibration of rectangular orthotropic plates with two opposite edges rotationally restrained with the remaining others free was studied by applying the method of finite integral transforms. A new alternative formulation was developed for vibration analysis, which provides much easier solutions. Exact series solutions were derived, and the excellent accuracy and efficiency of the method are demonstrated through considerable numerical studies and comparisons with existing results. Some new results have been presented. In addition, the effect of different degrees of rotational restraints on the mode shapes was also demonstrated. The present analytical method is straightforward and systematic, and the derived characteristic equation for eigenvalues can be easily adapted for broad applications.

The paper proposes the first 18 vibration modes for plates, and the first 14 vibration modes for cylinders and cylindrical shells. All the edges of these structures are simply supported and the free frequencies are calculated using an exact three-dimensional shell model. A comparison is proposed using two different numerical models such as a classical two-dimensional finite element model and a refined two-dimensional generalized differential quadrature model. The 3D exact model gives all types of vibration modes, when the four edges are simply supported, changing the imposed half-wave numbers m and n in the two in-plane directions α and β . Some of these modes have one of the two half-wave numbers equals zero. When this condition is simultaneously combined with the condition of transverse displacement different from zero, the resulting vibration mode is defined as cylindrical bending mode. The cylindrical bending case has all the derivatives made in the direction where m =0 or n =0 equal zero. This feature means that the vibrational behavior does not change along this particular direction. The numerical models with the simply supported boundary conditions for all the edges do not achieve these results. These cylindrical bending numerical results are obtained modifying the boundary conditions. Proposed results will demonstrate the validity of this idea and how to modify the mathematical models in order to obtain and improve the cylindrical bending solutions. [ABSTRACT FROM AUTHOR]

A Hamiltonian state space approach for analytic determination of deformation and stress fields in multilayered cross-ply symmetric laminates under extension and bending is presented, in which the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the bounding planes of the rectangular section, and the interfacial continuity conditions in multilayered laminates are satisfied, regardless of the number of layers. The solutions serve as useful benchmarks for numerical modeling and material characterization of composite laminates. [ABSTRACT FROM AUTHOR]

The Differential Quadrature Method (DMQ) is one of the-most powerful approximation methods for analyzing the free vibration of rectangular plates. It is easy to use and straightforward to implement. However, in spite of its many advantages, the conventional DQM has some limitations in determining the natural frequencies of rectangular plates involving free corners. This is because it is very difficult to implement the free corner boundary condition in conventional DQM. As a result, the method may exhibit some convergence problems and this may lead to erroneous and oscillatory results for natural frequencies of rectangular plates involving free corners. To overcome this difficulty, this paper presents a simple DQM formulation in which ail the natural boundary conditions, including the free corner boundary condition, are implemented in an easy manner. Its accuracy and efficiency are demonstrated through the vibration analysis of rectangular plates with different combinations of free edges and free corners. Numerical results prove that the proposed method can produce much better accuracy than the conventional DQM while exhibiting a monotonic convergence behavior with respect to the number of sampling points, furthermore, unlike the conventional DQM, solutions of the proposed method are not very sensitive to the sampling point distribution. [ABSTRACT FROM AUTHOR]

In this paper, we address the problem of the origin of in-plane stresses in continuous, two-dimensional high-speed webs. In the case of thin, slender webs, a typical modelling approach is the application of a stationary in-plane model, without considering the effects of the in-plane velocity field. However, for high-speed webs this approach is insufficient, because it neglects the coupling between the total material velocity and the deformation experienced by the material. By using a mixed Lagrange–Euler approach in model derivation, the solid continuum problem can be transformed into a solid continuum flow problem. Mass conservation in the flow problem and the behaviour of free edges in the two-dimensional case are both seen to influence the velocity field. We concentrate on solutions of a steady-state type, and study briefly the coupled nature of material viscoelasticity and transport velocity in one dimension. Analytical solutions of the one-dimensional equation are presented with both elastic and viscoelastic material models. The two-dimensional elastic problem is solved numerically using a nonlinear finite element procedure. An important new fundamental feature of the model is the coupling of the driving velocity field to the deformation of the material, while accounting for small deformations of the free edges. The results indicate that inertial effects produce an additional contribution to elastic contraction in unsupported, free webs. [ABSTRACT FROM AUTHOR]

