Variational principles for constrained systems: Theory and experiment

In this paper we present two methods, the nonholonomic method and the vakonomic method, for deriving equations of motion for a mechanical system with constraints. The resulting equations are compared. Results are also presented from an experiment for a model system: a ball rolling without sliding on a rotating table. Both sets of equations of motion for the model system are compared with the experimental results. The effects of various forms of friction are considered in the nonholonomic equations. With appropriate friction terms, the nonholonomic equations of motion for the model system give reasonable agreement with the experimental observations.     

Stability of whirling shafts with internal and external damping

Necessary and sufficient conditions for the stability of motion of whirling shafts are established using the direct method of Liapunov. The non-linear mathematical model employed is based on the work of V. V. Bolotin and includes the effects of both internal and external damping. A coordinate transformation is used to facilitate the analysis. In effect, this transformation establishes a mathematical equivalence between the governing equations for a whirling shaft with both internal and external damping, and the governing equations for a whirling shaft with internal damping only.     

Experimental strain analysis of the losipescu shear test specimen

An experimental strain analysis of the losipescu shear test specimen was performed, utilizing a 20-ply AS4/3501-6 carbon/epoxy unidirectional composite. Using three-element strain-gage rosettes, it was shown that the presence of loading-point-induced transverse normal strains in the gage section do not affect the measured shear strain. Thus, the shear modulus determined using the standard notch specimen is not affected. Likewise, modulus determination is not influenced by cracking at the notch tips, since this occurs at strains beyond the range over which modulus is determined. To further evaluate the effect of notch-tip cracking, material was removed adjacent to the standard V-notches where these cracks initiate. The measured shear strength was unaffected by removing this material, although the shear modulus was reduced slightly (by as much as eight percent for the more grossly exaggerated geometries). E.Q. Lewis, former graduate student, is now Engineer, Lockheed Corporation.     

On the fidelity of high-speed photographic systems for dynamic photoelasticity

A general theory has been developed which predicts the influence of the characteristics of a high-speed recording system on the fidelity of a dynamic photoelastic-fringe pattern. The general theory was applied to recording systems currently employed in dynamic photoelasticity which include the high-speed framing camera, the spark-gap camera and the Q-spoiled laser system. Equations for a nondimensional form of the exposure as a function of normalized position have been developed for each of these three recording systems. From these equations, criteria to measure the fidelity of the recording systems were established. The methods developed are applied to the spark-gap system and examples of resolution limits, time shift and distortion are illustrated.     

Large deflections of cantilever beams of non-linear materials of the Ludwick type subjected to an end moment

This paper deals with the large deflections (finite) of thin cantilever beams of non-linear materials of the Ludwick type. The beam is subjected to an end constant moment. Large deflections of beams induce geometrical non-linearity. Therefore, in formulating the analysis, the exact expression of the curvature is used in the Euler-Bernoulli law. A closed-form solution is presented for the resulting second-order non-linear differential equation. This solution is compared to previous results assuming linear elastic materials. Deflections at the free end of beams of aluminum alloy and annealed copper are obtained.     

Preparation for Practice: Elementary Preservice Teachers Learning and Using Scientific Classroom Discourse Community Instructional Strategies

Despite historical national efforts to improve elementary science education, science instruction continues to be marginalized, varying by state. This study was designed to address the ongoing challenge of educating elementary preservice teachers (PSTs) to teach science. Elementary PSTs are one of the science education community's major links to schools and science education reform. However, they often lack a strong background in science, knowledge of effective science teaching strategies, and consequently have low confidence and self‐efficacy. This investigation explored the initial learning of elementary PSTs using an interdisciplinary model of a scientific classroom discourse community during a science methods course. Findings post‐methods course suggested that the PSTs gained confidence in how to teach inquiry‐based elementary science and recognized inquiry‐based science as an effective means for engaging student learning. Additionally, PSTs embraced the interdisciplinary model as one that benefits students' learning and effectively uses limited time in a school day.     

Radionuclide and chemical hazards of a radium ore revigator

A study to characterize the radionuclide and chemical components in a radium-ore revigator has been completed. Measured activities of dissolved ²²²Rn, ²²⁶Ra, and U isotopes, determined in the water using radioanalytical techniques, exceeded recommended limits in drinking-water supplies. Trace-metal concentrations, determined using inductively coupled plasma mass spectrometry, increased in the water with exposure time and exceeded recommended drinking-water limits for V and As. The contribution to, and dose from, the airborne radon-gas level in a room due to radon emanation from a revigator were evaluated. The annual committed effective dose resulting from consuming the radionuclides in the revigator water were estimated to be ~100 μSv/y for combined uranium and radium.     

Anionic Polymerization Characteristics of the 1:1 Complex of n-Butylsodium and n-,s-Dibutylmagnesium (Sodium Tributylmagnesiate)

The behavior of isoprene and styrene polymerizations initiated by the complex of n-butylsodium and n-,s-dibutylmagnesium (sodium tributylmagnesiate) has been examined. The styrene-benzene system was found to yield stable active centers and polymers of predictable molecular weight and narrow molecular weight distributions. Isoprene, however, did not follow this behavior and yielded polydisperse material having molecular weights lower than those predicted on the basis that only n-butylsodium is capable of initiating chain growth. The polyisprene microstructure was found to consist of ～60% 3,4 and ～40% 1,4 units.