Semi-analytical solution for nonlinear vibration of laminated FGM plates with geometric imperfections

This paper investigates the nonlinear vibration of imperfect shear deformable laminated rectangular plates comprising a homogeneous substrate and two layers of functionally graded materials (FGMs). A theoretical formulation based on Reddy's higher-order shear deformation plate theory is presented in terms of deflection, mid-plane rotations, and the stress function. A semi-analytical method, which makes use of the one-dimensional differential quadrature method, the Galerkin technique, and an iteration process, is used to obtain the vibration frequencies for plates with various boundary conditions. Material properties are assumed to be temperature-dependent. Special attention is given to the effects of sine type imperfection, localized imperfection, and global imperfection on linear and nonlinear vibration behavior. Numerical results are presented in both dimensionless tabular and graphical forms for laminated plates with graded silicon nitride/stainless steel layers. It is shown that the vibration frequencies are very much dependent on the vibration amplitude and the imperfection mode and its magnitude. While most of the imperfect laminated plates show the well-known hard-spring vibration, those with free edges can display soft-spring vibration behavior at certain imperfection levels. The influences of material composition, temperature-dependence of material properties and side-to-thickness ratio are also discussed. (C) 2004 Elsevier Ltd. All rights reserved.

Influence of imperfect interfaces on bending and vibration of laminated composite shells

This paper is devoted to modeling elastic behavior of laminated composite shells, with special emphasis on incorporating interfacial imperfection. The conditions of imposing traction continuity and displacement jump across each interface are used to model imperfect interfaces. Vanishing transverse shear stresses on two free surfaces of a shell eliminate the need for shear correction factors. A linear theory underlying elastostatics and kinetics of laminated composite shells in a general configuration is presented from Hamilton's principle. In the special case of vanishing interfacial parameters, this theory reduces to the conventional third-order zigzag theory for perfectly bonded laminated shells. Numerical results for bending and vibration problems of laminated circular cylindrical panels are tabulated and plotted to indicate the influence of the interfacial imperfection. (C) 2000 Elsevier Science Ltd. All rights reserved.

Exact eigenvalue correspondences between laminated plate theories via membrane vibration

Based on Reddy's third-order theory, the first-order theory and the classical theory, exact explicit eigenvalues are found for compression buckling, thermal buckling and vibration of laminated plates via analogy with membrane vibration, These results apply to symmetrically laminated composite plates with transversely isotropic laminae and simply supported polygonal edges, Comprehensive consideration of a Winkler-Pasternak elastic foundation, a hydrostatic inplane force, an initial temperature increment and rotary inertias is incorporated. Bridged by the vibrating membrane, exact correspondences are readily established between any pairs of buckling and vibration eigenvalues associated with different theories. Positive definiteness of the critical hydrostatic pressure at buckling, the thermobukling temperature increment and, in the range of either tension loading or compression loading prior to occurrence of buckling, the natural vibration frequency is proved. (C) 2000 Elsevier Science Ltd. All rights reserved.

Vibration of symmetrically laminated thick super elliptical plates

This paper reports a free vibration analysis of thick plates with rounded corners subject to a free, simply-supported or clamped boundary condition. The plate perimeter is defined by a super elliptic function with a power defining the shape ranging from an ellipse to a rectangle. To incorporate transverse shear deformation, the Reddy third-order plate theory is employed. The energy integrals incorporating shear deformation and rotary inertia are formulated and the p-Ritz procedures are used to derive the governing eigenvalue equation. Numerical examples for plates with different shapes and boundary conditions are solved and their frequency parameters, where possible, are compared with known results. Parametric studies are carried out to show the sensitivities of frequency parameters by varying the geometry, fibre stacking sequence, and boundary condition. (C) 1999 Academic Press.

Analysis of the thermal stress behaviour of functionally graded hollow circular cylinders

This paper presents an analysis of the thermomechanical behavior of hollow circular cylinders of functionally graded material (FGM). The solutions are obtained by a novel limiting process that employs the solutions of homogeneous hollow circular cylinders, with no recourse to the basic theory or the equations of non-homogeneous thermoclasticity. Several numerical cases are studied, and conclusions are drawn regarding the general properties of thermal stresses in the FGM cylinder. We conclude that thermal stresses necessarily occur in the FGM cylinder, except in the trivial case of zero temperature. While heat resistance may be improved by sagaciously designing the material composition, careful attention must be paid to the fact that thermal stresses in the FGM cylinder are governed by more factors than are its homogeneous counterparts. The results that are presented here will serve as benchmarks for future related work. (C) 2003 Elsevier Science Ltd. All rights reserved.

Analysis of the free vibration of rectangular plates with central cut-outs using the discrete Ritz method

We present an analysis of the free vibration of plates with internal discontinuities due to central cut-outs. A numerical formulation for a basic L-shaped element which is divided into appropriate sub-domains that are dependent upon the location of the cut-out is used as the basic building element. Trial functions formed to satisfy certain boundary conditions are employed to define the transverse deflection of each sub-domain. Mathematical treatments in terms of the continuities in displacement, slope, moment, and higher derivatives between the adjacent sub-domains are enforced at the interconnecting edges. The energy functional results, from the proper assembly of the coupled strain and kinetic energy contributions of each sub-domain, are minimized via the Ritz procedure to extract the vibration frequencies and. mode shapes of the plates. The procedures are demonstrated by considering plates with central cut-outs that are subjected to two types of boundary conditions. (C) 2003 Elsevier Ltd. All rights reserved.

