The differential quadrature method for irregular domains and application to plate vibration

By its very basis, the differential quadrature method may be applied to domains having boundaries oriented along the coordinate axes. In this paper, it is shown that quadrature rules may also be formulated for irregular domains using the natural-to-Cartesian geometric mapping technique. The application of the technique is demonstrated through the vibration analysis of thin isotropic plates of general quadrilateral and sectorial planforms.     

Vibration analysis of corrugated Reissner–Mindlin plates using a mesh-free Galerkin method

A mesh-free Galerkin method for the free vibration analysis of unstiffened and stiffened corrugated plates is introduced in this paper, in which the corrugated plates are simulated with an equivalent orthotropic plate model. To obtain the corresponding equivalent elastic properties for the model, a constant curvature state is applied to the corrugated sheet. The stiffened corrugated plates are treated as composite structures of equivalent orthotropic plates and beams, and the strain energies of the plates and beams are added up by the imposition of displacement compatible conditions between the plate and the beams. The stiffness matrix of the whole structure is then derived. The proposed method is superior to the finite element methods (FEMs) because no mesh is needed, and thus stiffeners (beams) do not need to be placed along the mesh lines and the necessity of remeshing when the positions of the stiffeners change is avoided. To demonstrate the accuracy and convergence of the proposed method, several numerical examples are analyzed both with the proposed method and the finite element commercial software ANSYS. Examples from other research are also employed. A good agreement between the results for the proposed method, the results of the ANSYS analysis, and the results from other research is observed. Both sinusoidally and trapezoidally corrugated plates are studied.     

Natural frequencies of symmetrically laminated elliptical and circular plates

Elliptical and circular fibre reinforced composite plates are important structural elements in modern engineering structures. Vibration analysis of these elements are of interest to structural designers. The present paper deals with the free transverse vibration analysis of symmetrically laminated solid and annular elliptic and circular plates with several complicating effects.The approach developed is based on the Rayleigh–Ritz method where the deflection of the plate is approximated by a general shape function of polynomial type.The analysis includes several complicating effects, such as the presence of an internal hole, an internal ring support, several concentrated masses and the boundary elastically restrained against rotation and translation.Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for cross-ply and angle-ply elliptical and circular laminates with different boundary conditions.The algorithm developed can be applied to a wide range of elastic restraint conditions, to any aspect ratio and to higher modes. The effect of the restraint parameters along the boundary on the natural frequencies for plates with these complicating effects is considered.     

Modal characteristics of symmetrically laminated composite plates flexibly restrained at different locations

A method for determining modal characteristics (natural frequencies and mode shapes) of symmetrically laminated composite plates restrained by elastic supports at different locations in the interior and on the edges of the plates is presented. The classical lamination theory together with an appropriate set of characteristic functions are used in the Rayleigh-Ritz method to formulate the eigenvalue problem for determining the modal characteristics of the flexibly supported laminated composite plates. Sweep-sine vibration testing of several laminated composite plates flexibly restrained at different locations on the plates is performed to measure their natural frequencies. The close agreement between the experimental and theoretical natural frequencies of the plates has verified the accuracy of the proposed method. The effects of elastic restraint locations on the modal characteristics of flexibly supported laminated composite plates with different lamination arrangements and aspect ratios are studied using the present method. The usefulness of the results obtained for predicting sound radiation behavior of flexibly supported laminated composite plates is discussed.     

Differential quadrature method for Mindlin plates on Winkler foundations

This paper presents an approximate analysis of rectangular plates resting on Winkler foundations based on the Mindlin plate theory. The plates are subject to any combination of free, simply supported and clamped boundary conditions. Solutions to the problem are obtained using the differential quadrature method (DQM) by solving the governing differential equations. Numerical results are compared with existing literature to establish the validity and accuracy of the method. This study shows numerically the effects of shear deformation on the deflections and stress resultants at some selected locations. The distributions of the bending and twisting moments and shear force for several plates are presented graphically by varying the relative thickness ratio h/a to further show the significant effect of shear deformation.     

