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.

Involvement of Islet-2 in the Slit signaling for axonal branching and defasciculation of the sensory neurons in embryonic zebrafish

In Drosophila melanogaster, Slit acts as a repulsive cue for the growth cones of the commissural axons which express a receptor for Slit, Roundabout (Robo), thus preventing the commissural axons from crossing the midline multiple times. Experiments using explant culture have shown that vertebrate Slit homologues also act repulsively for growth cone navigation and neural migration, and promote branching and elongation of sensory axons. Here, we demonstrate that overexpression of Slit2 in vivo in transgenic zebrafish embryos severely affected the behavior of the commissural reticulospinal neurons (Mauthner neurons), promoted branching of the peripheral axons of the trigeminal sensory ganglion neurons, and induced defasciculation of the medial longitudinal fascicles. In addition, Slit2 overexpression caused defasciculation and deflection of the central axons of the trigeminal sensory ganglion neurons from the hindbrain entry point. The central projection was restored by either functional repression or mutation of Robo2, supporting its role as a receptor mediating the Slit signaling in vertebrate neurons. Furthermore, we demonstrated that Islet-2, a LIM/homeodomain-type transcription factor, is essential for Slit2 to induce axonal branching of the trigeminal sensory ganglion neurons, suggesting that factors functioning downstream of Islet-2 are essential for mediating the Slit signaling for promotion of axonal branching. (C) 2004 Elsevier Ireland Ltd. All rights reserved.

Relationship between laboratory-measured variables and heart rate during an ultra-endurance triathlon

The aim of the present study was to examine the relationship between the performance heart rate during an ultra-endurance triathlon and the heart rate corresponding to several demarcation points measured during laboratory-based progressive cycle ergometry and treadmill running. Less than one month before an ultra-endurance triathlon, 21 well-trained ultra-endurance triathletes (mean +/- s: age 35 +/- 6 years, height 1.77 +/- 0.05 in, mass 74.0 +/- 6.9 kg, (V) over dot O-2peak = 4.75 +/- 0.42 1 center dot min(-1)) performed progressive exercise tests of cycle ergometry and treadmill running for the determination of peak oxygen uptake ((V) over do O-2peak), heart rate corresponding to the first and second ventilatory thresholds, as well as the heart rate deflection point. Portable telemetry units recorded heart rate at 60 s increments throughout the ultra-endurance triathlon. Heart rate during the cycle and run phases of the ultra-endurance triathlon (148 +/- 9 and 143 +/- 13 beats center dot min(-1) respectively) were significantly (P < 0.05) less than the second ventilatory thresholds (160 +/- 13 and 165 +/- 14 beats center dot min(-1) respectively) and heart rate deflection points (170 +/- 13 and 179 +/- 9 beats center dot min(-1) respectively). However, mean heart rate during the cycle and run phases of the ultra-endurance triathlon were significantly related to (r = 0.76 and 0.66; P < 0.01), and not significantly different from, the first ventilatory thresholds (146 +/- 12 and 148 +/- 15 beats center dot min(-1) respectively). Furthermore, the difference between heart rate during the cycle phase of the ultra-endurance triathlon and heart rate at the first ventilatory threshold was related to marathon run time (r = 0.61; P < 0.01) and overall ultra-endurance triathlon time (r = 0.45; P < 0.05). The results suggest that triathletes perform the cycle and run phases of the ultra-endurance triathlon at an exercise intensity near their first ventilatory threshold

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.