Polygonal Plates Research Articles

꼭지점에서의 응력 집중 현상을 고려한 자유단 경계조건을 가진 임의 다각형 형상 평판의 자유 진동 해석

Free vibration analysis using the method of NDIF (non-dimensional dynamic influence function), which was developed by the author, is extended to arbitrarily shaped polygonal plates with free edges. Local Cartesian coordinate systems are employed to apply the free boundary condition to nodes distributed along the edges of the plate of interest. Furthermore, a new way for applying the free boundary condition to nodes located at corners of the plate is for the first time introduced by considering the phenomenon of stress concentration at the corners. Two case studies show that the proposed method is valid and accurate when the eigenvalues by the proposed method are compared to those by FEM(ANSYS).

Analytical 3-D p-element for quadrilateral plates—Part 1: Thick isotropic plate structures

An analytical three-dimensional (3-D) p-version element for the vibration analysis of arbitrary quadrilateral thick plates is presented. With the additional hierarchical shape functions and analytically integrated element matrices, the computed accuracy is considerably improved. The computed natural frequencies of cantilever and simply supported square plates show that the convergence rate of the present element is very fast with respect to the number of hierarchical terms and it can predict very accurate modes. The element is applicable to the free vibration analysis of quadrilateral, polygonal plates as well as 3-D space structures. The continuous wavelet transform (CWT) is applied for the identification of damping ratios. Based on the Rayleigh damping model, the damped vibration response is obtained. A simple experiment is performed to verify the predicted vibration responses. The results show that the proposed element is also efficient for the vibration response analysis of plates.

Fundamental frequency of clamped plates with circularly periodic boundaries

A boundary perturbation method is developed to determine the fundamental frequency of vibrating plates. The method is then applied to wavy, star shape and polygonal plates with clamped boundary conditions. Approximate analytical solutions of the fundamental frequency are obtained with an accuracy of O( ε 4), where ε is the deviation from the unit circle.

Truncatulus gen. nov., a new fossil resting spore morphogenus related to the marine diatom genus Chaetoceros (Bacillariophyceae)

I. Suto. 2006. Truncatulus gen. nov., a new fossil resting spore morphogenus related to the marine diatom genus Chaetoceros (Bacillariophyceae). Phycologia 45: 585–601. DOI: 10.2216/04-91.1A new fossil marine diatom resting spore morphogenus (form genus) Truncatulus I. Suto gen. nov. is described using samples from DSDP Site 338 in the Norwegian Sea, Sites 436 and 438 in the northwest Pacific Ocean and from the onland Newport Beach Section, California. Truncatulus is characterized by the circular, elliptical or polygonal flat plate on the truncated elevation of the oval to elliptic epivalve or/and hypovalve, and includes seven new species (T. simplex, T. atlanticus, T. ellipticus, T. norvegicus, T. californicus and T. hajosiae), and one new combination, T. tortonicus (Hajós) I. Suto. Truncatulus appeared in the early Oligocene and became extinct in the late Pliocene. The oldest species, T. ellipticus, arose in the early Oligocene. Truncatulus norvegicus, T. ellipticus, T. atlanticus and T. hajosiae might be endemic species in the Norwegian Sea, and the first and last occurrences of T. norvegicus and the first occurrences of T. ellipticus, T. atlanticus and T. hajosiae may be useful for North Atlantic diatom biostratigraphy. Truncatulus californicus is endemic in the northeastern Pacific and restricted to a relatively short interval in middle Miocene Zone NPD 5B; it is therefore an excellent stratigraphic marker for this horizon. The last and cosmopolitan species T. tortonicus became extinct in the late Pliocene in the northwestern Pacific.

Analytic 3-D p-element for vibration analyses of plates, Part 2: Laminated plates

An analytic 3-D p-version arbitrary quadrilateral plate element is applied to solve the free vibration of laminated plates. The computational accuracy is considerably improved due to the additional hierarchical shape functions and analytic integration. The study on a single layer orthotropic plate with simply supported boundary conditions shows the fast convergence and great accuracy of the present element. Then the analyses of rectangular plates with simply supported, cantilevered and fully clamped boundary conditions are carried out. Because of the great fitness to all kinds of geometry shapes, the present element is easily applied to various polygonal plates.

