Exact solutions for vibration and buckling of an SS-C-SS-C rectangular plate loaded by linearly varying in-plane stresses

Exact solutions are presented for the free vibration and buckling of rectangular plates having two opposite edges (x=0 and a) simply supported and the other two (y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress σ_x=−N₀[1−α(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement (w) to vary as sin(mπx/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients, for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and b yields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters α=0,0.5,1,1.5,2, for which α=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for α=0,1,2 obtained by the method of integration of the differential equation (α=0) or the method of energy (α=1,2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b=0.5,1,2 subjected to three types of loadings (α=0,1,2), with load intensities N₀/N_cr=0,0.5,0.8,0.95,1, where N_cr is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes are also shown.     

In vivo remineralization of acid-etched enamel in non-brushing areas as influenced by fluoridated orthodontic adhesive and toothpaste

This study aimed to evaluate the in vivo remineralization of acid-etched enamel in non-brushing areas as influenced by fluoridated orthodontic adhesive and toothpaste. One hundred and twenty teeth from 30 volunteers were selected. The teeth were assigned to four treatments: no treatment (negative control); 37% phosphoric acid-etching (PAE) (positive control); PAE + resin-modified glass ionomer cement (RMGIC); and, PAE + composite resin. Patients brushed teeth with fluoridated (n = 15) or non-fluoridated (n = 15) toothpastes, so that etched enamel was protected with screens and it was not in contact with the brush bristles. Remineralization was evaluated by means of laser fluorescence (LF), environmental scanning electronic microscopy, and energy dispersive spectrometry after extraction. The LF means were compared by means of Wilcoxon and Mann Whitney tests. Environmental scanning electron microscopy scores were compared among the groups using a Kruskal Wallis test, whereas the Ca/P ratio was evaluated by means of an Analysis of Variance with subparcels (treatments) and Tukey's post-hoc test. There were no statistically significant differences between the tooth pastes and between the orthodontic adhesives evaluated. Most teeth presented only partial enamel remineralization. Therefore, the fluoride released by the RMGIC was not enough to cause increased crystal regrowth in the acid-etched enamel. The use of fluoridated toothpaste did not provide positive additional effect.     

Coriolis acceleration analysis of planar mechanisms by complex-number algebra

One of the pitfalls in current methods of acceleration analysis of planar mechanisms is the difficulty in identifying the different types of acceleration components such as the “sliding” acceleration and the Coriolis contribution. Furthermore, the latter is often missed by the analyst altogether which then leads to completely false results in dynamic analysis. Even distinguished authors have on the record actual numerical examples where the wrong angular velocity was used in computing the Coriolis component. The present article demonstrates the acceleration analysis of planar mechanisms using complex-number algebra. This technique, when programmed for digital computation using complex-arithmetic, or using hand calculation, provides the magnitude and direction of all the acceleration components, including the Coriolis term, automatically without resort to such crutches as a “rule of thumb” for determining whether or not the latter is present, “traditional sign conventions”, and without the risk of using the wrong angular velocity. The procedure, derived here, is illustrated by examples.     

Modelling observed California Current mesoscale eddies and the ecosystem response

Satellite and in situ observations are used to test model dynamics for the California Current System (CCS). The model and data are combined to reconstruct the mesoscale ocean structure during a given three-week period. The resulting physical flow field is used to drive a 3D ecosystem model to interpret SeaWiFS and in situ chlorophyll-a (chl-a) variations. With this approach a more complete and consistent picture of the physical and ecosystem processes of the CCS is obtained, providing the basis for addressing fundamental questions about dynamics and predictability of the coastal ocean.     

Exploring How We Enjoy Antihero Narratives

Affective disposition theory (ADT), which nicely explains enjoyment of traditional hero narratives, appears somewhat limited in its ability to explain antihero narratives, primarily because of the moral complexity of the protagonists. Recent work proposes that viewers over time develop story schema that permit antihero enjoyment, despite character immorality. This article reports results from three studies that support this claim. Specifically, the findings indicate that moral judgment may be less important to antihero enjoyment than ADT would predict, that previous exposure to an antihero narrative alters responses to similar narratives, and that moral disengagement cues impact the enjoyment process. Ultimately, the studies offer empirical evidence of how antihero narratives are enjoyed differently than their traditional hero counterparts.     

Experimental Investigation of Wire Electrical Discharge Machining of NdFeB Permanent Magnets with an RC-Type Machine

This paper focuses on wire electrical discharge machining (WEDM) of devices made from commercially available sintered neodymium-iron-boron (NdFeB) rare-earth magnets that have been magnetized before machining. We conduct an experimental study to quantify the effects of the voltage and capacitance of an RC-type WEDM machine, as well as the magnet polarity, on slicing rate, mean kerf, and variation in kerf. We find that voltage and capacitance affect slicing rate, that voltage affects mean kerf, that no parameters tested affect the variation in kerf, and that the polarity of the magnet being machined does not affect the machining process. Linear regression is used to fit simple predictive models to the data with good agreement. Further analysis is performed to characterize the loss in permanent magnetization on the surface of the magnet due to heating during the machining process, and it is found that the outer layer of approximately 35 μm in depth is demagnetized when using the highest voltage and capacitance values tested.     

A Theorem about Computationalism and “Absolute” Truth

This article focuses on issues related to improving an argument about minds and machines given by Kurt Gödel in 1951, in a prominent lecture. Roughly, Gödel’s argument supported the conjecture that either the human mind is not algorithmic, or there is a particular arithmetical truth impossible for the human mind to master, or both. A well-known weakness in his argument is crucial reliance on the assumption that, if the deductive capability of the human mind is equivalent to that of a formal system, then that system must be consistent. Such a consistency assumption is a strong infallibility assumption about human reasoning, since a formal system having even the slightest inconsistency allows deduction of all statements expressible within the formal system, including all falsehoods expressible within the system. We investigate how that weakness and some of the other problematic aspects of Gödel’s argument can be eliminated or reduced.