Free vibration analysis of cantilever plates by the method of superposition

The method of superposition is employed to analyze the first five symmetric and antisymmetric free vibration modes of a cantilever plate for a wide range of aspect ratios. It is shown that this method provides a simple, straightforward and highly accurate means of solution for this family of problems. Convergence to exact values is shown to be remarkably rapid. The first two symmetric and antisymmetric modal shapes for a square plate are accurately described by means of contour line drawings. The numerous advantages of this method over previously used methods are discussed. It is shown that it lends itself readily to the entire family of rectangular plates with classical edge conditions: i.e., clamped, simply supported, and free. Its applicability to a wide family of rectangular plates with boundary conditions other than the classical type is also discussed.     

A method for computer analysis of kinetics of competing first- and second-order reactions

Competing first- and second-order reactions of transient molecular species (e.g., triplet states and free radicals) are a common occurrence in kinetic studies such as flash photolysis and pulse radiolysis. We have developed a method for analyzing the decay kinetics of any species (Y) whose disappearance is described by ?dY/dt = k₁Y + k₂Y². The computer program (written in time-sharing BASIC) employs an iterative technique to obtain the least-squares estimates of the three parameters in the integrated rate equation.     

Integrating the Kuramoto-Sivashinsky equation in polar coordinates: application of the distributed approximating functional approach

An algorithm is presented to integrate nonlinear partial differential equations, which is particularly useful when accurate estimation of spatial derivatives is required. It is based on an analytic approximation method, referred to as distributed approximating functionals (DAF's), which can be used to estimate a function and a finite number of derivatives with a specified accuracy. As an application, the Kuramoto-Sivashinsky (KS) equation is integrated in polar coordinates. Its integration requires accurate estimation of spatial derivatives, particularly close to the origin. Several stationary and nonstationary solutions of the KS equation are presented, and compared with analogous states observed in the combustion front of a circular burner. A two-ring, nonuniform counter-rotating state has been obtained in a KS model simulation of such a burner.     

Alkaloid studies–XIX Alkaloids of some Hawaiian Rauwolfia species: The structure of sandwicine and its interconversion with ajmaline and ajmalidine

The alkaloid composition of the following three Hawaiian Rauwolfia species–R. sandwicensis A.DC., R. degeneri Sherff and R. mauiensis Sheriff–was determined. Aside from the known aklakoids serpentinine, ajmaline, tetraphylline and tetraphyllicine there were encountered trace amounts of two new dihydroindole alkaloids, mauiensine and sandwicensine as well as larger quantities of an isomer of ajmaline, which was named sandwicine (C₂₀H₂₆N₂O₂). Since sandwicine and ajmaline yield different dihydro derivatives which are convertible by lead tetra-acetate oxidation to a common indole hemi-acetal, sandwicine represents the C-17 epimer of ajmaline. Dihydrosandwicine was found to be identical with tetrahydroajmalidine, the sodium borohydride reduction product of ajmalidine, thereby proving that ajmalidine is 17-dehydroajmaline.     

An experimental study of the effects of pulsating and steady internal fluid flow on an elastic tube subjected to external vibration

The results of an experimental study on both pulsating and steady Newtonian fluid flow in an initially stretched rubber tube subjected to external vibration are reported. A circulating loop system was designed to maintain constant hydrostatic pressure throughout the tests so that the influence of external excitation on the fluid flow could be properly distinguished. The effects of fluid flow velocity and initial stretch rates on the dynamic response and damping of the tube conveying fluid were examined, and it was observed that damping ratios increase with increasing flow velocities, and generally decrease with increasing initial stretch rates for the tube conveying fluid. It was also noted that dynamic responses increase with increasing initial stretch rates, and decrease with increasing flow velocities. The effect of external vibration on fluid flow rates is small in a tube with a thickness-to-radius ratio (D_out−D_in)/D_in=0.617. Fluid pressures vary, in terms of frequency and amplitude, with external vibration as well as Womersley number.     

Dimerization of the transmembrane domain of amyloid precursor proteins and familial Alzheimer's disease mutants

Background  

Amyloid precursor protein (APP) is enzymatically cleaved by γ-secretase to form two peptide products, either Aβ40 or the more neurotoxic Aβ42. The Aβ42/40 ratio is increased in many cases of familial Alzheimer's disease (FAD). The transmembrane domain (TM) of APP contains the known dimerization motif GXXXA. We have investigated the dimerization of both wild type and FAD mutant APP transmembrane domains.     

Free vibration analysis of the completely free rectangular plate by the method of superposition

While the subject of free vibration analysis of the completely free rectangular plate has a history which goes back nearly two centuries it remains a fact that most theoretical solutions to this classical problem are considered to be at best approximate in nature. This is because of the difficulties which have been encountered in trying to obtain solutions which satisfy the free edge conditions as well as the governing differential equation. In a new approach to this problem, by using the method of superposition, it is shown that solutions which satisfy identically the differential equation and which satisfy the boundary conditions with any desired degree of accuracy are obtained. Eigenvalues of four digit accuracy are provided for a wide range of plate aspect ratios and modal shapes. Exact delineation is made between the three families of modes which are characteristic of this plate vibration problem. Accurate modal shapes are provided for the response of completely free square plates.     

The solution photochemistry of substituted cycloheptatrienes

The solution photochemistry of several ethoxycarbonyl- and ethoxycarbonyl-methoxy-substituted cycloheptatrienes has been investigated. The results have been used to analyse the directional specificity of ring-closure and 1,7-hydrogen migration reactions. This specificity is interpreted in terms of polarisation within the S₁ state which undergoes either (a) allowed photochemical reactions to give the observed products directly or (b) isomerisation to a trans, cis, cis-cyclohepatriene which then reacts via allowed ground-state processes. In at least two instances the directional specificity of the ring-closure reaction is wavelength dependent and this is attributed to the differing reactivities of the S₁ and S₂ states.