Morphology and crystallography of Ti2Pd phase precipitated in B2 parent and B19 martensite matrices in Ti-rich Ti–Pd alloys

Morphology and crystallography of Ti2Pd phase of C11b structure precipitated in B2 parent and B19 martensite matrices in Ti-rich Ti–Pd shape memory alloy have been investigated by transmission electron microscopy observations. Three Ti2Pd variants were recognized in the specimen aged above Af temperature, i.e., in the B2 matrix. On the other hand, four Ti2Pd variants were confirmed in the specimen aged below As temperature, i.e., in the B19 matrix. The orientation relationship between the Ti2Pd precipitate and each matrix is consistent with the number of Ti2Pd variants. The Ti2Pd precipitates in the B2 and the B19 matrices have a disk and a polygonal plate shapes, respectively. The c-axis of Ti2Pd precipitate in the B2 matrix is perpendicular to the disk surface. On the other hand, that in the B19 matrix is parallel to the plate surface. These differences are well explained by the magnitude of coherent strain.

Microwave‐Assisted Synthesis of Metallic Nanostructures in Solution

AbstractFor Abstract see ChemInform Abstract in Full Text.

Facile synthesis of micrometer-sized gold nanoplates through an aniline-assisted route in ethylene glycol solution

Micrometer-sized edge, polygonal gold plates of several 10 nm thickness, called gold nanoplates, have been synthesized in large quantities through simply introducing aniline to a heated ethylene glycol (EG) solution of hydrogen tetrachloroaurate (HAuCl 4·4H 2O) without any other capping agents or surfactants. Electron diffraction (ED) and X-ray diffraction (XRD) patterns identified the as-prepared gold nanoplates were single crystals bound primarily by {1 1 1} facets. The study of the optical properties showed these large gold nanoplates had strong absorption in near infrared region (NIR). Investigations suggested the amount of aniline added to the reaction solution played a key role in producing gold nanoplates and the size of the gold nanoplates can be tuned by adjusting the stirring speed. The possible formation mechanism of the as-prepared gold nanoplates was also discussed.

Transverse Vibration of Mindlin Plates on Two-Parameter Foundations by Analytical Trapezoidal p-Elements

An analytical trapezoidal hierarchical element for the transverse vibration of Mindlin plates resting on two-parameter foundations is presented. Legendre orthogonal polynomials are used as enriching shape functions to avoid the shear-locking problem and to improve considerably the computational efficiency. Element matrices are integrated in closed form eliminating the numerical integration errors conventionally found. With the C0 continuity requirement, the element can be used to analyze any triangular and polygonal plates without difficulty, while the Kirchhoff p -version elements requiring C1 continuity are not as versatile. The computed natural frequencies for rectangular, skew, trapezoidal, triangular, annular, and polygonal plates on two-parameter foundations show that the convergence of the proposed element is very fast compared to the conventional linear finite elements with respect to the number of degrees of freedom used. Many numerical examples are given.

A new species of Rineloricaria (Siluriformes: Loricariidae) from the Paraná and Uruguay River basins, Misiones, Argentina

Rineloricaria misionera is a new species from the Paraná and Uruguay River basins, Misiones, Argentina. The new species is distinguished from all others in the genus by the following combination of characters: anterior abdomen covered by plates, except for the area corresponding to the pectoral girdle, which usually lacks plates, when present in this region, plates are relatively small and few; posterior abdomen with a well-developed preanal plate, bordered anteriorly by a series of 3–5 usually polygonal plates; premaxillary and dentary teeth with asymmetric cusps; uppermost caudal ray not prolonged in a filament; and snout tip with an oval naked area not reaching the last pore of the infraorbital sensory canal.

Vallodiscus gen. nov., a new fossil resting spore morpho-genus related to the marine diatom genus Chaetoceros (Bacillariophyceae)

A new fossil marine diatom resting spore morphogenus (form genus) Truncatulus I. Suto gen. nov. is described using samples from DSDP Site 338 in the Norwegian Sea, Sites 436 and 438 in the northwest Pacific Ocean and from the onland Newport Beach Section, California. Truncatulus is characterized by the circular, elliptical or polygonal flat plate on the truncated elevation of the oval to elliptic epivalve or/and hypovalve, and includes seven new species (T. simplex, T. atlan

Passive and Active Controls of Three-Dimensional Wake of Bluff-Body

Passive and active controls of wakes behind axisymmetric bluff-bodies are presented. The passive controls include base-bleed (slotted disks), edge-induced longitudinal vortices behind three-dimensional polygonal plates, the fineness ratio and surface protrusion. The disk wake was further actively controlled in air using actuated tabs and in water using net-zero mass actuators along the edge. The active control suppressed the helical mode of oscillation, but enhanced the closing of the reverse flow region with reduced base pressure. Unsteady velocity vector fields from the time-resolved PIV are presented and issues related to future feedback flow control for the bluff-body wake will be addressed.

