Journal of Applied Mechanics, Transactions ASME
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Theory of Buckling of a Porous Slab and Its Thermoelastic Analogy A theory is developed for the buckling of a fluid-saturated porous slab under axial compression. The problem is discussed in the context of the thermodynamics of irreversible processes. It is shown that there is a range of compressive loads, between a lower and upper critical value, for which the slab exhibits creep buckling. The problem of folding instability of a porous layer embedded in a viscous or viscoelastic medium is also analyzed and the dominant wavelength is evaluated. Identical behavior is derived by analogy for a thermoelastic slab with a critical range between isothermal and adiabatic buckling. The theory is applicable to a large class of two-phase materials obeying the same thermodynamics. It also provides a simple analysis of thermoelastic damping of plates.
Journal of Applied Mechanics, Transactions ASME - Tập 31 Số 2 - Trang 194-198 - 1964
Funnel Flow in Hoppers Detailed observations of funnel flows of dry granular materials in wedge-shaped hoppers of different geometries are presented. The variations of the flow regime with changes in the height of material in the hopper/vertical bin configuration, the width of the vertical bin, the hopper angle and the hopper opening width were investigated and a number of specific flow regimes identified (mass flow and several forms of funnel flow). In the first part of the paper particular attention is paid to the conditions for transition from one flow regime to another; in particular it is shown that the existence of a funnel depends not only on the hopper angle but is also strongly dependent on the geometry of the hopper/bin system. In the second part of the paper the variations in the shape of the funnel near the exit opening are explored in detail.
Journal of Applied Mechanics, Transactions ASME - Tập 47 Số 4 - Trang 729-735 - 1980
Dynamic Axisymmetric Buckling of Shallow Conical Shells Subjected to Impulsive Loads A theoretical investigation is made of the axisymmetric snap-through buckling of a shallow conical shell subjected to an idealized impulse applied uniformly over the surface of the shell. The shell is assumed to behave as a single-degree-of-freedom system, and a study is made of the strain energy at maximum displacement: i.e., zero velocity. Under certain conditions this equilibrium position becomes unstable and the shell can snap through (or buckle). Nonlinear strain displacement equations are used and solutions are obtained for clamped and simply supported boundaries at the edge of the shell. Results for the cone are compared with similar results for a shallow spherical cap having the same rise as the cone. This comparison indicates that the spherical shell can resist a larger impulse than the conical shell before buckling.
Journal of Applied Mechanics, Transactions ASME - Tập 32 Số 1 - Trang 129-134 - 1965
Influences of Large Amplitudes, Transverse Shear Deformation, and Rotatory Inertia on Lateral Vibrations of Transversely Isotropic Plates In the present paper, using an improved Reissner’s variational theorem along with Berger’s hypothesis, a set of governing equations which include the effects of transverse shear deformation and rotatory inertia is derived for the large amplitude free vibrations of plates composed of a transversely isotropic material. Applying the possibility of neglecting the rotatory inertia in primarily flexural vibration (discussed in the previous work [1]2), the lateral free vibrations of simply supported plates are treated in detail and the solution is compared with those of previous investigators. The free vibration of beams is studied as a special case of plates, while the small amplitude vibrations are treated as a special case of large amplitude vibrations. The numerical results show that the effect of transverse shear deformation is significant when applying to the plate constructions made of pyrolytic graphite-type materials.
Journal of Applied Mechanics, Transactions ASME - Tập 36 Số 2 - Trang 254-260 - 1969
Some Solutions of the Timoshenko Beam Equations Abstract
Solutions are obtained by the method of Laplace transformation for four types of loadings applied to a semi-infinite beam. Numerical results are presented for two of these, both for suddenly applied and gradually varying loads. The effects of shear deformations and rotatory inertia are taken into account according to Timoshenko’s beam model. A comparison with the corresponding results of the Bernoulli-Euler theory are briefly presented.
Journal of Applied Mechanics, Transactions ASME - Tập 22 Số 4 - Trang 579-586 - 1955
Flexural Vibrations in Uniform Beams According to the Timoshenko Theory Abstract
The general series solution is given for the flexural vibrations in a uniform beam according to the Timoshenko equations, which include the secondary effects of shear and rotatory inertia. In addition, the series solution is presented for the case of a pin-ended beam. For the special case of a concentrated transient force at the mid-point of a pin-ended beam, the bending-moment and shear-force solutions according to the Timoshenko and elementary equations are compared.
Journal of Applied Mechanics, Transactions ASME - Tập 20 Số 4 - Trang 504-510 - 1953
Flexural Vibrations of Rectangular Plates Abstract
The influence of rotatory inertia and shear deformation on the flexural vibrations of isotropic, rectangular plates is investigated. Three independent families of modes are possible when the edges are simply supported. Coupling of the modes is studied for the case of one pair of parallel edges free and the other pair simply supported. The development of the coupling is traced by means of a solution for elastically supported edges. Special attention is given to the higher modes and frequencies of vibration which are beyond the range of applicability of the classical theory of thin plates.
Journal of Applied Mechanics, Transactions ASME - Tập 23 Số 3 - Trang 430-436 - 1956
Influence of Large Amplitudes on Free Flexural Vibrations of Rectangular Elastic Plates Abstract
In a recent paper (1) a set of plate equations was derived, which governs motions with small elongations and shears, but moderately large rotations, valid for an isotropic material obeying Hooke’s law. The resulting theory, which may be considered the dynamic analog of the von Karman plate theory, is applied presently to the study of free vibrations of a rectangular, elastic plate with hinged, immovable edges. The nonlinear equations are solved approximately by employing a perturbation procedure and also the principle of conservation of energy directly. The influence of large amplitudes on the period of free vibration and on the maximum normal stress is established. The free vibrations of a beam are studied as a special case and the resulting period compared with a previous investigation.
Journal of Applied Mechanics, Transactions ASME - Tập 23 Số 4 - Trang 532-540 - 1956
The Effects of Various Parameters on the Dynamic Stability of a Shallow Arch The effects of various parameters on the dynamic stability of shallow arches against snap-through when subjected to impulsive loads are investigated in this paper. The parameters are the amplitudes of the higher harmonics in the arch shape, the initial thrust, and the stiffness of the elastic supports at the arch ends. The results are expressed in terms of sufficiency regions of stability in a phase space of infinite dimensions, which, in turn, lead to simple and practical energy criteria. The study of the effects of the higher harmonics in the arch shape shows that the sufficiency stability criterion is sensitive only to the second harmonic. Moreover, for a sinusoidal arch with small amounts of imperfection, it is possible to give an explicit formula for the sufficiency criterion. The analysis presented here takes into account all modes in the response; consequently, the results are free from any uncertainties usually associated with most of the approximate analyses.
Journal of Applied Mechanics, Transactions ASME - Tập 34 Số 2 - Trang 349-358 - 1967
Stability of Shallow Arches Against Snap-Through Under Timewise Step Loads The dynamic stability of simply supported, shallow arches subjected to timewise step loads is studied in this paper. Presented is a general method which allows us to treat arches of arbitrary shape and load of arbitrary spatial distribution. Specific problems investigated are sinusoidal arches under sinusoidal loads, the effects of the second harmonics in the arch shape and in the load distribution, and sinusoidal arches subjected to uniform loads or concentrated and eccentric loads. The results are expressed in the form of sufficiency conditions for stability and sufficiency conditions for instability. The criteria given in this paper are reliable because the analysis does not involve truncating the solutions to a small number of modes.
Journal of Applied Mechanics, Transactions ASME - Tập 35 Số 1 - Trang 31-39 - 1968
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