Elastic Edges Research Articles

Safety-Guaranteed Distributed Formation Control of Multi-Robot Systems Over Graphs With Rigid and Elastic Edges

Safety-Guaranteed Distributed Formation Control of Multi-Robot Systems Over Graphs With Rigid and Elastic Edges

A semi-analytical method using auxiliary sine series for vibration and sound radiation of a rectangular plate with elastic edges

This paper proposes an efficient semi-analytical method using auxiliary sine series for transverse vibration and sound radiation of a thin rectangular plate with edges elastically restrained against translation and rotation. The formulation, constructed by two-dimensional sine and/or cosine series, can approximately express the bending displacement, and calculate vibration and sound radiation under excitation of point force, arbitrary-angle plane wave, or diffuse acoustic field with acceptable accuracy. It is also applied for baffled or unbaffled conditions. A post-process program is developed to predict vibrating frequencies and modes, mean square velocity spectrum, and sound transmission loss via reduced-order integrals of radiation impedances. The method is validated by experiment and simulation results, demonstrating accurate and efficient computation using a single program for transverse vibration and sound radiation of a plate under different elastic boundary conditions and different excitations. Formulas given in this paper provide a basis for the code development on transverse vibration and sound radiation analysis of thin plates.

Dynamical characteristics of fastening of a cylindrical shell with a hemispherical shell made of graded porous power ceramic-metal under elastic boundary edges

For the first time, the dynamical assessment of the fastened hemispherical-cylindrical shell structure (FHCSS) made of porous functionally graded ceramic-metal (FGCM) materials under elastic edge conditions is carried out here. In conformity with this, three forms of pores’ distributions add the effect of the pores on the power law FGCM materials. Add-on, ten artificial springs, including six transition and four rotational springs at the start and end of the FHCSS, determine the effect of the elastic edge constraints on the system's dynamic. In addition, the influential relationships of the shell elements of the FHCSS are set up by combining the first shear deformation theory and Donnell's simplifications. Additionally, Hamilton's principle sets up the influential motion equations (IMEs) of shell elements of the FHCSS. Then, a mesh-less procedure, named the generalized differential quadrature method, is set up to discretize the IMEs, fastening equations, and edge equations of the shell elements of the FHCSS. Also, the standard eigenvalue is set up to determine the natural frequencies of the FHCSS. Finally, various novel examples are set up and solved to indicate the effect of the material values, pores, elastic boundary constraints, and geometrical appearance values on the responses of the FHCSS.

Analytic modeling and comprehensive transverse deflection analysis of elastically restrained piezoelectric actuators with silicone layer

The impacts of electro-mechanic-fluid parameters on the transverse deflection behavior of the silicone-based piezoelectric diaphragm (SPD) with translational and rotational elastic edges were investigated. The bottommost silicone layer was assumed to be an elastic plate with uniformly distributed elastic restraints along the edges. The closed-form analytical expression for SPD deflections was derived by using classical laminated plate theory based on Kirchhoff’s plate assumptions. The analytical model was validated by experimental, FE methods and the results of the other study. The deflection responses of SPD were examined according to uniform fluid pressure, electric voltage, elastic parameters, dimensions, and material properties.

First-principles calculations to investigate structural, electronic and optical properties of two-dimensional ZnIn2S4

Based on density functional theory (DFT), we considered a two-dimension material ZnIn2S4 with potential p-type transparent conducting performance. The crystal structures, elastic, electronic properties and band edges of 2D ZnIn2S4 are investigated. The calculated density of states and charge distributions show that substituting nitrogen atom for sulfur atom in 2D ZnIn2S4 is beneficial to the enhancement of orbitals hybridization, resulting in relative lower hole effective masses and thus facilitate the hole mobility. Moreover, the optical properties involving dielectric function, reflectivity, absorption coefficients, transmittance are shown and analyzed. The obtained results lead to a conclusion that ZnIn2S3.89N0.11 is a promising p-type transparent conducting material and expected to apply in practice.