Axisymmetric free vibration of thick annular plates

This paper presents a numerical analysis of the axisymmetric free vibration of moderately thick annular plates using the differential quadrature method (DQM). The plates are described by Mindlin’s first-order shear-deformation theory. The first five axisymmetric natural frequencies are presented for uniform annular plates, of various radii and thickness ratios, with nine possible combinations of free, clamped and simply supported boundary conditions at the inner and outer edges of the plates. The accuracy of the method is established by comparing the DQM results with some exact and finite element numerical solutions and, therefore, the present DQM results could serve as a benchmark for future reference. The convergence characteristics of the method for thick plate eigenvalue problems are investigated and the versatility and simplicity of the method is established.     

基于主动磁化的钢板应力测量性能提升方法研究

提出一种提高基于磁弹效应的钢板应力测量灵敏度和一致性的方法。从力磁耦合理论模型出发,分析强磁化和弱交流磁化对力磁耦合所起的作用：强磁化能通过降低初始磁导率和统一力磁耦合参数,提高应力测量的灵敏度及一致性;弱交流磁化提供小幅振荡磁场,能有效消除干扰磁场影响。开展了基于磁弹法的钢板应力测量有限元仿真研究,表明当初始相对磁导率较低时,应力作用下的钢板法向磁感应强度变化率较大,即应力测量灵敏度较高。开展了不同强磁化条件下不同厚度钢板的拉伸试验,测量其法向磁感应强度变化。实验结果表明：与未磁化相比,强磁化后钢板应力测量灵敏度有数十倍提升,一致性有数倍至百倍提高。其中,3 mm厚度钢板采用单磁铁移动磁化方式的应力测量灵敏度和一致性参数提高至1.665 mGs/MPa和2%;5 mm厚度钢板采用双磁移动磁化方式的应力测量灵敏度提高至1.41 mGs/MPa,采用单磁铁移动磁化方式的一致性参数提高至0.2%;7 mm厚度钢板采用双磁铁移动磁化方式的应力测量灵敏度和一致性参数提高至1.2 mGs/MPa和1.8%。     

Levy solutions for vibration of multi-span rectangular plates

This paper presents the Levy method to investigate the vibration behaviour of multi-span rectangular plates. The Levy method is applicable and analytical for rectangular plates with at least two parallel simply supported edges. The continuity at an interface between two spans is maintained by imposing both the essential and natural boundary conditions along the interface. The impact of the internal line supports on the vibration behaviour of the plates is investigated by varying both the number of internal lines and the line positions. Results for the vibration of two- and three-span rectangular plates are presented, in which the first-known exact solutions for plates involving free edges are included. The present results may serve as benchmark solutions for such plates.     

Frequency solutions for circular plates with internal supports and discontinuous boundaries

The paper presents a study of the free-flexural vibration analysis of circular plates continuous over point supports, partial internal curved supports, and with mixed-edge boundary conditions. An approximate model which combines the advantages of the Rayleigh-Ritz and the Lagrangian multiplier methods is developed for analyzing this class of circular plate problems. The Rayleigh-Ritz method is used to formulate plates with classical boundary conditions, such as free, simply-supported or clamped, while the Lagrangian multiplier method is used to handle plates with point supports, partial internal curved supports and mixed-edge boundary conditions. The admissible pb-2 Ritz function consists of the product of a two-dimensional polynomial and a basic function. The basic function is defined by the product of the equations of the prescribed piecewise-continuous boundary shape each raised to the power of 0, 1 or 2, corresponding to free, simply-supported or clamped edge, respectively. The set of functions automatically satisfies all the kinematic boundary conditions of the plate at the outset. The geometric boundary conditions associated with the internal supports and discontinuous edges are simulated using a sufficient number of closely-spaced point constraints. Numerical results for several selected plate problems are presented to demonstrate the various features and accuracy of the present method.     

