Static analysis of multi-support spindle shafts with nonlinear elastic bearings

In this paper a mathematical model and computational tool are developed for the static analysis of multi-bearing spindle shafts with nonlinear elastic supports. Based on the Timoshenko beam theory a resolving system of equations is obtained that takes into account the nonlinear dependence of the bearing stiffness on the reaction forces acting upon them. A solution method is proposed and appropriate software is developed that implements the static analysis of multi-support spindle shafts with non-linearly elastic bearings in MATLAB environment. Key words: spindle, shaft, nonlinear elastic support, multi-bearing, nonlinear elastic stiffness, Timoshenko beam.

Manometric Tubular Springs Oscillatory Processes Modeling with Consideration of its Viscoelastic Properties

This article is dedicated to the operation and management of systems of machine-building and aviation enterprises, systems of production, transport, storage of oil and gas, issues of control of technological processes are of great importance. Control of technological processes is carried out by monitoring the pressure and other parameters. These measuring instruments must have high reliability and the necessary accuracy. In this connection, there is a sharp increase in interest in determining the dynamic parameters of the elements of measuring devices. The main elements of such devices are monomeric tubular springs (Bourdon tubes). The paper considers the natural and forced steady-state oscillations of a thin curved rod interacting with a liquid. Based on the principle of possible displacements, a resolving system of partial differential equations and the corresponding boundary conditions are obtained. The problem is solved numerically by the Godunov orthogonal run method, and the Muller method and the Eigen frequencies found are compared with the experimental results. As a result, for a given axial perturbation, it was possible to select such an effect, in the orthogonal direction, that the amplitude of the longitudinal vibrations of the rod at the first resonance decreased by 20 times. The described vibration damping effect is due to the interrelation of transverse and longitudinal vibrations and is fundamentally impossible in the case of a straight rod.

Forecast of precipitation for the 1994 flood in Piedmont: performance of an ensemble system at convection-permitting resolution

The major flood that affected the Piedmont region in Italy in November 1994 is re-forecast after 25 years in ensemble mode at the convection-permitting resolution of 2.2 km using the regional model COSMO. The performance of the probabilistic forecast of precipitation is assessed against rain-gauge observations, also in comparison with the driver system, i.e., the probabilistic re-forecast produced by ECMWF based on the operational IFS (Cycle 46r1) at grid spacings of 18 km. The convection-allowing system dynamically downscales the ECMWF ensemble and includes an explicit treatment of deep convection. Results indicate that both systems can predict up to 4 days in advance the timing and the spatial patterns of the precipitation, although with higher confidence for the convection-resolving system. The benefit of high resolution is shown mainly in the prediction of intense precipitation and in terms of correct amounts and locations, and confidence of occurrence (at day 3, the estimated probability of exceedance of 200 mm was higher than 90% over areas actually hit by such rainfall amounts). Additionally, convection-permitting resolution improves the representation of orographic precipitation, reducing the upwind precipitation displacement typical of coarser models and including the possible development of strong convection episodes embedded in the large-scale-forced orographic rise. For the high-resolution ensemble, the spread indicates large uncertainty at the local scale, mainly in defining the flow tendency to flank or flow over each mountain.

Fibers-based temporal super-resolved imaging

In this paper we present a new technique for a fiber-based temporal super resolving system allowing to improve the resolution of a temporal imaging system. The proposed super resolving concept is based upon translating the field of view multiplexing method that is used to increase resolution in spatial imaging systems from the spatial domain to the temporal domain. In this paper, an optical realization of our proposed system is presented, using optical fibers and electro-optic modulators. In addition, we show how one can apply this method using low-rate electronics for the required modulation. We also show simulation results that demonstrate the high resolution accepted in our method compares to the basic temporal imaging system. Experimental results which demonstrate resolution improvement by a factor of 1.5 based on the proposed method are presented together with an additional experiment that shows the ability to generate the desired modulation with low rate electronics.

Plane contact problem on the interaction of a pre-stressed strip with an infinite inhomogeneous stringer

The article is devoted to the study of problems of contact interaction of an infinite elastic inhomogeneous stringer with a prestressed strip clamped along one edge. As a result of the research, we have obtained a resolving system of recurrent systems of integro-differential equations. In general, the studies were carried out for the theory of large initial and various versions of the theory of small initial deformations within the framework of the linearized theory of elasticity with an elastic potential of an arbitrary structure. Integral integer differential equations are obtained using the integral Fourier transform. Their solution is presented in the form of quasiregular infinite systems of algebraic equations. The article also investigates the influence of the initial (residual) stresses in strips on the distribution law of contact stresses along the line of contact with an infinite stringer. The system is solved in a closed form using the Fourier transform. The stress expressions are represented by Fourier integrals with a fairly simple structure. The influence of the initial stress on the distribution of contact stresses has been studied and mechanical effects have been found under the action of concentrated loads.

Nonlinear creep in a steel-reinforced concrete beam

Problems of taking into account nonlinear creep in steel- reinforced concrete beams are considered basing on the integral equation of viscous-elastic-plasticity of concrete. There has been obtained the resolving system of nonlinear integral equations, a linearization of this system has been carried out, its asymptotic solutions have been written out for the theory of elastic heredity case. The analysis of taking into account nonlinear creep has been performed compared with the linear creep equations and an instantaneous (short-term) loading allowing for concrete’s nonlinear diagram.

CHARACTER OF MANIFESTATION OF NONLINEARITIES FOR VIBRATION DISTURBANCE OF MOTION OF ELLIPSOIDAL RESERVOIR WITH LIQUID WITH A FREE SURFACE

The problem with vibration disturbance of the reservoir of ellipsoidal shape, partially filled with a liquid, is under consideration. For the construction of the model, we use the before developed method, based on the use of non-Cartesian parametrization of the domain, occupied by a liquid. And the method of the auxiliary domain for satisfying boundary conditions on tank walls above the unperturbed free surface of a liquid, where the liquid can pass in its perturbed motion. The liquid is considered as ideal incompressible. The mathematical model of the system is constructed based on the variational formulation of the problem in the form of the Hamilton–Ostrogradskiy principle. The motion of a liquid free surface is given in the form of decomposition with respect to normal modes of oscillations. Amplitude parameters of oscillations of a liquid free surface together with parameters of the translational motion of the reservoir form a complete independent system of parameters, for which the resolving system of ordinary differential equations is constructed. The constructed model includes nonlinear properties of the system and corresponds to the model of the combined motion of the liquid with the reservoir. According to its structure, the model has considerable similarities with the case of the cylindrical reservoir. The practical implementation of the method is done for vibration disturbance of the system motion in the horizontal plane for the case of extended and compressed ellipsoidal reservoirs. The analysis of the character of manifestation of the dynamical behavior of the system in different ranges of frequencies of motion disturbance shows that mainly this system behaves as a system with the soft type of nonlinearities. The system output to the steady mode of oscillations is not observed. Modulation of oscillations of a liquid free surface is considerably manifested for most modes. Increased attention is paid to the study of regularities of variation of a period of the oscillation modulation. It was ascertained that due to compression of the spectrum of liquid oscillations with the increase of the wavenumber, the simultaneous considerable effect of several frequencies is manifested in the system reservoir–liquid, which leads to complex modulation envelope lines.