615 research outputs found
Stability of parametrically forced linear systems
The stability analysis of constant-coefficient linear systems is extended to systems with periodically-varying coefficients. Although this theory is mathematically well-understood, little work has been done regarding its application to physical problems. All previous results are based on asymptotic analysis. A review of the theory of parametrically-forced linear systems will be presented, followed by a detailed stability analysis of a pendulum with a harmonically moving base
Three dimensional inelastic finite element analysis of laminated composites
Formulations of the inelastic response of laminated composites to thermal and mechanical loading are used as the basis for development of the computer NALCOM (Nonlinear Analysis of Laminated Composites) computer program which uses a fully three dimensional isoparametric finite element with 24 nodes and 72 degrees of freedom. An incremental solution is performed with nonlinearities introduced as pseudoloads computed for initial strains. Equilibrium iteration may be performed at every step. Elastic and elastic-plastic response of boron/epoxy and graphite/epoxy graphite/epoxy and problems of curing 0/90 sub s Gr/Ep laminates with and without circular holes are analyzed. Mechanical loading of + or - 45sub s Gr/Ep laminates is modeled and symmetry conditions which exist in angle-ply laminates are discussed. Results are compared to experiments and other analytical models when possible. All models are seen to agree reasonably well with experimetnal results for off-axis tensile coupons. The laminate analyses show the three dimensional effects which are present near holes and free corners
On a general solution of Hill's equation
i. ON A GENERAL SOLUTION OF HILL'S EQUATION.
BY
E. LINDSAY INCE. Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,
Vol. LXIV. No. 5. •
ii. NOTES ON THE GENERAL SOLUTION OF HILL'S
EQUATION.
BY
E. LINDSAY INCE. Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,
Vol. LXXVI. No. 5. •
iii. FURTHER NOTES ON THE GENERAL SOLUTION
OF HILL'S EQUATION.
BY
E. LINDSAY INCE.
Reprinted from the MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY,
Vol. LXXVIII. No. 2. •
iv. On the continued fractions associated with the hypergenerative equatio
Dynamics of a class of vortex rings
The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows
Periodic orbits for space-based reflectors in the circular restricted three-body problem
The use of space-based orbital reflectors to increase the total insolation of the Earth has been considered with potential applications in night-side illumination, electric power generation and climate engineering. Previous studies have demonstrated that families of displaced Earth-centered and artificial halo orbits may be generated using continuous propulsion, e.g. solar sails. In this work, a three-body analysis is performed by using the circular restricted three body problem, such that, the space mirror attitude reflects sunlight in the direction of Earth’s center, increasing the total insolation. Using the Lindstedt–Poincaré and differential corrector methods, a family of halo orbits at artificial Sun–Earth L2 points are found. It is shown that the third order approximation does not yield real solutions after the reflector acceleration exceeds 0.245 mm s−2, i.e. the analytical expressions for the in- and out-of-plane amplitudes yield imaginary values. Thus, a larger solar reflector acceleration is required to obtain periodic orbits closer to the Earth. Derived using a two-body approach and applying the differential corrector method, a family of displaced periodic orbits close to the Earth are therefore found, with a solar reflector acceleration of 2.686 mm s−2
The influence of gyroscopic forces on the dynamic behavior and flutter of rotating blades
The structural dynamics of a cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever turbomachine blade mounted on a spinning and precessing rotor are investigated. Both stability and forced vibration are considered with a blade model that increases in complexity (and verisimilitude) from a spring-restrained point mass, to a uniform cantilever, to a twisted uniform cantilever, to a tapered twisted cantilever of arbitrary cross-section. In every instance the formulation is from first principles using a finite element based on beam theory. Both ramp-type and periodic-type precessional angular displacements are considered. In concluding, forced vibrating and flutter are studied using the final and most sophisticated structural model. The analysis of stability is presented and a number of numerical examples are worked out
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