Exponential and polynomial stability results for networks of elastic and thermo-elastic rods

<p style='text-indent:20px;'>In this paper, we investigate a network of elastic and thermo-elastic materials. On each thermo-elastic edge, we consider two coupled wave equations such that one of them is damped via a coupling with a heat equation. On each elastic edge (undamped), we consider two coupled conservative wave equations. Under some conditions, we prove that the thermal damping is enough to stabilize the whole system. If the two waves propagate with the same speed on each thermo-elastic edge, we show that the energy of the system decays exponentially. Otherwise, a polynomial energy decay is attained. Finally, we present some other boundary conditions and show that under sufficient conditions on the lengths of some elastic edges, the energy of the system decays exponentially on some particular networks similar to the ones considered in [<xref ref-type="bibr" rid="b18">18</xref>].</p>

Study on the Dynamic Performance of Locally Resonant Plates with Elastic Unit Cell Edges

A Floquet–Bloch approach is employed to demonstrate the stop bands for an infinite locally resonant plate. In addition, the effects of the connection stiffness of the unit cells on the band gap and dynamic performance of a locally resonant plate are analysed. The results show that the degree of inhibition of elastic waves in the band gaps increases rapidly when the connection stiffness of the unit cells increases within the scope of the transition stage stiffness. However, outside of the range of transition stage stiffness, the degree of inhibition of elastic waves in the band gaps basically remains unchanged. This discovery widens the application scope for vibration and noise control using locally resonant plates.

On the duality of space trusses and plate structures of rigid plates and elastic edges

Dualities have been known to map space trusses and plate structures to each other since the 1980s. Yet the computational similarity of the two has not been used to solve the unfamiliar plate structure with the methods of the well-known truss. This article gives a method to find the forces and displacements of a plate structure with rigid plates and elastic edges, using a dual truss. The plates are assumed to be rigid in their respective planes only and deformable otherwise. The method provided is applicable for both statically determinate and indeterminate structures, subjected to both statical and kinematical loads.

Vibration and damping analysis of cylindrical shell treated with viscoelastic damping materials under elastic boundary conditions via a unified Rayleigh-Ritz method

The present article presents an improved unified approach of Rayleigh-Ritz method to investigate the vibration and damping behavior of thin short cylindrical shell with viscoelastic damping materials treatment under arbitrary elastic edges. In the frame of the Donnell's thin shell application, the governing equation of dynamic of shell treated with the constrained layer damping (CLD) is established, in which the effects of shear stress due to viscoelastic damping material layer are considered. Then, the formulation of the CLD shell with traditional boundary supports is derived according to the Rayleigh-Ritz method being unified with expanding a serious of orthogonal polynomials as the admissible displacement functions. Next, a set of artificial springs are imported on the free edges of the shell to simulate the possible elastic supports of the CLD shell. Further, the convergence of the presented method in dealing with CLD shell with various boundary supports are confirmed by presenting an experiment and some numerical comparisons. Finally, some further numerical investigations are carried out to illustrate the influence of the variations of boundaries stiffness values on the vibration frequencies and model loss factors of constrain layer damping shell.

Membrane- and plate-type acoustic metamaterials with elastic unit cell edges

Membrane- and plate-type acoustic metamaterials are thin membranes or plates consisting of periodic unit cells with small added masses. It has been shown in numerous studies, that these metamaterials exhibit tunable anti-resonances with transmission loss values much higher than the corresponding mass-law. However, in most studies it is assumed that the unit cell edges (or grid) of the metamaterial are fixed. This idealised boundary condition is not applicable to real world applications in noise control. Therefore, the acoustic performance of these metamaterials under more realistic circumstances, where the grid structure cannot be perfectly rigid, can be expected to be different. In this contribution, the vibro-acoustic behavior of membrane- and plate-type acoustic metamaterials with a non-rigid grid is investigated. For this purpose, an efficient analytical model is developed to predict the eigenmodes and sound transmission loss of such metamaterials. In this model, elastic unit cell edges are modelled using a grid of Euler-Bernoulli beams and the sound transmission loss can be calculated for oblique incidence. A comparison to FEM simulations shows that the proposed model yields the same results but with a considerably reduced computational effort. The analytical model is then used to discuss the vibro-acoustic properties of the metamaterial, with particular focus on the influence of the mass and stiffness of the grid beams. It is shown that even when a non-rigid grid and diffuse incident sound fields are considered, the transmission loss of the metamaterial exhibits anti-resonances with remarkably high noise reduction values. These anti-resonances can be tuned by choosing appropriate values of the grid parameters. Furthermore, the formation of band gaps in the propagation of bending waves is discussed by investigating the dispersion curves of the metamaterial. The results in this contribution show that membrane- and plate-type acoustic metamaterials can still efficiently reduce low-frequency noise, even when the unit cell edges are not assumed to be fixed. This important finding and the proposed analytical modal can support the utilization of these metamaterials in practical noise control applications.

