Journal of Applied Mechanics, Transactions ASME
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On the Stability of Some Linear Nonautonomous Random Systems A theorem and two corollaries for the almost sure stability of linear nonautonomous random systems are presented. These results are applied to the study of the stability properties of some often encountered second-order equations and the obtained stability conditions are compared to previously known criteria.
Journal of Applied Mechanics, Transactions ASME - Tập 35 Số 1 - Trang 7-12 - 1968
Crack-Extension Force for a Part-Through Crack in a Plate The crack stress-field parameter K and crack-extension force G at boundary points of a flat elliptical crack may be derived from knowledge that normal tension produces an ellipsoidal crack opening. Rough correction procedures can be employed to adapt this result for application to a part-through crack in a plate subjected to tension. Experimental measurements suggest this adapted result has a useful range of accuracy.
Journal of Applied Mechanics, Transactions ASME - Tập 29 Số 4 - Trang 651-654 - 1962
Analysis of Stresses and Strains Near the End of a Crack Traversing a Plate Abstract
A substantial fraction of the mysteries associated with crack extension might be eliminated if the description of fracture experiments could include some reasonable estimate of the stress conditions near the leading edge of a crack particularly at points of onset of rapid fracture and at points of fracture arrest. It is pointed out that for somewhat brittle tensile fractures in situations such that a generalized plane-stress or a plane-strain analysis is appropriate, the influence of the test configuration, loads, and crack length upon the stresses near an end of the crack may be expressed in terms of two parameters. One of these is an adjustable uniform stress parallel to the direction of a crack extension. It is shown that the other parameter, called the stress-intensity factor, is proportional to the square root of the force tending to cause crack extension. Both factors have a clear interpretation and field of usefulness in investigations of brittle-fracture mechanics.
Journal of Applied Mechanics, Transactions ASME - Tập 24 Số 3 - Trang 361-364 - 1957
Capillary Flow in Triangular Grooves Solutions to the two-dimensional equations of motion for steady laminar flow in grooves are obtained by the Galerkin boundary method. The two independent parameters which characterize the flow configuration are the half angle of the liquid-filled triangular groove and the contact angle of the shear-free meniscus. The analytical results include dimensionless velocity contours, average velocity, hydraulic diameter, and area. The friction factor coefficient K, where f = K/Re and Re is Reynolds number based upon hydraulic diameter, is also found. Results are reported for channel half angles from 5–60 deg and contact angles from 0.1 deg to the complementary angle (full groove condition). Comparisons with analysis and experimental data for the full groove are made and found to be excellent.
Journal of Applied Mechanics, Transactions ASME - Tập 41 Số 2 - Trang 332-336 - 1974
On Natural Vibrations and Waves in Laminated Orthotropic Plates A solution method is presented for studying the vibrations of a laminated plate composed of an arbitrary number of bonded elastic, orthotropic layers. The analysis is carried out within the framework of linear elasticity for plane-strain behavior. The essence of the method is a discretization of the plate into arbitrarily large number of laminas, each of which comprise a separate entity. An approximate displacement field is assumed for each lamina and is characterized by a discrete number of generalized coordinates at the laminar bounding planes and at its midsurface. An algebraic eigenvalue problem results, whose solution yields the frequencies and modal displacement patterns, the 10 lowest which are determined. Stresses are calculated in a straightforward manner from eigenvectors. A homogeneous isotropic plate is studied to ascertain the accuracy and effectiveness of this method and examples on homogeneous and laminated orthotropic plates are given to offer some insight on their physical behavior.
Journal of Applied Mechanics, Transactions ASME - Tập 39 Số 3 - Trang 739-745 - 1972
Edge Vibrations in Laminated Composite Plates Plane strain edge vibrations or end modes in laminated composite plates are investigated by means of finite elements. This method is capable of modeling the behavior of any laminate construction whose properties are completely anisotropic within the plane. Two eigenvalue problems involving nonsymmetric matrices are derived. The form of each eigenvalue problem depends on the parameter chosen for the eigenvalue, i.e., either the frequency or the axial wave number. Orthogonality relations are discussed. Examples on two four-ply composite plates are given as illustrations. The analogy of the analysis procedure as the dynamic counterpart of the quantitative measure of Saint-Venant’s principle is called to attention.
Journal of Applied Mechanics, Transactions ASME - Tập 52 Số 2 - Trang 433-438 - 1985
Waves in Prismatic Guides of Arbitrary Cross Section A formulation based on extended Rayleigh-Ritz is presented for waves and vibrations in orthotropic prismatic bars of arbitrary cross section. The scope and effectiveness of the method is demonstrated through case study of square guides. Basic features of the analysis such as accuracy are discussed.
Journal of Applied Mechanics, Transactions ASME - Tập 40 Số 4 - Trang 1067-1072 - 1973
Vortex-Induced Oscillations: A Selective Review This paper reviews the vortex-induced oscillations in a few specific fundamental cases. Research topics discussed are vortex shedding from a stationary bluff body; consequences of the synchronization phenomenon; wake-oscillator models; added mass, damping, and dynamic response measurements; flow-field models and the discrete-vortex method; mechanism of synchronization; and, finally, in-line oscillations. Because of the selective nature of the review, a fairly comprehensive listing of recent contributions to the literature on these and related aspects of flow-induced oscillations research is an essential part of the exposition.
Journal of Applied Mechanics, Transactions ASME - Tập 46 Số 2 - Trang 241-258 - 1979
Multiscale, Multiphenomena Modeling and Simulation at the Nanoscale: On Constructing Reduced-Order Models for Nonlinear Dynamical Systems With Many Degrees-of-Freedom The large number of degrees-of-freedom of finite difference, finite element, or molecular dynamics models for complex systems is often a significant barrier to both efficient computation and increased understanding of the relevant phenomena. Thus there is a benefit to constructing reduced-order models with many fewer degrees-of-freedom that retain the same accuracy as the original model. Constructing reduced-order models for linear dynamical systems relies substantially on the existence of global modes such as eigenmodes where a relatively small number of these modes may be sufficient to describe the response of the total system. For systems with very many degrees-of-freedom that arise from spatial discretization of partial differential equation models, computing the eigenmodes themselves may be the major challenge. In such cases the use of alternative modal models based upon proper orthogonal decomposition or singular value decomposition have proven very useful. In the present paper another facet of reduced-order modeling is examined, i.e., the effects of “local” nonlinearity at the nanoscale. The focus is on nanoscale devices where it will be shown that a combination of global modal and local discrete coordinates may be most effective in constructing reduced-order models from both a conceptual and computational perspective. Such reduced-order models offer the possibility of reducing computational model size and cost by several orders of magnitude.
Journal of Applied Mechanics, Transactions ASME - Tập 70 Số 3 - Trang 328-338 - 2003
The Nonlinear Gaussian Spectrum of Log-Normal Stochastic Processes and Variables A procedure is presented in this paper for developing a representation of lognormal stochastic processes via the polynomial chaos expansion. These are processes obtained by applying the exponential operator to a gaussian process. The polynomial chaos expansion results in a representation of a stochastic process in terms of multidimensional polynomials orthogonal with respect to the gaussian measure with the dimension defined through a set of independent normalized gaussian random variables. Such a representation is useful in the context of the spectral stochastic finite element method, as well as for the analytical investigation of the mathematical properties of lognormal processes.
Journal of Applied Mechanics, Transactions ASME - Tập 66 Số 4 - Trang 964-973 - 1999
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