Microwave‐Assisted Synthesis of Metallic Nanostructures in Solution

Microwave (MW) rapid heating has received considerable attention as a new promising method for the one-pot synthesis of metallic nanostructures in solutions. In this concept, advantageous application of this method has been demonstrated by using some typical examples for the preparation of Ag, Au, Pt, and AuPd nanostructures. Not only spherical nanoparticles, but also single crystalline polygonal plates, sheets, rods, wires, tubes, and dendrites were prepared within a few minutes under MW heating. Morphologies and sizes of nanostructures could be controlled by changing various experimental parameters, such as the concentration of metallic salt and surfactant polymer, the chain length of the surfactant polymer, the solvent, and the reaction temperature. In general, nanostructures with smaller sizes, narrower size distributions, and a higher degree of crystallization were obtained under MW heating than those in conventional oil-bath heating. The origin of these characteristic features under MW irradiation is discussed in terms of thermal and non-thermal effects under MW irradiation.

First Record of an Ectoparasitic Dinoflagellate, Oodinium inlandicum (Dinophyta) Infecting a Chaetognath, Sagitta crassa from the Korean Coasts

An ectoparasitic din flagellate infesting plank tonic chaetognath, Sagitta crassa Tokioka was found, for the first time, from Korean coasts. In order to identify the species, we investigated detailed morphology of the din flagellate using Nomarski interference optics as well as epifluorescent microscopes. The parasitic din flagellate consists of an oval to rod-shaped cell with a peduncle, by which the organism attaches to the host. The cell is covered with polygonal thecal plates. The nucleus displays two different shapes according to cell cycle stages: in young trophont the nucleus is elongated and shows typical din flagellate nucleus (dinokaryon), while in matured trophont, the nucleus is dome-shaped and non-dinokaryotic. The peduncle is variable in length and is ornamented with the longitudinal striations. All these characteristics point to identity that the ectoparasitic din flagellate infecting Sagitta crassa in Korean coasts is Oodinium inlandicum Horiguchi et Ohtsuka, originally described from the Seto Inland Sea of Japan. Relationship between prevalence and host sizes differed from those in Japan.

Asymptotic closed form for the capacitance of an arbitrarily shaped conducting plate

Closed-form results for the capacitance of an arbitrarily shaped conducting plate are presented. If the charge density suitable for fringe conditions and the appropriate charge barycentre are supposed, the asymptotic closed-form for the capacitance C can be achieved with high accuracy by simple curve integrals or the superposition of basic triangles. Some typical examples, such as an elliptical plate, a regular polygonal plate and a rectangular plate, are given.

Plastic Buckling of Simply Supported, Polygonal Mindlin Plates

This paper is concerned with the plastic buckling of Mindlin plates of polygonal plan shape and whose straight edges are simply supported. The plates are subjected to a uniform in-plane compressive stress. Two well-known competing theories of plasticity are considered here: the incremental theory of plasticity (with the Prandtl-Reuss constitutive relations) and the deformation theory of plasticity (with the Hencky constitutive relation). Based on an analogy approach, the plastic buckling stresses of such Mindlin plates are expressed in terms of their corresponding elastic buckling stresses of Kirchhoff (classical thin) plates, albeit in a transcendental form. Using this buckling stress relationship and the readily available elastic buckling solutions, one may deduce the plastic buckling stresses of the corresponding Mindlin plates. Tabulated herein are some buckling stress factors for various polygonal shaped plates with material properties defined by the Ramberg-Osgood relation.

Transverse vibration of thick polygonal plates using analytically integrated trapezoidal Fourier p-element

A trapezoidal Fourier p-element for the transverse vibration analyses of thick plates is introduced. Trigonometric functions are used as enriching shape functions to avoid ill-conditioning problems associated with high order polynomials in a conventional p-element. The element matrices are analytically integrated in closed form. With the enriching Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly improved. A simply supported square thick plate is analyzed by a rectangular Fourier p-element, two trapezoidal Fourier p-elements and the conventional linear finite elements, respectively. The results show that the convergence of the present element is very fast with respect to the number of trigonometric terms and it produces higher accurate modes than the linear finite elements for the same number of degrees of freedom. The proposed element is applied to find the natural modes of the rectangular, skew and trapezoidal plates with different boundary conditions. Since one can always break a triangle into three trapezoids, the range of application of the present element is as good as the triangular element. A triangular, an irregular quadrilateral and two polygonal thick plates are analyzed by the present element. The solutions of the trapezoidal Fourier p-element are in excellent agreement with those of available published methods.