Dynamic stability of an axially moving paper board with added subsystems

Paper board with bending stiffness is usually used as the substrates on cigarette package printing industry. The vibration of these paper boards in high speed affects the printing precision. The dynamic characteristics and stability of moving paper board with finite interior elastic point supports and elastic edges restrained are investigated. First, the energy function of the system is established by using the extended Hamilton’s principle; second, the dimensionless equations of motion for the moving paper board are obtained using the element-free Galerkin method. The equations of motion and the eigenvalue equations of the system are established. The relationship between the first three complex frequencies of the system and the moving speed is then obtained by the numerical calculation. The effects of the elastic point supports, the elastically restrained edges, and the dimensionless speed of the motion on the dynamic stability of the paper board are analyzed. The critical speed when the paper board is in a stable state under different conditions is obtained. The results improve the dynamic stability of the paper board in printing process and provide the theoretical basis for the optimization of printing equipment.

The influence of structural arrangement on long-duration blast response of annealed glazing

This paper investigates the influence of structural arrangement on long-duration blast loaded annealed glazing via variable thickness, area, aspect ratio and edge support conditions. Initially, the findings of eighteen full-scale air-blast trials employing 33 annealed glazing panels are reported where it is demonstrated that fracture mode and fragmentation are a strong function of edge supports. Rigidly clamped edges are shown to induce localised stress transmission, producing significant cracking and small fragments. In contrast, elastic edges are shown to produce large, angular fragments, demonstrating the importance of accurately modelling edge conditions when analysing fragment hazard. Quantification of peak centre panel deflection and breakage time is then presented where variable results indicate the influence of edge supports and aspect ratio to be dependent on proximity to the threshold area as a function of glazing thickness. An initial Applied Element Method (AEM) analysis is then employed to model the influence of structural arrangement on long-duration blast-loaded annealed glazing. AEM models are shown to reasonably predict glazing fragmentation behaviour, breakage time and peak panel deflection at the moment of breakage. Thus indicating AEM's potential suitability to provide a predictive capacity for annealed glazing response during long-duration blast.

A Design Method for a New Type of Cylindrical Roller Bearing Based on Edge Effect

The elastic composite cylindrical roller bearing is a new type of bearing designed with polytetrafluoroethylene filling in a deep hole hollow roller. This design can improve the stress concentration and also performance of the bearing. A study was conducted to parameterize the deep hole structure to obtain its design variables, the angle a and radius c by studying the influence of the design on stress concentration in elastic composite cylindrical roller bearing edge; to determine the BP neural network sample data using orthogonal test and finite element methods; to establish mapping relationship between the design variables and the maximum stress by BP neural network learning algorithm and to obtain the objective function required for structural optimization of genetic algorithm. The study attempts to optimize, search and calculate the most fitting structural parameters of elastic composite cylindrical roller by genetic algorithm with NU318E bearing as the optimization object and obtain the values of optimal design variables as a = 48.68° and c=9.67mm. The work also includes minimization of the comprehensive value of the maximum contact stress and the maximum equivalent stress of the edge and elliptic zones of elastic composite cylindrical roller after optimizing and increasing the contact fatigue service and bearing capacity of the bearing. The optimization procedure and method presented in this paper can serve as a useful reference to the optimization of structure for other elastic composite cylindrical roller edges.

Buckling analysis of laminated plate structures with elastic edges using a novel semi-analytical finite strip method

A novel semi-analytical finite strip method is presented for buckling analysis of composite plate structures with boundary edges elastically supported. A set of unique Fourier series functions is introduced to represent the longitudinal variation of deflection along a strip, and they are capable of handling elastic edges with translational and rotational spring supports. The proposed hybrid method overcomes limitation of classical finite strip method only capable of handling simple end boundary conditions of structures, and it avoids the ill-conditioning when a set of standard Fourier series functions is used for buckling analysis. Accuracy and validity of the proposed method are demonstrated by the convergence and comparative studies in comparison with the numerical finite element method. As an example, the present method is applied to buckling analysis of a composite Z-stiffened panel under pure shear, and its capability and efficiency of treating different edge conditions in the panel skin and stiffeners are illustrated.

