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991.
Nonlinear response of a parametrically excited buckled beam 总被引:6,自引:0,他引:6
A nonlinear analysis of the response of a simply-supported buckled beam to a harmonic axial load is presented. The method of multiple scales is used to determine to second order the amplitude- and phase-modulation equations. Floquet theory is used to analyze the stability of periodic responses. The perturbation results are verified by integrating the governing equation using both digital and analog computers. For small excitation amplitudes, the analytical results are in good agreement with the numerical solutions. The large-amplitude responses are investigated by using a digital computer and are compared with those obtained via an analog-computer simulation. The complicated dynamic behaviors that were found include period-multiplying and period-demultiplying bifurcations, period-three and period-six motions, jump phenomena, and chaos. In some cases, multiple periodic attractors coexist, and a chaotic attractor coexists with a periodic attractor. Phase portraits, spectra of the responses, and a bifurcation set of the many solutions are presented. 相似文献
992.
Isothermal melt, fiber-spinning was recently analyzed by means of a nonlinear, integral, constitutive equation that incorporates shear history effects, spectrum of relaxation times, shear-thinning, and extension thinning or thickening when either the drawing force or the draw ratio is specified. The predictions agreed with experimental data on spinning of polystyrene, low-density polyethylene, and polypropylene melts. The predicted apparent elongational viscosity along the threadline (which, as shown in this work, must be identical to that measured experimentally by fiber spinning type of elongational rheometers) is compared with the true elongational viscosity predicted by the same constitutive equation under well-defined experimental conditions of constant extension rate, independent of any strain history. It is concluded that the apparent elongational viscosity, as measured by fiber-spinning, approaches the true elongational viscosity at low Weissenberg numbers (defined as the product of the liquid's relaxation time multiplied by the extension rate). At moderate Weissenberg numbers, the two viscosities may differ by an order of magnitude and their difference grows even larger at high Weissenberg numbers. 相似文献
993.
The finite element analysis of crack problems often incorporates the asymptotic character of the local solution into the formulation. Embedment of stress or strain singularities can impose serious restrictions on the outcome and inconsistencies in predicting crack and/or growth. These restrictions are discussed in connection with the problem of two diametrically opposite corner cracks near a circular hole subjected to remote uniform tension. Enforced in the numerical treatment is the 1/r character of the strain energy density function local to the corner crack border where r is the radial distance measured from the crack front. The tendency for the corner crack to become a through crack is predicted by assuming that each point of the crack border extends by an amount proportional to the strain energy density factor. The path would correspond to the loci of minimum strain energy density function. Numerical results are displayed graphically and discussed in connection with crack initiation and non-self-similar crack growth. 相似文献
994.
Y. Ootao R. Kawamura Y. Tanigawa T. Nakamura 《Archive of Applied Mechanics (Ingenieur Archiv)》1998,68(10):662-676
Summary A neural network model is applied to optimization problems of material compositions for a functionally graded material plate
with arbitrarily distributed and continuously varied material properties in the thickness direction. Unsteady temperature
distribution is evaluated by taking into account the bounds of the number of the layers. Thermal stress components for an
infinite functionally graded material plate are formulated under traction-free mechanical conditions. As a numerical example,
a plate composed of zirconium oxide and titanium alloy is considered. In the optimization problem of minimizing the thermal
stress distribution, the numerical calculations are carried out making use of the neural network. The optimum material composition
is determined by taking into account the effect of temperature-dependence of material properties. The results obtained by
neural network and ordinary nonlinear programming method are compared.
Received 3 March 1998; accepted for publication 22 May 1998 相似文献
995.
Application of X-ray diffraction, micromagnetic and hole drilling methods for residual stress determination in a ball bearing steel ring 总被引:1,自引:0,他引:1
C. O. D. Martins Ph.D. T. R. Strohaecker A. S. Rocha T. K. Hirsch 《Experimental Mechanics》2005,45(4):344-350
A basic understanding of distortion problems requires the analysis of a complete manufacturing process including an almost
complete overview of residual stress states in the component during each production step. To reduce the measurement time in
the future, three measurements methods (X-ray diffraction, micromagnetic and blind hole drilling methods) have been used to
analyze residual stress states in machined AISI 52100 ball bearing rings. X-ray diffraction was used as a state-of-the-art
method for machining induced residual stresses with pronounced gradients. The ring exhibited a complex residual stress state
with high tensile residual stresses at the surface, a strong gradient in depth, and also showed some variation along the outer
circumference due to a superimposition of machining induced residual stresses and effects from the clamping device process.