Revision of the Genus Cryptomonas (Cryptophyceae): a Combination of Molecular Phylogeny and Morphology Provides Insights into a Long-Hidden Dimorphism

Seventy-three strains of cryptophytes assigned to the genera Cryptomonas, Campylomonas or Chilomonas were studied by light microscopy, spectrophotometry and whole-mount electron microscopy. Twelve groups of strains were distinguished by light and whole mount electron microscopy using a combination of characters, mainly cell size, type of periplast and presence/absence and number of pyrenoids. However, characters previously used to distinguish Cryptomonas from Campylomonas (e.g. the type of periplast: polygonal periplast plates vs. a continuous periplast sheet) were found to occur together in dimorphic strains, indicating that periplast types relate to different life-history stages of a single taxon. To evaluate the taxonomic significance of the type of periplast and other characters previously used to distinguish genera and species, representatives of each strain group were subjected to molecular phylogenetic analyses using two nuclear ribosomal DNA regions (ITS2, partial LSU rDNA) and a nucleomorph ribosomal gene (SSU rDNA). The results of the phylogenetic study provide molecular evidence for a life history-dependent dimorphism in the genus Cryptomonas: the genus Campylomonas represents the alternate morph of Cryptomonas. Campylomonas and Chilomonas are reduced to synonyms of Cryptomonas, the genus Cryptomonas is revised and typified, two new species are described and six species are emended.

Stress state of compound polygonal plate

The constructions made of bars and plates with holes, openings and bulges of various forms are widely used in modern industry. By loading these structural elements with different efforts, there appears concentration (accumulation) of stress whose values sometimes exceeds the admissible one. The durability of the given element is defined according to the quantity of these stresses. Since the failure of details and construction itself begins from the place where the stress concentration has the greatest value. Therefore the exact determination of stress distribution in details (bars, plates, beams) is of great scientific and practical interest and is one of the important problems of the solid fracture. Compound details (when the nucleus of different material is soldered to the hole) are often used to decrease the stress concentration. In the present paper, we study a stress–strain state of polygonal plate weakened by a central elliptic hole with two linear cracks info which a rigid nucleus (elliptic cylinder with two linear bulges) of different material was put in (soldered) without preload. The problem is solved by a complex variable functions theory stated in papers [Theory of Elasticity, Higher School, Moscow, 1976, p. 276; Plane Problem of Elasticity Theory of Plates with Holes, Cuts and Inclusions, Publishing House Highest School, Kiev, 1975, p. 228; Bidimensional Problem of Elasticity Theory, Stroyizdat, Moscow, 1991, p. 352; Science, Moscow (1996) 708; MSB AH USSR OTH 9 (1948) 1371]. Kolosov–Mushkelishvili complex potential ϕ( z) and ψ( z) satisfying the definite boundary conditions are sought in the form of sums of functional series. After making several strict mathematical transformations, the problem is reduced to the solution of a system of linear algebraic equations with respect to the coefficients of expansions of functions ϕ( z) and ψ( z). Determining the values of ϕ( z) and ψ( z), we can find the stress components σ r , σ θ and τ rθ at any point of cross-section of the plate and nucleus on the basis of the known formulae. The obtained solution is illustrated by numerical example. Changing the parameters A 1, m 1, e, A 2, and m 2 we can get the various contour plates. For example, if we assume m 1=0, A 1= r, then the internal contour of L 1 becomes the circle of radius r with two rectilinear cracks (for the nucleus––a rectilinear bulges). Further, if we assume a small semi-axis of the ellipse b 1 to be equal to zero ( b 1=0), then a linear crack becomes the internal contour of L 1 (and the nucleus becomes the linear rigid inclusion made of other material). For m 2=0; A 2= R, the external contour L 2 turns into the circle of radius R. The obtained method of solution may be applied and in other similar problems of elasticity theory; tension of compound polygonal plate, torsion and bending of compound prismatic beams, etc.

Two-dimensional viscoelastic vibration by analytic Fourier p-elements

Three new Fourier p-elements of rectangular, skew and trapezoidal shapes are given analytically for plane viscoelastic vibration problems. The natural frequencies of the plane viscoelastic structures with complex Young’s modulus are computed by a complex eigenvalue solver. With the additional Fourier degrees of freedom, the accuracy of the computed natural frequencies is greatly increased. Since trigonometric functions are used as enriching functions instead of polynomials in the proposal elements, the ill-conditioning problems associated with polynomials of higher degree in the traditional p-version finite element method are avoided. The two mapped plane coordinates in the Jacobian are uncoupled for trapezoidal elements whose element matrices can then be integrated analytically. A triangle can easily be divided into three trapezoids. Therefore, any plane viscoelastic problem with polygonal shape can be analyzed by a combination of rectangular and trapezoidal elements. Numerical examples show that the convergence of the present elements is very fast with respect to the number of trigonometric terms. The natural frequencies of several polygonal viscoelastic plates subject to in-plane vibration are presented.