Configuration Design Sensitivity Analysis of Kinematic Responses of Mechanical Systems∗

Abstract

A continuum-based configuration design sensitivity analysis method is presented for kinematically driven mechanical systems. Configuration design variable for mechanical systems are defined. The 3-1-3 Euler angle is used as the orientation design variable. The reassembly process for a mechanical system after a configuration design change is eliminated by imposing kinematic admissibility conditions of the velocity field. The direct differentiation method is used to derive design sensitivity equations. Numerical examples are presented to demonstrate the validity and effectiveness of the proposed method.     

Synthesis and properties of isopropylamine borane i-C3H7NH2 · BH3

Isopropylamine borane i-C₃H₇NH₂ · BH₃ was synthesized by the reaction of sodium tetrahydroborate NaBH₄ with isopropylamine hydrochloride in tetrahydrofuran followed by extraction with diethyl ether. Its synthesis conditions were determined and optimized. The compound was characterized by chemical analysis, IR spectroscopy, and differential thermal analysis.     

Cyclization of citronellal in a supercritical solvent in a flow reactor in the presence of Al2O3

The reactivity of citronellal under supercritical solvent conditions in a flow reactor in the presence of Al₂O₃ is examined. It is shown that at 160°C, the main transformation product of citronellal is isopulegol, and when the temperature is increased to 190°C, they are monoterpenes with a para-menthane framework and myrcene.     

A least‐square weighted residual method for level set formulation

In this paper, a least‐square weighted residual method (LSWRM) for level set (LS) formulation is introduced to achieve interface capturing in two‐dimensional (2D) and three‐dimensional (3D) problems. An LSWRM was adopted for two semi‐discretized advection and reinitialization equations of the LS formulation. The present LSWRM provided good mathematical properties such as natural numerical diffusion and the symmetry of the resulting algebraic systems for the advection and reinitialization equations. The proposed method was validated by solving some 2D and 3D benchmark problems such as those involving a rotating slotted disk, the rotation of a slotted sphere, and a time‐reversed single‐vortex flow and a deformation problem of a spherical fluid. The numerical results were compared with those obtained from essentially non‐oscillatory type formulations and particle LS methods. Further, the proposed LSWRM for the LS formulation was coupled with a splitting finite element method code to solve the incompressible Navier–Stokes equations, and then, the collapse of a 3D broken dam flow was well simulated; in the simulation, the entrapping of air and the splashing of the surge front of water were reproduced. The mass conservation of the present method was found to be satisfactory during the entire simulation. Copyright © 2011 John Wiley & Sons, Ltd.     

Rate responses of auditory nerve fibers to tones in noise near masked threshold

The rate responses of auditory nerve fibers were measured for best frequency (BF) tone bursts in the presence of continuous background noise. Rate functions for BF tones were constructed over a 32-dB range of levels, centered on the behavioral masked thresholds of cats. The tone level at which noticeable rate changes are evoked by the tones corresponds closely to behavioral masked threshold at all noise levels used (-10- to 30-dB spectrum level). As the noise level increases, the response rate to the background noise approaches saturation, and the incremental rate response to tones decreases. At high noise levels, the rate responses to tones of low and medium spontaneous rate fibers are larger than those of high spontaneous rate fibers. Empirical statistics of auditory nerve fiber spike counts are reported; these differ from those expected of a Poisson process in that the variance is smaller than the mean. A new measure of discharge rate is described that allows rate changes to be expressed in units of a standard deviation. This measure allows tone-evoked responses to be interpreted in terms of their detectability in a signal detection task. Rate responses of low and medium spontaneous rate fibers are more detectable than those of high spontaneous rate fibers, especially at high noise levels. There appears to be sufficient information in the rate response of a small number of auditory nerve fibers to support behaviorally observed levels of detection performance.