Due to this surface state, micromagnetic signals depend on the analyzing frequency. A calibration of the signals was only
possible with the X-ray diffraction data. The results of the three different measurement methods correlate reasonably well. 相似文献
996.
The Newtonian potential is used to solve an inverse problem in which we seek the shape of an inhomogeneity in an infinite elastic matrix under uniform applied stresses at infinity such that certain stress components are uniform on the boundary of the inhomogeneity. It is shown that ellipsoids furnish the solution of this inverse problem. Exact and general expressions for the stress and displacement are given explicitly for points in the elastic matrix outside the inhomogeneity. The solution of the corresponding plane deformation problem is found as a limiting case. Several applications are presented, and results from the literature are confirmed as special cases. 相似文献
997.
This paper discusses the stress fields when a spheroidal inclusion, free to slip along its interface, is subjected to a constant nonshear eigenstrain, and when an elastic body containing the inhomogeneity is under all-around tension or uniaxial tension at infinity. In each case the stress field in the inclusion or the inhomogeneity is not constant, contrary to Eshelby's solution. When sliding takes place, the stress increases locally compared with the perfect bonding case, but the elastic energy decreases due to the relaxation. The relative displacement (slip) along the interface is also evaluated. 相似文献
998.
The linear theory of small-amplitude waves is used to construct a solution to the problem of the diffraction of surface gravity waves by a system of arbitrarily oriented vertical circular cylinders. Analytic expressions are obtained for the wave forces and overturning moments acting on each cylinder of the system. A system of two rows of cylinders with three cylinders in each row is considered as an example. It is shown that for certain relationships between the diameter of the cylinders, the distance between them, the angle of approach of the wave, and its wavelength, the maximal values of the hydrodynamic forces acting on the cylinders of the system with allowance for the interaction of the diffracted fields may be appreciably greater than when no allowance is made for it.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 1, pp. 177–181, January–February, 1984. 相似文献
999.
In order to develop criteria for the physical evaluation of wood for soundboards of musical instruments, measurements were made of dynamic Young's modulusE, static Young's modulusE, internal frictionQ
–1 in longitudinal direction, and specific gravity for numerous species of broad-leaved wood. From the results obtained, including those of our previous paper on coniferous wood [1], it was found that the suitability of wood for soundboards could be evaluated by the quantity ofQ
–1/(E/), and that there were very high correlations betweenQ
–1/(E/) andE/, and betweenE andE, regardless of wood species. Consequently, it becomes possible to select practically any wood suitable for soundboards by using the value ofE/, which can be measured easily, and it was derived that the relation betweenE/ andQ
–1 of wood could be expressed by an exponential equation regardless of wood species. 相似文献
1000.
Only a few studies have been devoted to the experimental study of the initial stage of the motion of a liquid from the state of rest in a closed delivery conduit [1]. It can be concluded on the basis of the results of these studies that at the beginning of the process the mechanical energy losses are smaller than in quasistationary flow. These studies also suggest that the laminar nature of the flow persists in the nonstationary flow. However, investigations are of an integral nature and therefore in them the flow structure is not determined. In the present study the development of the motion of the liquid in a delivery conduit from the state of rest is investigated. The tangential frictional stresses at the wall of the conduit, measured by the thermal anemometric method, show that the transitional Reynolds number, at which the laminar flow regime changes into turbulent, depends on the acceleration of the flow and far exceeds the critical value for the case of the stationary flow. At maximum acceleration of the flow equal to 11.78 m/sec2 the transition of the laminar regime to the turbulent at the wall of the conduit occurs at Re = 234, 500. The loss coefficients of mechanical energy have been computed from experimental results, which show that the use of the corresponding coefficient of quasistationary turbulent flow in the computation leads to appreciable errors.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 79–85, November–December, 1977. 相似文献