Showing papers on "Elasticity (economics) published in 1972"
TL;DR: In this article, a theory of non-local elasticity is presented via the vehicles of global balance laws and the second law of thermodynamics via the use of a localized Clausius-Duhem inequality and a variational statement of Gibbsian global thermodynamics.
2,201 citations
TL;DR: In this article, the dispersion relations for one dimensional plane waves were obtained by fitting the nonlocal material moduli to exactly the acoustical branch of elastic waves within one Brillouin zone in periodic one dimensional lattices.
1,101 citations
TL;DR: In this paper, a variational principle governing frictionless contact between two elastic bodies is established, which is valid both for linear and for non-linear elasticity, in the case of linear elasticity it appears to lead to an infinite dimensional convex quadratic programming problem.
Abstract: A variational principle governing the frictionless contact between two elastic bodies is established, which is valid both for linear and for non-linear elasticity. In the case of linear elasticity it appears to lead to an infinite dimensional convex quadratic programming problem. It is applied to the half-space geometry in linear elasticity and it is established that non-Hertzian normal half-space contact problems are physically meaningful. A Hertzian and a non-Hertzian normal contact problem are investigated numerically, to which end the principle is discretised on a triangular network. In the case of the Hertz problem it is found that the exact relationships between penetration, maximum pressure, and total normal force are well satisfied. The form of the contact area is given only crudely, unless the discretisation network is considerably refined. It appeared that such a refinement is only necessary close to the edge, in which case passable results will be obtained.
186 citations
TL;DR: In this article, a new theory was proposed which considers molecular repulsions and thus properly predicts the minimal nature of the interaction functions and the influence of elastic flattening on the interaction force and energy.
174 citations
TL;DR: In this paper, the authors measured compressional and shear wave velocities in 13 directions at pressures to 10 kb in olivine and bronzitite at the Twin Sisters peaks, Washington and the Stillwater Complex, Montana, respectively.
Abstract: Compressional and shear wave velocities in 13 directions at pressures to 10 kb were measured in dunite from the Twin Sisters peaks, Washington, and in bronzitite from the Stillwater Complex, Montana. Dunite is characterized by a strong preferred orientation of olivine grains, leading to anisotropy of velocity of 15% at 10 kb. The bronzitite is more nearly isotropic, the greatest difference of P wave velocities reaching 6%. The comparison of elasticity diagrams, obtained at pressures of 0.5 kb and 10 kb, shows that the system of pores, more open at low pressure, is of minor influence; anisotropy is controlled mainly by the preferred orientation of olivine and bronzite in both rocks. Most of the compressional and shear wave velocities, calculated according to Voigt's scheme on the basis of petrofabric determinations and published single-crystal data for olivine and bronzitite, are in good agreement with the ultrasonic velocities measured at 10 kb. The results confirm the possibility of using this procedure to determine anisotropic elasticity of simple aggregates and suggest a possibility of using ultrasonic measurements in petrostructural analysis.
98 citations
TL;DR: A survey of the literature which describes the dynamic behavior of mechanism links with continuously distributed mass and elasticity is presented and selected references on other mechanism problems which also give rise to parametrically excited systems are discussed.
81 citations
72 citations
TL;DR: In this paper, two-dimensional equations of successively higher orders of approximation for elastic, isotropic plates are deduced from the three-dimensional theory of elasticity by a series expansion in terms of simple thickness-modes for infinite plates.
69 citations
51 citations
Patent•
06 Nov 1972
TL;DR: In this paper, a piezoelectric type electroacoustic transducer element having a high sensitivity in a high frequency region is composed of a PEG polymer sheet having on one surface thereof a backing of a material having a larger elasticity (Young''s Modulus) and mass than the elasticity and mass of the PEG sheet.
Abstract: A piezoelectric type electroacoustic transducer element having a high sensitivity in a high frequency region is composed of a piezoelectric polymer sheet having on one surface thereof a backing of a material having a larger elasticity (Young''s Modulus) and mass than the elasticity and mass of the piezoelectric polymer sheet.
01 Jan 1972
TL;DR: In this paper, the second-order elasticity problem is reduced to the solution of an equation of the form E 4 ψ = ƒ(R, Z) where E 2 is Stokes' differential operator, R, Z are cylindrical polar coordinates, and depends only on the first-order solution.
Journal Article•
TL;DR: In this article, a small-scale apparatus was used to examine the effects of surface materials on the initiation of waves on water by the action of wind, and the effect of various forms of subsequent contamination were investigated, using a sensitive moire fringe wave slope observation technique.
Abstract: A small-scale apparatus was used to examine the effects of surface materials on the initiation of waves on water by the action of wind. Rigorous procedures were followed to ensure freedom from contamination of the initial water surface, and the effect of various forms of subsequent contamination were investigated, using a sensitive moire fringe wave slope observation technique. Provision was made in the design of the water container for insoluble films to circulate, avoiding the downwind buildup of contamination.In measurements on pure water surfaces, no evidence of a ‘critical wind velocity’ was found, although slightly contaminated water was found to be appreciably less responsive to the wind excitation at wind speeds up to 4 m s−l. Measurements on monolayer-covered surfaces showed that, at these wind speeds, a compressed monolayer of relatively high surface tension and low dilational elasticity can have a greater stilling effect than one of low surface tension and high dilational elasticity. Measurements on a series of solutions of surface-active material, covering a range of surface tensions from 63 to 26 mN m−l at a concentration expected to reduce dilational elasticity by bulk-to-surface diffusion, indicated that the damping effect becomes steadily greater as the surface tension decreases.
