Differential equation based method for accurate approximations in optimization

A method to efficiently and accurately approximate the effect of design changes on structural response is described. The key to this method is to interpret sensitivity equations as differential equations that may be solved explicitly for closed form approximations, hence, the method is denoted the Differential Equation Based (DEB) method. Approximations were developed for vibration frequencies, mode shapes and static displacements. The DEB approximation method was applied to a cantilever beam and results compared with the commonly-used linear Taylor series approximations and exact solutions. The test calculations involved perturbing the height, width, cross-sectional area, tip mass, and bending inertia of the beam. The DEB method proved to be very accurate, and in most cases, was more accurate than the linear Taylor series approximation. The method is applicable to simultaneous perturbation of several design variables. Also, the approximations may be used to calculate other system response quantities. For example, the approximations for displacements are used to approximate bending stresses

Rotor blade dynamic design

The rotor dynamic design considerations are essentially limitations on the vibratory response of the blades which in turn limit the dynamic excitation of the fuselage by forces and moments transmitted to the hub. Quantities which are associated with the blade response and which are subject to design constraints are discussed. These include blade frequencies, vertical and inplane hub shear, rolling and pitching moments, and aeroelastic stability margin

Recent advances in multidisciplinary optimization of rotorcraft

A joint activity involving NASA and Army researchers at NASA LaRC to develop optimization procedures to improve the rotor blade design process by integrating appropriate disciplines and accounting for all of the important interactions among the disciplines is described. The disciplines involved include rotor aerodynamics, rotor dynamics, rotor structures, airframe dynamics, and acoustics. The work is focused on combining these five key disciplines in an optimization procedure capable of designing a rotor system to satisfy multidisciplinary design requirements. Fundamental to the plan is a three-phased approach. In phase 1, the disciplines of blade dynamics, blade aerodynamics, and blade structure are closely coupled while acoustics and airframe dynamics are decoupled and are accounted for as effective constraints on the design for the first three disciplines. In phase 2, acoustics is integrated with the first three disciplines. Finally, in phase 3, airframe dynamics is integrated with the other four disciplines. Representative results from work performed to date are described. These include optimal placement of tuning masses for reduction of blade vibratory shear forces, integrated aerodynamic/dynamic optimization, and integrated aerodynamic/dynamic/structural optimization. Examples of validating procedures are described

Sensitivity derivatives and optimization of nodal point locations for vibration reduction

A method is developed for sensitivity analysis and optimization of nodal point locations in connection with vibration reduction. A straightforward derivation of the expression for the derivative of nodal locations is given, and the role of the derivative in assessing design trends is demonstrated. An optimization process is developed which uses added lumped masses on the structure as design variables to move the node to a preselected location; for example, where low response amplitude is required or to a point which makes the mode shape nearly orthogonal to the force distribution, thereby minimizing the generalized force. The optimization formulation leads to values for added masses that adjust a nodal location while minimizing the total amount of added mass required to do so. As an example, the node of the second mode of a cantilever box beam is relocated to coincide with the centroid of a prescribed force distribution, thereby reducing the generalized force substantially without adding excessive mass. A comparison with an optimization formulation that directly minimizes the generalized force indicates that nodal placement gives essentially a minimum generalized force when the node is appropriately placed

Optimal placement of tuning masses for vibration reduction in helicopter rotor blades

Described are methods for reducing vibration in helicopter rotor blades by determining optimum sizes and locations of tuning masses through formal mathematical optimization techniques. An optimization procedure is developed which employs the tuning masses and corresponding locations as design variables which are systematically changed to achieve low values of shear without a large mass penalty. The finite-element structural analysis of the blade and the optimization formulation require development of discretized expressions for two performance parameters: modal shaping parameter and modal shear amplitude. Matrix expressions for both quantities and their sensitivity derivatives are developed. Three optimization strategies are developed and tested. The first is based on minimizing the modal shaping parameter which indirectly reduces the modal shear amplitudes corresponding to each harmonic of airload. The second strategy reduces these amplitudes directly, and the third strategy reduces the shear as a function of time during a revolution of the blade. The first strategy works well for reducing the shear for one mode responding to a single harmonic of the airload, but has been found in some cases to be ineffective for more than one mode. The second and third strategies give similar results and show excellent reduction of the shear with a low mass penalty

An Empirically Derived Three-Dimensional Laplace Resonance in the Gliese 876 Planetary System

We report constraints on the three-dimensional orbital architecture for all four planets known to orbit the nearby M dwarf Gliese 876 based solely on Doppler measurements and demanding long-term orbital stability. Our dataset incorporates publicly available radial velocities taken with the ELODIE and CORALIE spectrographs, HARPS, and Keck HIRES as well as previously unpublished HIRES velocities. We first quantitatively assess the validity of the planets thought to orbit GJ 876 by computing the Bayes factors for a variety of different coplanar models using an importance sampling algorithm. We find that a four-planet model is preferred over a three-planet model. Next, we apply a Newtonian MCMC algorithm to perform a Bayesian analysis of the planet masses and orbits using an n-body model in three-dimensional space. Based on the radial velocities alone, we find that a 99% credible interval provides upper limits on the mutual inclinations for the three resonant planets ($\Phi_{cb}<6.20^\circ$ for the "c" and "b" pair and $\Phi_{be}<28.5^\circ$ for the "b" and "e" pair). Subsequent dynamical integrations of our posterior sample find that the GJ 876 planets must be roughly coplanar ($\Phi_{cb}<2.60^\circ$ and $\Phi_{be}<7.87^\circ$), suggesting the amount of planet-planet scattering in the system has been low. We investigate the distribution of the respective resonant arguments of each planet pair and find that at least one argument for each planet pair and the Laplace argument librate. The libration amplitudes in our three-dimensional orbital model supports the idea of the outer-three planets having undergone significant past disk migration.Comment: 19 pages, 11 figures, 8 tables. Accepted to MNRAS. Posterior samples available at https://github.com/benelson/GJ87