Radiation of waves by a cylinder submerged in water with ice floe or polynya

The problems of radiation (sway, heave and roll) of surface and flexural-gravity waves by a submerged cylinder are investigated for two configurations, concerning; (i) a freely floating finite elastic plate modelling an ice floe, and (ii) two semi-infinite elastic plates separated by a region of open water (polynya). The fluid of finite depth is assumed to be inviscid, incompressible and homogeneous. The linear two-dimensional problems are formulated within the framework of potential-flow theory. The method of mass sources distributed along the body contour is applied. The corresponding Green’s function is obtained by using matched eigenfunction expansions. The radiation load (added mass and damping coefficients) and the amplitudes of vertical displacements of the free surface and elastic plates are calculated. Reciprocity relations which demonstrate both symmetry of the radiation load coefficients and the relation of damping coefficients with the far-field form of the radiation potentials are found. It is shown that wave motion essentially depends on the position of the submerged body relative to the elastic plate edges. The results of solving the radiation problem are compared with the solution of the diffraction problem. It is noted that resonant frequencies in the radiation problem correlate with those frequencies at which the reflection coefficient in the diffraction problem has a local minimum.

Static and Dynamic Analysis of Annular Sector Plates Subjected to Arbitrary Boundary Conditions

In this investigation, an improved Fourier series method (IFSM) is employed to predict the static and dynamic characteristics of annular sector plates with arbitrary boundary conditions. Regardless of boundary supports, the displacement function is invariantly expressed as a modified two-dimensional Fourier series containing sine and cosine function. It is capable of dealing with the possible discontinuities at elastic boundary edges. The unknown Fourier coefficients are treated as generalized coordinates, and determined using Rayleigh-Ritz method. Unlike most of the existing solution techniques, the current approach can be universally applied to a variety of edge restraints including all classical cases and their combinations. The accuracy and reliability of the current method are fully illustrated through all the numerical examples.

The Damping Forced Vibration of Rectangular Stiffened Plates with Elastic Boundary Edges Including Boundary Damping

The paper proposes an analytical-numerical method for damping forced vibration problem of the rectangular stiffened plates with elastic boundary restraints. By enforcing applicable continuity conditions between plate and beams, coupled equations of beams-plate system are established. The displacement function is expressed as a modified two-dimensional Fourier series, which converts the differential equations of plate-beam systems into linear algebraic equations. Furthermore, Rayleigh’s proportional damping is introduced into beams-plate system so that damping parameters of stiffened plate can be inserted into vibration equations. It is derived that the present method demonstrates good agreement with standard finite element analysis. In subsequent analysis, it can be found that the boundary damping can reduce vibration energy of stiffened plate to same extent.

Free vibration of moderately thick antisymmetric laminated annular sector plates with elastic edge constraints

Abstract This study presents, for the first time, free vibration results of laminated sector plates having elastic edges. Each layer is cylindrically orthotropic. A differential quadrature method (DQM) based formulation is used for studying the problem of shear-deformable laminated sector plates having translational as well as rotational edge constraints. By varying the edge stiffnesses, several combinations of simply supported and clamped edge conditions are simulated. The results are further validated by comparison with the results of laminated square plates (with elastic edges) and of laminated sector plates (without elastic edges) available in the literature.

A novel approach to fixture layout optimization on maximizing dynamic machinability

In the aerospace industry, the reasonable layout of fixture can efficiently suppresses machining vibration of thin-walled aerospace structure during machining. Based on the analysis of typical structural components encountered in the aerospace industry, a general frame-structure workpiece with fixture constraints can be equivalent as Mindlin plates with simultaneous elastic edges and internal supports. On basis of the equivalent models, the powerful pb-2 Ritz method defined by the product of a two-dimensional polynomial and basic functions can be introduced to be taken as trial functions. Substituting displacement functions into energy functional and minimizing total energy by differentiation leads to eigenfrequency equations of the workpiece–fixture system. Consequently, a novel nonlinear programming problem based on the frequency sensitivity can be built to optimize the layout of fixture supports to maximize the fundamental nature frequency of the workpiece–fixture system. The feasibility of the proposed approach is validated by a machining case.

Exponential stability of a network of elastic and thermoelastic materials

In this paper, we study the stability of a network of some elastic and thermoelastic edges. We establish the exponential decay rate of the whole system. Copyright © 2012 John Wiley & Sons, Ltd.