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.

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.

Tetra- and tribromopbenoxyanisoles in Marine Samples from Oceania

Some methoxylated polybrominated diphenyl ethers (MeO-BDEs) are known halogenated natural products (HNPs) and are frequently detected in higher organisms of the marine environment. In this study we demonstrate that a prominent MeO-BDE, previously detected in marine mammals from Australia, is identical to 3,5-dibromo-2-(2',4'-dibromo)phenoxyanisole(BC-3,6-MeO-BDE47). Up to 1.9mg/ kg of 6-MeO-BDE 47 was present in cetaceans from Australia, 0.2-0.3 mg/kg in two crocodile eggs from Australia, but concentrations of 1 or 2 orders of magnitude lower were found in shark liver oil from New Zealand and in marine mammals from Africa and the Antarctic. Concentrations of 6-MeO-BDE47 in samples from Australia were in the same range as anthropogenic pollutants such as PCB 153 and p,p'-DDE. Along with 6-MeO-BDE 47 and the known HNP 4,6-dibromo-2-(2',4'-dibromo)phenoxyanisole (BC-2,2'-MeO-BDE 68), several tribromophenoxyanisoles (MeO-triBDE) were present in tissue of Australian cetaceans. To determine their structure, abiotic debromination experiments were performed using 6-MeO-BDE 47 and 2'-MeO-BDE 68 and superreduced di cyanocobalamine. These experiments resulted in formation of eight MeO-triBDEs, all of which were detected in the cetacean samples. Five of these eight MeO-triBDEs could be identified based on two standard compounds as well as gas chromatographic and mass spectrometric features. It was also shown that the first eluting isomer (compound 1), 6-MeO-BDE 17 (compound 2), and 2-MeO-BDE 39 (compound 5) were the most prominent MeO-triBDEs in the Australian cetacean samples. The concentrations of the MeO-triBDEs in two cetacean samples were 0.20 and 0.36 mg/kg, respectively. Although the reductive debromination with dicyanocobalamine resulted in a different congener pattern than was found in the marine mammals, it could not be excluded that the tribromo congeners of 6-MeO-BDE 47 and 2'-MeO-BDE 68 in the samples were metabolites of the latter.

Changes in joint stability with muscle contraction measured from transmission of mechanical vibration

A non-invasive in vivo technique was developed to evaluate changes in wrist joint stability properties induced by increased co-activation of the forearm muscles in a gripping task. Mechanical vibration at 45, 50 and 55 Hz was applied to the radial head in ten healthy volunteers. Vibrations of the styloid process of the radius and the distal end of the metacarpal bone of the index finger were measured with triaxial accelerometers. Joint stability properties were quantified by the transfer function gain between accelerations on either side of the wrist-joint. Gain was calculated with the muscles at rest and at five force levels ranging from 5% to 25% of maximum grip force (%MF). During contraction the gain was significantly greater than in control trial (0%MF) for all contractions levels at 45 and 50 Hz and a trend for 15%MF and higher at 55 Hz. Group means of contraction force and gain were significantly correlated at 45 (R-2 = 0.98) and 50 Hz (R-2 = 0.72), but not at 55 Hz (R-2 = 0.10). In conclusion, vibration transmission gain may provide a method to evaluate changes in joint stability properties. (c) 2005 Published by Elsevier Ltd.

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.

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.