The interlaminar stresses are confined to a region near the free edge. Therefore, the laminate stacking sequence and the free edge finishing are some of the factors that affect the strength of the laminate and limit its life. The use of molded edges eliminates the need for trimming and machining the laminates edges thus improving productivity. However, this fabrication technique may have a detrimental effect on the laminate strength for certain stacking sequences. This effect in the presence of moisture has not been characterized. This work presents the results of a comparative study of the resistance to delamination of laminates with machined edges and molded edges. Additionally, two environmental conditions were considered: dry laminates and laminates saturated with moisture. The tensile strength of the laminates were measured and micrographs were used to analyze the microstructure of the laminates near the free edges. It is concluded that the mechanical properties of advanced composites depend on the environmental conditions and the fabrication techniques used to produce the laminates. Therefore, it is necessary to account for these factors when experimentally determining the design allowables.

Abstract: Large-amplitude (geometrically nonlinear) forced vibrations of completely free sandwich rectangular plates are investigated experimentally. Harmonic excitation is applied by using an electro-dynamic exciter and the plate vibration is measured by using laser Doppler vibrometers. A scanning laser Doppler vibrometer is used for experimental modal analysis since it provides non-contact vibration measurements with very high spatial resolution. The large-amplitude vibration experiments are carried out by using a single point laser Doppler vibrometer and a stepped-sine testing procedure. The nonlinear frequency response curves are obtained by increasing and decreasing the excitation frequency in very small steps at specific force amplitudes controlled in a closed-loop. The experimental results are compared to numerical simulations obtained by reduced-order models and show very good agreement. The nonlinear damping is experimentally obtained as a function of the vibration amplitude. [Copyright &y& Elsevier]

Nonlinear vibrations of completely free laminated and sandwich rectangular plates are investigated for the first time. The equations of motion are obtained via multi-modal energy approach based on Lagrange equations and by using classical and higher-order shear deformation theories with von Kármán type nonlinearities. The numerical analysis is carried out in two steps. First, the plate displacements and rotations are expanded in terms of Chebyshev polynomials and a linear analysis is performed to obtain the natural frequencies and modes of vibration. Then, the energy functional is discretized by using the natural modes of vibration and a system of nonlinear ordinary differential equations with quadratic and cubic nonlinear terms is obtained. A code based on pseudo arc-length continuation and collocation scheme is used for bifurcation analysis and the near resonance nonlinear vibrations are studied. The frequency-response curves, time histories and phase space diagrams are presented. [ABSTRACT FROM AUTHOR]

Abstract: Recently, the present authors proposed a simple mixed Ritz-differential quadrature (DQ) methodology for free and forced vibration, and buckling analysis of rectangular plates. In this technique, the Ritz method is first used to discretize the spatial partial derivatives with respect to a coordinate direction of the plate. The DQ method is then employed to analogize the resulting system of ordinary or partial differential equations. The mixed method was shown to work well for vibration and buckling problems of rectangular plates with simple boundary conditions. But, due to the use of conventional Ritz method in one coordinate direction of the plate, the geometric boundary conditions of the problem can only be satisfied in that direction. Therefore, the conventional mixed Ritz-DQ methodology may encounter difficulties when dealing with rectangular plates involving adjacent free edges and skew plates. To overcome this difficulty, this paper presents a modified mixed Ritz-DQ formulation in which all the natural boundary conditions are exactly implemented. The versatility, accuracy and efficiency of the proposed method for free vibration analysis of thick rectangular and skew plates are tested against other solution procedures. It is revealed that the proposed method can produce highly accurate solutions for the natural frequencies of thick rectangular plates involving adjacent free edges and skew plates using a small number Ritz terms and DQ sampling points. [Copyright &y& Elsevier]

