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.

Non-linear analysis of the thermo-electro-mechanical behaviour of shear deformable FGM plates with piezoelectric actuators

This paper investigates the non-linear bending behaviour of functionally graded plates that are bonded with piezoelectric actuator layers and subjected to transverse loads and a temperature gradient based on Reddy's higher-order shear deformation plate theory. The von Karman-type geometric non-linearity, piezoelectric and thermal effects are included in mathematical formulations. The temperature change is due to a steady-state heat conduction through the plate thickness. The material properties are assumed to be graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The plate is clamped at two opposite edges, while the remaining edges can be free, simply supported or clamped. Differential quadrature approximation in the X-axis is employed to convert the partial differential governing equations and the associated boundary conditions into a set of ordinary differential equations. By choosing the appropriate functions as the displacement and stress functions on each nodal line and then applying the Galerkin procedure, a system of non-linear algebraic equations is obtained, from which the non-linear bending response of the plate is determined through a Picard iteration scheme. Numerical results for zirconia/aluminium rectangular plates are given in dimensionless graphical form. The effects of the applied actuator voltage, the volume fraction exponent, the temperature gradient, as well as the characteristics of the boundary conditions are also studied in detail. Copyright (C) 2004 John Wiley Sons, Ltd.

Influence of charge size distribution on net-power draw of tumbling mill based on DEM modelling

Modelling and optimization of the power draw of large SAG/AG mills is important due to the large power draw which modern mills require (5-10 MW). The cost of grinding is the single biggest cost within the entire process of mineral extraction. Traditionally, modelling of the mill power draw has been done using empirical models. Although these models are reliable, they cannot model mills and operating conditions which are not within the model database boundaries. Also, due to its static nature, the impact of the changing conditions within the mill on the power draw cannot be determined using such models. Despite advances in computing power, discrete element method (DEM) modelling of large mills with many thousands of particles could be a time consuming task. The speed of computation is determined principally by two parameters: number of particles involved and material properties. The computational time step is determined by the size of the smallest particle present in the model and material properties (stiffness). In the case of small particles, the computational time step will be short, whilst in the case of large particles; the computation time step will be larger. Hence, from the point of view of time required for modelling (which usually corresponds to time required for 3-4 mill revolutions), it will be advantageous that the smallest particles in the model are not unnecessarily too small. The objective of this work is to compare the net power draw of the mill whose charge is characterised by different size distributions, while preserving the constant mass of the charge and mill speed. (C) 2004 Elsevier Ltd. All rights reserved.

Comparison of beam theory and finite-element analysis with in vivo bone strain data from the alligator cranium

The mechanical behavior of the vertebrate skull is often modeled using free-body analysis of simple geometric structures and, more recently, finite-element (FE) analysis. In this study, we compare experimentally collected in vivo bone strain orientations and magnitudes from the cranium of the American alligator with those extrapolated from a beam model and extracted from an FE model. The strain magnitudes predicted from beam and FE skull models bear little similarity to relative and absolute strain magnitudes recorded during in vivo biting experiments. However, quantitative differences between principal strain orientations extracted from the FE skull model and recorded during the in vivo experiments were smaller, and both generally matched expectations from the beam model. The differences in strain magnitude between the data sets may be attributable to the level of resolution of the models, the material properties used in the FE model, and the loading conditions (i.e., external forces and constraints). This study indicates that FE models and modeling of skulls as simple engineering structures may give a preliminary idea of how these structures are loaded, but whenever possible, modeling results should be verified with either in vitro or preferably in vivo testing, especially if precise knowledge of strain magnitudes is desired. (c) 2005 Wiley-Liss, Inc.

Post-hatching growth and development of the pectoral and pelvic limbs in the black noddy, Anous minutus

The black tern (Anous minutus) uses a semi-precocial growth strategy. Terrestrial locomotor capacity occurs soon after hatching, but pectoral limb development is delayed and flight is not possible until about post-hatching day 50. A growth series (hatchlings to fledglings) was used to explore how limb musculoskeletal development varied with body mass. In the pelvic limb, bone lengths scaled isometrically or with negative allometry. Gastrocnemius muscle mass and the failure load and stiffness of the tibiotarsus scaled isometrically. In the pectoral limb, pectoralis and supracoracoideus muscle masses increased with strong positive allometry that was mirrored by increases in wing bone strength and stiffness. Bending strength (σult) and modulus (E) remained fairly constant throughout development to fledging for all limb bones. The moment of inertia (I) scaled with negative allometry for the tibiotarsus and with strong positive allometry in the wing bones. Differences in σult and E of the tibiotarsus between pre-fledged chicks and adults was due, primarily, to increases in bone density rather than increases in the moment of inertia of the skeletal elements, whereas σult of wing bones was a function of increases in both bone density and I. Early development of functional pelvic limbs in tree-nesting birds is relatively unusual, and presumably reflects a familial trait that does not appear to compromise breeding success in this species.

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.

Engineering of needle-free physical methods to target epidermal cells for DNA vaccination

A challenge in epidermal DNA vaccination is the efficient and targeted delivery of polynucleotides to immunologically sensitive Langerhans cells. This paper investigates this particular challenge for physical delivery approaches. The skin immunology and material properties are examined in the context of the physical cell targeting requirements of the viable epidermis. Selected current physical cell targeting technologies engineered to meet these needs are examined: needle and syringe; diffusion patches; liquid jet injectors; microneedle arrays/patches; and biolistic particle injection. The operating methods and relative performance of these approaches are discussed, with a comment on potential future developments and technologies. (c) 2005 Elsevier Ltd. All rights reserved.

Preparation and electrochemical properties of the layered material of LixVyO2 (x=0.86 and y=0.8)

Layered lithium-vanadium oxide with a composition of LixVyO2 (x = 0.86 and y = 0.8) was prepared by the hydrothermal reaction of V2O3 with LiOH center dot H2O at 180 degrees C. This material corresponds to a layered rhombohedral structure related to alpha-NaFeO2 in which the vanadium ions are disordered in alternate layers of octahedral 3a (0, 0, 0) and 3b (0, 0, 1/2) sites. The electrochemical properties of this Li0.86V0.8O2 material were investigated and compared with those of the layered Li0.96VO2 made by the conventional solid-state reaction. It was found that the electrochemical capacity and reversibility of the Li0.86V0.8O2 material are significantly improved compared to those of the Li0.96VO2 material; the reversible specific capacities of the Li/Li0.86V0.8O2 and Li/Li0.96VO2 systems are similar to 100 and similar to 50 mAh g(-1), respectively, under the current densities of 7.14 mA g(-1) over 20 charge-discharge cycles with a potential window of 1.50-4.50 V. Such a reversibility results from the structural stability of Li0.86V0.8O2, whereas the increase in the reversible specific capacity can be qualitatively interpreted in terms of the presence of vanadium vacancies in the structure. (c) 2005 The Electrochemical Society.