Optimization of Dimensions of a Device for Circular Magnetization of Cylindrical Components. V. Circular Field Component in One Sector of Toroidal Coil

Analytical expressions for calculating the distribution of the circular magnetic field component generated by a coil shaped as a toroid sector have been obtained. The field distribution has been analyzed for different parameters of a toroidal coil divided into sectors. The maximal circular component of magnetic field is generated in a limited region in space by a coil composed of different sectors containing turns wound in several layers on top of one another. The field intensity depends on the sectorial angle, its inside and outside radius, and the number of layers in the winding. The sectorial angle corresponding to the maximal circular component depends on the radius-vector of the observation point.     

The deflection coefficient of a rectangular plate reinforced in the middle

In this paper, we investigated the deflection coefficients of rectangular plates that are reinforced in the middle. For reinforced plates with three different aspect ratios and two types of boundary conditions (simply supported and clamped), we derived the deflection coefficients with respect to the elastic modulus ratio and the relative length of the inner plate using the least-squares method. We performed a finite element analysis of the models, and calculated the deflection coefficients of reinforced plates in terms of the deflection coefficients of simple (nonreinforced) plates. The results can be extended to various types of reinforced rectangular plates.     

Generating multi-section silicon steel sheet cutting patterns in the manufacturing industry of electric generators

Circular and sectorial blanks are often cut from silicon steel sheet to make stators and rotors of electric generators. This paper presents an algorithm to generate optimal multi-section cutting patterns for the blanks. A cutting pattern includes one or more sections, each of which consists of strips of the same direction and length. Blanks in a strip are of the same size. The algorithm employs dynamic programming to generate cutting patterns, and linear programming to determine the cutting scheme. Cutting stock data from a factory that produces electric generators are analyzed, and the results indicate that the algorithm is efficient in improving material usage.     

Vibrations of rectangular plates with internal cracks or slits

This work applies the famous Ritz method to analyze the free vibrations of rectangular plates with internal cracks or slits. To retain the important and useful feature of the Ritz method providing the upper bounds on exact natural frequencies, the paper proposes a new set of admissible functions that are able to properly describe the stress singularity behaviors near the tips of the crack and meet the discontinuous behaviors of the exact solutions across the crack. The validity of the proposed set of functions is confirmed through comprehensive convergence studies on the frequencies of simply supported square plates with horizontal center cracks having different lengths. The convergent frequencies show excellent agreement with published accurate results obtained by an integration equation technique, and are more accurate than those obtained by a previously published approach using the Ritz method combined with a domain decomposition technique. Finally, the present solution is employed to obtain accurate natural frequencies and mode shapes for simply supported and completely free square plates with internal cracks having various locations, lengths, and angular orientations. Most of the configurations considered here have not been analyzed in the previously published literature. The present results are novel, and are the first published vibration data for completely free rectangular plates with internal cracks and for plates with internal cracks, which are not parallel to the boundaries.     

Free vibration analysis of functionally graded plates with multiple circular and non-circular cutouts

Cutouts are inevitable in structures due to practical consideration.In order to investigate the free vibration of functionally graded plates with multiple circular and non-circular cutouts,finite eleme...     

A method of increasing hard-alloy wear resistance via aerodynamic impact

The paper presents the effect of an increase in wear resistance after several operating cycles of hard-alloy plates is investigated and the results of investigations. The plate is heated to one-third of the melting temperature and subjected to air fluctuations with frequencies of 160–800 Hz. A hypothesis on how aerodynamic impacts occur on hard alloy surfaces is presented. An experimental way to strengthen the surface layer of metal cutting plates is described. It is revealed that under industrial condition the mean time between failures for the plates processed by mentioned procedure is 1.8–2.2 times higher than for the standard delivery plates.     

Vibration of circular Mindlin plates with concentric elastic ring supports

This paper studies the vibration behaviour of circular Mindlin plates with multiple concentric elastic ring supports. Utilizing the domain decomposition technique, a circular plate is divided into several annular segments and one core circular segment at the locations of the elastic ring supports. The governing differential equations and the solutions of these equations are presented for the annular and circular segments based on the Mindlin-plate theory. A homogenous equation system that governs the vibration of circular Mindlin plates with elastic ring supports is derived by imposing the essential and natural boundary and segment interface conditions. The first-known exact vibration frequencies for circular Mindlin plates with multiple concentric elastic ring supports are obtained and the modal shapes of displacement fields and stress resultants for several selected cases are presented. The influence of the elastic ring support stiffness, locations, plate boundary conditions and plate thickness ratios on the vibration behaviour of circular plates is discussed.     