TL;DR: The elastic properties of plant cell walls are major factors controlling the swelling and shrinking of plant cells under conditions of varying water stress and the importance of these properties for the adaptation of plants to the changing water stresses they encounter is discussed in this paper.
Abstract: The elastic properties of plant cell walls are major factors controlling the swelling and shrinking of plant cells under conditions of varying water stress. The importance of these properties for the adaptation of plants to the changing water stresses they encounter is discussed.
Patent•
09 Nov 1972
TL;DR: A woven fabric is a laminate that consists of a warp comprising metallic fibers with or without non-metallic fibers, and a weft that comprises nonmetallic resilient fibers, adjacent portions of the weft being offset in opposite directions to have a wave form as discussed by the authors.
Abstract: A woven fabric comprising a laminate that consists of a warp comprising metallic fibers with or without non-metallic fibers, and a weft that comprises non-metallic resilient fibers, adjacent portions of the weft being offset in opposite directions to have a wave form, the fabric thus formed being coated with an elastomer and has non-setting elasticity as a wrapper around objects such as poles, tubes, and the like.
Patent•
17 Mar 1972
TL;DR: A FLEXIBLE SYNTHETIC SURFACE STRUCTURED WEB MATERIAL EMBODYING a DISCONTINUOUS UPPER LAYER FORMED of CROSSLINKED PLASTIC with a YouNG's Bending MODULUS of ELASTICITY in a RANGE of 10,000 to 30,000 KG/CM.2, there is APPLIED SUCH QUANTITY of this MASS TOTHE MOLD ING BAND that only the RECESSES THEREOF are
Abstract: A FLEXIBLE SYNTHETIC SURFACE STRUCTURED WEB MATERIAL EMBODYING A DISCONTINUOUS UPPER LAYER FORMED OF CROSSLINKED PLASTIC WITH A YOUNG''S BENDING MODULUS OF ELASTICITY IN A RANGE OF 10,000 TO 30,000 KG./CM.2 AND A CONTINUOUS LOWER ALYER OR STRATUM FORMED OF CROSS-LINKED PLASTIC WITH A YOUNG''S BENDING MODULUS OF ELASTICITY IN A RANGE OF 3,000 TO 10,000 KG./CM.2 BOTH LAYERS BEING BONDED TO ONE ANOTHER BY COMMON OR JOINT POLYMERIZATION. THE METHOD FOR THE PRODUCTION OF SUCH FLEXIBLE SYNTHETIC SURFACE STRUCTURED WEB MATERIALS COMPRISES APPLYING TO A MOLDING BAND POSSESSING RECESSES A FIRST MASS CONTAINING A HARDENABLE POLYESTER MIIXTURE, POSSESSING A YOUNG''S BENDING MODULUS OF ELASTICITY FOLLOWING POLYMERIZATION WHICH IS IN A RANGE OF 10,000 TO 30,000 KG./CM.2, THERE IS APPLIED SUCH QUANTITY OF THIS MASS TOTHE MOLD ING BAND THAT ONLY THE RECESSES THEREOF ARE FILLED, AND THEREAFTER SUCH MASS IS GELLED. A SECOND MASS IS APPLIED TO THE GELLED COOLED MASS DICUSSED ABOVE, THIS SECOND MASS CONTAINING A HARDENABLE POLYESTER MIXTURE POSSESSING A YOUNG''S BENDING MODULUS OF ELASTICITY FOLLOWING POLYMERIAZTION WHICH IS IN A RANGE OF 3,000 TO 10,000 KG./ CM.2, THE SECOND MASS IS THEN LEVELLED INTO A LAYER AND THE ENTIRE STRUCTURE OR ARRANGEMENT IS THEN HARDENED AT ELEVATED TEMPERATURES AND REMOVED FROM THE MOLDING BAND SO THAT THERE IS OBTAINED A DUAL-LAYER STRUCTURED WEB MATERIAL.
TL;DR: In this article, the lattice dynamics and the anharmonic properties of the hexagonal Zirconium are worked out using Keating's approach and dispersion curves are fitted using twelve second order parameters and the six second order elastic constants are evaluated.
Patent•
18 Jul 1972
TL;DR: In this paper, a cotter pin of a special form that tends to endow it with maximum elasticity, which is housed in the conjugated cavity of the tooth-holder, was employed to act as a fixing element and a shock absorbing element simultaneously.
Abstract: The most important characteristic of this invention consists of the employment of a cotter pin of a special form that tends to endow it with maximum elasticity, which is housed in the conjugated cavity of the tooth-holder, while it rests on the tooth, thus acting as a fixing element and a shock-absorbing element simultaneously, permitting an automatic fit, which absorbs the wear and tear that may be produced by working stresses.
TL;DR: A considerable number of methods have been published as discussed by the authors, some of them are primarily analytical, others more empirical, and several deal with isolated problems, such as aerodynamics, dynamics, and elasticity.
Abstract: The inflation of a parachute encompasses problems of aerodynamics, dynamics, and elasticity. The most noticeable effects of the interaction of the events are the opening force and the filling time. Attempts to analyse the opening process and to predict the opening force date back to 1927. Since then a considerable number of methods have been published. Some of them are primarily analytical, others more empirical, and several deal with isolated problems. The earliest and most analytically oriented studies are by Scheube and O'Hara.