Analysis of the free vibration of a coupled plate/fluid interacting system and interpretation using sub-system modal energy

This paper describes a method for describing and quantifying the vibratory behaviour of interacting structural/fluid systems based upon reference to the relative energy associated with each of the sub-systems. The particular case selected is that of a circular plate in interaction with a cylindrical fluid cavity. A theoretical analysis is performed, based upon the Euler Bernoulli and Helmholtz equations combined through a Galerkin technique, from which the natural frequencies and associated mode functions of the interacting system are calculated. The convergence of the analysis is investigated and the opportunity is taken to investigate the sensitivity of the coupled natural frequencies to different assumed mode shapes of the plate in vacuo. Subsequently the coupled mode functions are used to describe details of the energy associated with the plate and the fluid. It is found that presentation of these relative energies renders a satisfactory insight into the vibration behaviour of the coupled system

Analysis of the vibration of pipes conveying fluid

The dynamic equilibrium matrix equation for a discretized pipe element containing flowing fluid is derived from the Lagrange principle, the Ritz method and consideration of the coupling between the pipe and fluid. The Eulerian approach and the concept of fictitious loads for kinematic correction are adopted for the analysis of geometrically non-linear vibration. The model is then deployed to investigate the vibratory behaviour of the pipe conveying fluid. The results for a long, simply supported, fluid-conveying pipe subjected to initial axial tensions are compared with experimentally obtained results and those from a linear vibration model

Vibration analysis of a circular disc backed by a cylindrical cavity

This paper describes the free vibration analysis of a thin disc vibrating and interacting with an acoustic medium contained in a cylindrical duct. The effects of structural-acoustic coupling are studied by means of an analytical-numerical method that is based upon classical theory and the Galerkin method. The coupling effects are discussed, and results obtained from the analysis are compared with corresponding values obtained both experimentally and from a finite element analysis. There is good agreement between the three sets of results

Vibration of a flexible pipe conveying viscous pulsating fluid flow

The non-linear equations of motion of a flexible pipe conveying unsteadily flowing fluid are derived from the continuity and momentum equations of unsteady flow. These partial di!erential equations are fully coupled through equilibrium of contact forces, the normal compatibility of velocity at the fluid} pipe interfaces, and the conservation of mass and momentum of the transient fluid. Poisson coupling between the pipe wall and fluid is also incorporated in the model. A combination of the finite difference method and the method of characteristics is employed to extract displacements, hydrodynamic pressure and flow velocities from the equations. A numerical example of a pipeline conveying fluid with a pulsating flow is given and discussed

Relaxation dynamics of the toric code in contact with a thermal reservoir: Finite-size scaling in a low temperature regime

We present an analysis of the relaxation dynamics of finite-size topological qubits in contact with a thermal bath. Using a continuous-time Monte Carlo method, we explicitly compute the low-temperature nonequilibrium dynamics of the toric code on finite lattices. In contrast to the size-independent bound predicted for the toric code in the thermodynamic limit, we identify a low-temperature regime on finite lattices below a size-dependent crossover temperature with nontrivial finite-size and temperature scaling of the relaxation time. We demonstrate how this nontrivial finite-size scaling is governed by the scaling of topologically nontrivial two-dimensional classical random walks. The transition out of this low-temperature regime defines a dynamical finite-size crossover temperature that scales inversely with the log of the system size, in agreement with a crossover temperature defined from equilibrium properties. We find that both the finite-size and finite-temperature scaling are stronger in the low-temperature regime than above the crossover temperature. Since this finite-temperature scaling competes with the scaling of the robustness to unitary perturbations, this analysis may elucidate the scaling of memory lifetimes of possible physical realizations of topological qubits.Comment: 14 Pages, 13 figure

The Effect of Prior Exposures on the Notched Fatigue Behavior of Disk Superalloy ME3

Environmental attack has the potential to limit turbine disk durability, particularly in next generation engines which will run hotter; there is a need to understand better oxidation at potential service conditions and develop models that link microstructure to fatigue response. More efficient gas turbine engine designs will require higher operating temperatures. Turbine disks are regarded as critical flight safety components; a failure is a serious hazard. Low cycle fatigue is an important design criteria for turbine disks. Powder metallurgy alloys, like ME3, have led to major improvements in temperature performance through refractory additions (e.g. Mo,W) at the expense of environmental resistance (Al, Cr). Service conditions for aerospace disks can produce major cycle periods extending from minutes to hours and days with total service times exceeding 1,000 hours in aerospace applications. Some of the effects of service can be captured by extended exposures at elevated temperature prior to LCF testing. Some details of the work presented here have been published

Revisiting Joseph Campbell’s The Power of Myth

This paper considers the relevance of The Power of Myth to the secular study of religion. First, I identify the scholars from whom Campbell borrows concepts. I organize these scholars into three groups – the qualitative religious scholars, the quantitative religious scholars, and those who draw from both approaches. Next, I identify Joseph Campbell’s key ideas (the monomyth, the hero’s journey, the existence of a higher power or energy, the lack of myth in the modern world, and the notion that religion possesses given qualities). I then analyze the contradictions inherent within Campbell’s argument, for Campbell fails to synthesize three scholarly traditions into one coherent theory of religion. Additionally, I discuss Campbell’s descriptive reductionism, his reactionary views regarding secularization, and the political conservatism found within the book. I conclude that Power is not an authoritative work of secular religious scholarship, but rather one man’s subjective blend of research and personal beliefs