The Vibration Of Beams And Plates Studied Using Orthogonal Polynomials

The orthogonally generated polynomials proposed by R. B. Bhat as admissible functions for use in the Rayleigh-Ritz method by dynamic and static problems of single-span beams and rectangular plates are generalized for use in the study of various more complicated beam and plate problems. The orthogonal polynomials themselves are discussed in some detail. These functions are then used in the Rayleigh-Ritz method to obtain solutions for the free vibration problems of slender beams, thin rectangular plates, a box-like structure, and thin annular, circular and sectorial plates. Various complicating effects are included.;The approach presented in this thesis is straightforward but more general than the approaches presented previously in the literature. The accuracy and versatility of the approach are demonstrated using various example problems. Numerical results are generated both for new problems and for problems for which comparison results are available in the literature.;For the vibration problem of slender beams, the analysis is presented for beams subject to complicating factors which include the existence of an arbitrary number of concentrated masses (with or without rotary inertia) and/or intermediate simple supports, and subject to any combination of free, simply supported or clamped boundary conditions and/or elastic supports. The effects of constant axial loading (either constant directional or tangential follower force) and variable cross section are also included.;For thin rectangular plates, the analysis is presented for rectangularly orthotropic plates (which include the isotropic case) with any number of intermediate line supports and point supports. (The Lagrangian multiplier method is used for point supported plates.) The analysis is further extended to one type of box-like structure.;The analysis of annular plates includes the effects of polar orthotropy, intermediate concentric ring supports and radially varying thickness. By permitting the inner radius to become very small, circular plates are also treated, including the case with a central point support.;Finally, annular and circular sectorial plates are treated. Again the analysis includes several complicating effects such as polar orthotropy, intermediate simple supports in both radial and circumferential directions and varying thickness in both directions

Optimal Design of a Fully Parallel Robot Manipulator.

Optimal design of a six degrees-of-freedom, fully parallel manipulator, called a Stewart platform is investigated. In order to optimize the mechanism, new performance measures are introduced since use of the previous methods suffer from lack of physical meaning due to dimensional inhomogeneity. To overcome the dimensional inhomogeneity problem, an Euclidean norm definition of each output space with homogeneous dimension is used to find input-output norm relation. As a result, four sets of eigenvalues are obtained which characterize translational and rotational velocity, force and torque, and position and orientation accuracy. From the four sets of eigenvalues, four determinant measures are defined, which represent the magnitude of the input-output transformation and four condition number measures are defined which are indices of uniform transformation. The invariant property of the new measures is investigated under the scaling operation. By the simplification of the design problem, the explicit equations of performance measures are derived which provide the valuable tools to analyze the parametric space of the design variables. Using the explicit formulation, singular configurations can be identified at home positions of the manipulator. It is shown that parameters satisfying the isotropic condition form the surfaces of the simple geometric entities, called the cones and cylindroids in cylindrical coordinates. These geometric entities provide the insight to figure out the behavior of the performance measures in the parametric space. Using the geometric entities, three optimum solutions are found: one for force capacity and position accuracy and one for the torque capacity and rotation accuracy and one for both aspects. It is shown that there are two isotropic surfaces corresponding to each given condition number not equal to one and in all the region bounded by the two surfaces the condition numbers are less than the given condition number. Using these facts, a minimax problem is solved for condition number measures. It is shown that the achievable minimum condition number is obtained when the geometric average of the upper and lower limit of the operating height is on the isotropic surface. The result is used to determine the adequate operating range

Epidemic Response Coordination Networks in “Living Documents”

Response plans developed thoroughly are suggestive of a successful action, but there is a gap in the literature with respect to the way concerted efforts among organizations are planned and change during crises. Using organizational network data extracted from the South Korean government’s MERS response manuals, we examined the changes in the response coordination network planned during the epidemic’s distinct stages. The greatest difference in predicting tie formation was found in the networks planned before the event and revised during the outbreak. Local and governmental actors tend to form more ties consistently in the revised manuals. Two actors that are intended to transfer medical and/or personnel resources tend to form more ties across all stages. These findings suggest that transferring material and/or human resources are key activities in the epidemic response and planners tend to increase the connection of local and governmental actors over time

Geomagnetic field influences probabilistic abstract decision-making in humans

To resolve disputes or determine the order of things, people commonly use binary choices such as tossing a coin, even though it is obscure whether the empirical probability equals to the theoretical probability. The geomagnetic field (GMF) is broadly applied as a sensory cue for various movements in many organisms including humans, although our understanding is limited. Here we reveal a GMF-modulated probabilistic abstract decision-making in humans and the underlying mechanism, exploiting the zero-sum binary stone choice of Go game as a proof-of-principle. The large-scale data analyses of professional Go matches and in situ stone choice games showed that the empirical probabilities of the stone selections were remarkably different from the theoretical probability. In laboratory experiments, experimental probability in the decision-making was significantly influenced by GMF conditions and specific magnetic resonance frequency. Time series and stepwise systematic analyses pinpointed the intentionally uncontrollable decision-making as a primary modulating target. Notably, the continuum of GMF lines and anisotropic magnetic interplay between players were crucial to influence the magnetic field resonance-mediated abstract decision-making. Our findings provide unique insights into the impact of sensing GMF in decision-makings at tipping points and the quantum mechanical mechanism for manifesting the gap between theoretical and empirical probability in 3-dimensional living space.Comment: 32 pages, 5 figures, 4 supplementary figures, 2 supplementary tables, and separate 15 ancillary file

The characteristic comparison of the accelerometer and the gyroscope in the measurement of human body sway

This study investigated the human body sway measuring instruments. An accelerometer and a gyroscope were used to examine patients with postural control related diseases in many studies. Some studies used either an accelerometer or a gyroscope attached to the head, chest, or waist to obtain the balance assessment parameters of body sway such as area, direction, etc. The purpose of this study is to identify the reliability between both sensors in human body sway analysis by assuming the human body sway as a simple pendulum model, and suggest an optimal measurement method using the acceleration and the gyroscope. The characteristic differences between the accelerometer and the gyroscope were illustrated, focusing mainly on the differences with respect to the position of the sensors. We confirmed that the magnitude, instead of three axis vector information, may be more useful in the body sway analysis