Microscopic studies of the influence of main exposure time on parameters of flexographic printing plate produced by digital thermal method

The digital thermal technology of producing flexographic printing plates from photopolymer plates is one of the newest technologies. This technology allows to develop flexographic plates without the use of any solvent. The process of producing flexographic printing plates by the digital thermal method consists of several main stages: back exposure, laser exposure, main exposure, thermal development, post exposure, and light finishing. The studies carried out with the use of optical stereoscopic microscopy allowed to determine the effect of time of main exposure to ultraviolet radiation on the dot area, diameter, and edge factor of halftone dots reproduced on flexographic printing plate produced by the digital thermal method, as well as on the quality of reproducing the surface and on the profiles of free‐standing printing microelements. The results of the microscopic studies performed have allowed to define the criteria of establishing optimum time of main exposure of photopolymer plates used in the digital thermal technology of producing flexographic printing plates. A precise definition of the criteria for determining the optimum time of main exposure will enable to reduce the time‐consuming control tests and to eliminate errors in both the process of manufacturing flexographic printing plates and in the printing process carried out with the use of such plates. Microsc. Res. Tech., 2009. © 2009 Wiley‐Liss, Inc.     

带有空间伸展机构的复杂航天器柔性多体动力学分析

依据Ｋａｎｅ方程,提出带有多个柔性矩形板的复杂航天器的动力学建模方法。该方法是依据３个假设条件得到的,通过引入矩形板在中面内不可伸展的假设,并在适当的阶级进行线性化处理,可在动力学方程中自然地引入“动力刚化”项,数值仿真的结果为航天器的设计提供了重要的理论依据,本方法也可推广到其它多柔性系统。     

Vibration of skew plates by the MLS-Ritz method

This paper presents a study on the vibration of skew plates by a numerical method, the moving least square Ritz (MLS-Ritz) method which was proposed by the authors in a previous study [Zhou L, Zheng WX. A novel numerical method for the vibration analysis of plates. Computational mechanics WCCM VI in conjunction with APCOM’04, Beijing, China, 5-10 September 2004; Zhou L, Zheng WX. MLS-Ritz method for vibration analysis of plates. Journal of Sound and Vibration 2006;290(3-5):968-90]. One of the most challenging numerical difficulties in analysing the vibration of a skew plate with a large skew angle is the slow convergence due to the stress singularities at the obtuse corners of the plate. The MLS-Ritz method is employed in this paper to address such problem. This method utilises the moving least square technique to establish the trial function for the transverse displacement of a skew plate and the Ritz method is applied to derive the governing eigenvalue equation for the skew plate. The boundary conditions of the plate are enforced through a point substitution technique that forces the MLS-Ritz trial function satisfying the essential boundary conditions along the plate edges. Due to the flexibility of the arrangement of the MLS-Ritz grid points, more grid points can be placed around the obtuse corners of a skew plate so as to address the stress singularity problem at the corners. A series of cases for rhombic plates of various edge support conditions are presented to demonstrate the efficiency and accuracy of the MLS-Ritz method.     

Design of a two-phase loop thermosyphon for telecommunications system (II)

A computer simulation is performed for a two-phase loop thermosyphon for the B-ISDN telecommunications. The aim of this code development is to provide capabilities to predict the affects of many variables on the performance of the proposed TLT system using different empirical correlations obtained from the literature for the evaporation and condensation, and the shape factors available. In the present study, the simulation code is based on the sectorial thermal resistance network built on the flow regimes of the two-phase flows involved. The nodal resistances are solved by the typical Gauss-Seidal iteration method. The code can predict whether the proposed design is possible based on the Hooding limit calculation of the system and its results are compared with the experimental results.