Studies on the Acculturation of Young Refugees in the Educational Domain: A Scoping Review of Research and Methods

Given that children and adolescents constitute a growing and significant share of forced migrants worldwide, assessing the state of research on and the methods used to study the acculturation of this group is both timely and essential. The acculturation of refugee children and adolescents in host countries occurs primarily within educational institutions and through the acquisition of the language of the new host society. This scoping review of peer-reviewed journal articles published between 1987 and 2016 (N = 192 eligible studies) examined the extent to which individual-level factors (e.g., gender, age) and contextual factors (e.g., country of residence) emphasized by acculturation models have been considered in research involving young refugees in the educational domain. In addition, the research designs and methods applied in these studies were evaluated, and content analysis was performed to examine whether individual-level factors considered in the sample of studies were related to educational outcomes of young refugees. Overall, the review revealed that very few studies provided adequate information on sample composition, or considered individual and contextual factors, thus leaving crucial gaps in the knowledge about the acculturation of young refugees. Guidelines for future research are proposed to remedy the identified research deficits

Heavy Drinking in University Students With and Without Attention-Deficit/Hyperactivity Disorder: Contributions of Drinking Motives and Protective Behavioral Strategies

This study examined rates of heavy drinking and alcohol problems in relation to drinking motives and protective behavioral strategies in university students with a documented current diagnosis of attention-deficit/hyperactivity disorder (ADHD; n = 31) compared with students with no history of ADHD (n = 146). Participants completed a Web-based questionnaire, and logistic regression models tested interactions between ADHD/comparison group membership and motives and protective strategies. Group differences in rates of heavy drinking and alcohol problems were not statistically significant, but medium-sized risk ratios showed that students without ADHD reported heavy drinking at a rate 1.44 times higher than students with ADHD and met screening criteria for problematic alcohol use at a rate of 1.54 times higher than students with ADHD. Other key findings were, first, that drinking to enhance positive affect (e.g., drinking because it is exciting), but not to cope with negative affect (e.g., drinking to forget your worries), predicted both heavy drinking and alcohol problems. Second, only protective behavioral strategies that emphasize alcohol avoidance predicted both heavy drinking and alcohol problems. Contrary to expectations, we found no ADHD-related moderation of effects of motives or protective strategies on our alcohol outcomes. Results of this study are limited by the small sample of students with ADHD but highlight tentative similarities and differences in effects of motives and strategies on drinking behaviors and alcohol problems reported by students with and without ADHD

The impact of impaired semantic knowledge on spontaneous iconic gesture production

Background: Previous research has found that people with aphasia produce more spontaneous iconic gesture than control participants, especially during word-finding difficulties. There is some evidence that impaired semantic knowledge impacts on the diversity of gestural handshapes, as well as the frequency of gesture production. However, no previous research has explored how impaired semantic knowledge impacts on the frequency and type of iconic gestures produced during fluent speech compared with those produced during word-finding difficulties. Aims: To explore the impact of impaired semantic knowledge on the frequency and type of iconic gestures produced during fluent speech and those produced during word-finding difficulties. Methods & Procedures: A group of 29 participants with aphasia and 29 control participants were video recorded describing a cartoon they had just watched. All iconic gestures were tagged and coded as either “manner”, “path only”, “shape outline” or “other”. These gestures were then separated into either those occurring during fluent speech or those occurring during a word-finding difficulty. The relationships between semantic knowledge and gesture frequency and form were then investigated in the two different conditions. Outcomes & Results: As expected, the participants with aphasia produced a higher frequency of iconic gestures than the control participants, but when the iconic gestures produced during word-finding difficulties were removed from the analysis, the frequency of iconic gesture was not significantly different between the groups. While there was not a significant relationship between the frequency of iconic gestures produced during fluent speech and semantic knowledge, there was a significant positive correlation between semantic knowledge and the proportion of word-finding difficulties that contained gesture. There was also a significant positive correlation between the speakers’ semantic knowledge and the proportion of gestures that were produced during fluent speech that were classified as “manner”. Finally while not significant, there was a positive trend between semantic knowledge of objects and the production of “shape outline” gestures during word-finding difficulties for objects. Conclusions: The results indicate that impaired semantic knowledge in aphasia impacts on both the iconic gestures produced during fluent speech and those produced during word-finding difficulties but in different ways. These results shed new light on the relationship between impaired language and iconic co-speech gesture production and also suggest that analysis of iconic gesture may be a useful addition to clinical assessment