A simple and accurate mixed finite element-differential quadrature formulation is proposed to study the free vibration of rectangular and skew Mindlin plates with general boundary conditions. In this technique, the original plate problem is reduced to two simple bar (or beam) problems. One bar problem is discretized by the finite element method (FEM) while the other by the differential quadrature method (DQM). The mixed method, in general, combines the geometry flexibility of the FEM and high accuracy and efficiency of the DQM and its implementation is more easier and simpler than the case where the FEM or DQM is fully applied to the problem. Moreover, the proposed formulation is free of the shear locking phenomenon that may be encountered in the conventional shear deformable finite elements. A simple scheme is also presented to exactly implement the mixed natural boundary conditions of the plate problem. The versatility, accuracy and efficiency of the proposed method for free vibration analysis of rectangular and skew Mindlin plates are tested against other solution procedures. It is revealed that the proposed method can produce highly accurate solutions for the natural frequencies of rectangular and skew Mindlin plates with general boundary conditions. [ABSTRACT FROM AUTHOR]

The stability of a rectangular plate under two different compressive loading scenarios applied to the free edges of the plate has been investigated. It is assumed that under the applied load the edges have translational and rotational degrees of freedom. In the first case, a conservative external force, that is assumed to have a fixed direction with respect to the deforming body, is applied while in the second case the load is directed to be tangential to the deflected middle surface, the follower force. It is found that for a sufficiently narrow plate the buckling is localized in the neighborhood of free edges as the conservative load is applied. A similar phenomenon is known for the case when a plate is uniformly compressed along hinged edges. In the case of a follower force, the static formulation of the problem leads to the conclusion that localized buckling does not exist. However, depending on the parameters of the problem, the usual (global) buckling is predicted. [ABSTRACT FROM AUTHOR]

Capability of continuum damage mechanics (CDM) to predict the damage mechanism evolution of composite laminates has rarely been carried out, and most of the previous CDM works mainly focused on the overall response of the laminates. In this paper, progressive damage and overall response of the composite laminates under quasi-static, monotonic increasing loading are investigated using three-dimensional (3D) CDM implementation in a finite element method that is based on the layer-wise laminate plate theory. In the damage formulation, each composite ply is treated as a homogeneous orthotropic material exhibiting orthotropic damage in the form of distributed microscopic cracks that are normal to the three principal material directions. The progressive damage of different angle-ply composite laminates under quasi-static loading that exhibit free edge effects is investigated. It is shown that using CDM global behaviour and various damage mechanisms affected by the complex nature of free edges can be qualitatively well predicted. [ABSTRACT FROM AUTHOR]

Abstract: A class of problems of composite laminates and functionally graded materials (FGM) under extension, twisting, and bending is formulated in the state space setting. A solution approach for exact analysis of the deformation and stress fields in the media is developed. Exact solutions for torsion of cross-ply laminates and certain FGM are derived, which satisfy exactly the equations of anisotropic elasticity, the end conditions, the traction-free boundary conditions on the bounding planes of the rectangular section, and the interfacial continuity conditions in multilayered composite laminates, regardless of the number of layers. The solutions serve as useful benchmarks for numerical modeling and material characterization of composite laminates and FGM. [Copyright &y& Elsevier]

A two-dimensional linearized problem on plane buckling modes (BMs) of a rectangular plate with free edges, made of an elastic orthotropic material, underbiaxial tension-compression is considered. With the use of double trigonometric basis functions, displacement functions exactly satisfying all static boundary condition on plate edges are constructed. It is shown that the exact analytic solutions found describe only the pure shear BMs, and if the normal stress in one direction is assumed equal to zero, an analog of the solution given by the kinematic Timoshenko model can be obtained. Upon performing the limit passage to the zero harmonic in the displacement functions of one of the directions, the solution to the problem of biaxial compression can be obtained by equating the Poisson ratio to zero; in the case of uniaxial compression, this solution exactly agrees with that following from the classical Bernoulli-Euler model. [ABSTRACT FROM AUTHOR]