Geological and trace element evidence for a marine sedimentary environment of deposition and biogenicity of 3.45 Ga stromatolitic carbonates in the Pilbara Craton, and support for a reducing Archaean ocean

Bedded carbonate rocks from the 3.45 Ga Warrawoona Group, Pilbara Craton, contain structures that have been regarded either as the oldest known stromatolites or as abiotic hydrothermal deposits. We present new field and petrological observations and high-precision REE + Y data from the carbonates in order to test the origin of the deposits. Trace element geochemistry from a number of laminated stromatolitic dolomite samples of the c. 3.40 Ga Strelley Pool Chert conclusively shows that they precipitated from anoxic seawater, probably in a very shallow environment consistent with previous sedimentological observations. Edge-wise conglomerates in troughs between stromatolites and widespread cross-stratification provide additional evidence of stromatolite construction, at least partly, from layers of particulate sediment, rather than solely from rigid crusts. Accumulation of particulate sediment on steep stromatolite sides in a high-energy environment suggests organic binding of the surface. Relative and absolute REE + Y contents are exactly comparable with Late Archaean microbial carbonates of widely agreed biological origin. Ankerite from a unit of bedded ankerite–chert couplets from near the top of the stratigraphically older (3.49 Ga) Dresser Formation, which immediately underlies wrinkly stromatolites with small, broad, low-amplitude domes, also precipitated from anoxic seawater. The REE + Y data of carbonates from the Strelley Pool Chert and Dresser Formation contrast strongly with those from siderite layers in a jasper–siderite–Fe-chlorite banded iron-formation from the base of the Panorama Formation (3.45 Ga), which is clearly hydrothermal in origin. The geochemical results, together with sedimentological data, strongly support: (1) deposition of Dresser Formation and Strelley Pool Chert carbonates from Archaean seawater, in part as particulate carbonate sediment; (2) biogenicity of the stromatolitic carbonates; (3) a reducing Archaean atmosphere; (4) ongoing extensive terrestrial erosion prior to ∼3.45 Ga.

Diplacanthid acanthodians from the Aztec Siltstone (late Middle Devonian) of southern Victoria Land, Antartica

One articulated and several partial, semi-articulated specimens of acanthodians were collected in 1970 from the freshwater deposits of the Aztec Siltstone (Middle Devonian; Givetian), Portal Mountain, southern Victoria Land, Antarctica, during a Victoria University of Wellington Antarctic Expedition. The Portal Mountain fish fauna, preserved in a finely laminated, non-calcareous siltstone, includes acanthodians, palaeoniscoids, and bothriolepid placoderms. The articulated acanthodian specimens are the most complete fossil fish remains documented so far from the Aztec assemblage, which is the most diverse fossil vertebrate fauna known from Antarctica. They are described as a new taxon, Milesacanthus antarctica gen. et sp. nov., which is assigned to the family Diplacanthidae. Its fin spines show some similarities to spine fragments named Byssacanthoides debenhami from glacial moraine at Granite Harbour, Antarctica, and much larger spines named Antarctonchus glacialis from outcrops of the Aztec Siltstone in the Boomerang Range, southern Victoria Land. Both of these are reviewed, and retained as form taxa for isolated spines. Various isolated remains of fin spines and scales are described from Portal Mountain and Mount Crean (Lashly Range), and referred to Milesacanthus antarctica gen. et sp. nov. The histology of spines and scales is documented for the first time, and compared with acanthodian material from the Devonian of Australia and Europe. Distinctive fin spines from Mount Crean are provisionally assigned to Culmacanthus antarctica Young, 1989b. Several features on the most complete of the new fish specimens - in particular, the apparent lack of an enlarged cheek plate - suggest a revision of the diagnosis for the Diplacanthidae.

Random vibration of the functionally graded laminates in thermal environments

This work deals with the random free vibration of functionally graded laminates with general boundary conditions and subjected to a temperature change, taking into account the randomness in a number of independent input variables such as Young's modulus, Poisson's ratio and thermal expansion coefficient of each constituent material. Based on third-order shear deformation theory, the mixed-type formulation and a semi-analytical approach are employed to derive the standard eigenvalue problem in terms of deflection, mid-plane rotations and stress function. A mean-centered first-order perturbation technique is adopted to obtain the second-order statistics of vibration frequencies. A detailed parametric study is conducted, and extensive numerical results are presented in both tabular and graphical forms for laminated plates that contain functionally graded material which is made of aluminum and zirconia, showing the effects of scattering in thermo-clastic material constants, temperature change, edge support condition, side-to-thickness ratio, and plate aspect ratio on the stochastic characteristics of natural frequencies. (c) 2005 Elsevier B.V. All rights reserved.