Abstract: The Reissner–Mindlin plate model in presence of free boundary conditions is considered. It is known that in this case the solution can suffer, for small thickness, from some boundary layer effects that reduce the regularity of the solution, in particular of the rotations and shear strains. This causes a loss of convergence order in the numerical approximation. For this reason a new model that modifies the free boundary conditions is considered. The approximation of this new model by means of an element of low degree of the partial selective reduced integration family has been analyzed both from the theoretical and the numerical point of view. Some numerical results have been presented showing the performance of this element when applied to free plates. [Copyright &y& Elsevier]

The linear problem on plane modes of free oscillations of a rectangular orthotropic plate with free unloaded edges is considered. A procedure for constructing displacement functions exactly satisfying the boundary conditions, with the use of double-trigonometric basis functions, is offered. Exact and approximated analytical solutions to the problem formulated are found, which presumably describe all plane modes of free oscillations of the plate in the class of the functions indicated. It is established that, in the use of variational principles, the variations of required functions must be considered not only arbitrary, but also mutually independent. Therefore, the solutions constructed give physically reliable results for the frequencies and modes of free oscillations only if the problem is stated in the form of Bubnov variation equations, which depend on the structure of displacement functions. It is found that the exact analytical solutions of the problem correspond to oscillation modes without shear strains. It is shown that it is possible to select such solutions from them which correspond to trigonometric functions with a zero harmonic in one direction. These solutions describe only flexural oscillation modes of the plate, and the results obtained are equivalent to those given by the classical Kirchhoff model known in the theory of rods, plates, and shells. [ABSTRACT FROM AUTHOR]

The method of superposition is exploited to obtain accurate analytical type solutions for resonant frequencies and mode shapes of completely free symmetric cross-ply laminated rectangular plates. Verification tests are performed by comparing computed eigenvalues with known eigenvalues for the special case of thin orthotropic plates. Results of an analytical study of the free vibration behaviour of a typical symmetric cross-ply laminated completely free plate are tabulated. These results provide valuable checkpoints against which future researchers can compare their findings. This appears to be the first analytical type free vibration solution made available for the completely free laminated plate of this type. [Copyright &y& Elsevier]

The uniaxial compressive behavior of fiber-reinforced polymer (FRP) composites is investigated in this paper. In the present study, the analytical model developed by the authors in previous studies is applied to investigate the effect of free edges and interfacial debonding upon the compressive strength of unidirectional composites. Results show that interfacial debonding has a great effect on the compressive strength, with fiber microbuckling strength falling to zero for the extreme case of complete fiber/matrix debonding with a frictionless interface. It is also found that free edges significantly affect the microbuckling behavior of unidirectional FRP composites by lowering the compressive strength of fibers located along a free edge as compared to that of inner fibers. Furthermore, the model indicates that the compressive strength of surface fibers can be strengthened by increasing the thickness of the outer matrix coating to the extent of theoretically being twice as high as the inner fibers. This finding may have significant practical implications for the strengthening of composite structures under compression by suppressing kink band initiation at free edges of the structure. [ABSTRACT FROM PUBLISHER]

For the first time, the double half-Sinusoidal series is adopted as integral kernel to construct integral transform pair for new precise vibration analysis of orthotropic rectangular thin plates, supported with two adjacent edges rotationally-restrained and the other edges are free. Impose the defined single/double transforms on both the vibration governing partial differential equation (PDE) and some of the boundaries investigated, which gives the Fourier coefficient for the deflection expressed by some specific unknown constants. Utilizing the inverse formular to satify the remaining boundaries leads to a set of linear algebraic simultaneous equations, which yields the solutions of the natural frequency parameter and the associated mode shapes. Moreover, plates under classical boundary conditions also can be investigated via changing the rotating fixed coefficients introduced. Finally, more than 500 comprehensive analytical solutions were well validated by numerical results presented by finite element method (FEM), which can be treated as new reference results for further studies. Since its straightforward and rational solution procedure, the presented approach is promising to be further extended to solve more complicated boundary value problems (BVPs) of plates. [ABSTRACT FROM AUTHOR]