Contact problems for an inhomogeneous elastic wedge with variable Poisson’s ratio

Plane contact problems of the elasticity theory are investigated for a wedge when Poisson’s ratio is an arbitrary smooth function with respect to the angular coordinate while shear modulus is constant. For this case Young’s modulus is also variable with respect to the angular coordinate. A finite contact domain is given on one wedge face, it does not include the wedge apex, while the other wedge face is rigidly fixed (problem A) or stress-free (problem B). To reduce the problems to integral equations with respect to the contact pressure, we use the general Freiberger type representation for the solution of elastic equilibrium equations written in polar coordinates with variable Poisson’s ratio. Exact solutions of auxiliary problems are constructed with the help of Mellin integral transforms. The regular asymptotic method employed is effective for contact domains relatively distant from the wedge apex. It is shown that logarithmic terms appear in the asymptotic solutions for the inhomogeneous material which are missing in the well-known asymptotics for the homogeneous one. In contact problem C which is corresponding to problem A, the friction and roughness are taken into account in the contact region. The roughness of the wedge surface is simulated by a Winkler type coating. The collocation method is used for solving integral equations of the second kind. Unlike problem A, in problem C the contact pressure does not have square root singularities at end-points where it takes finite values. Calculations are made for the cases when Poisson’s ratio and Young’s modulus increase or decrease from the surface of the wedge.

Calculation of the stress state of a noncircular helicoidal tube based on the tensor theory of shells

The purpose of the study was to develop an algorithm for calculating helical-symmetric shells with a closed contour in oblique Gaussian coordinates. The twist and length of the shell were taken unchanged. The method is based on the representation of the generating contour of the helicoidal surface by a discrete set of points with the replacement of differentiation along the angular coordinate by finite differences. The unknown were the displacement vectors at the indicated points of the contour. Due to the helicoidal symmetry, the differentiation of vector quantities with respect to the helical coordinate was replaced by vector multiplication. The tensor of deformations and the tensor of the parameters of the change in curvature were calculated using the nabla operator, represented in oblique Gaussian coordinates. Integration over the contour coordinate was replaced by summation over discrete points. The tensors found, which characterize the deformed state, were used to calculate the strain energy of one period of the helicoidal shell, and then the total potential of the mechanical system was compiled. The unknown displacements were determined by minimizing the total potential, taking into account the constraints that prohibit the displacement of the shell as a rigid whole. The study gives a numerical example of the application of the developed approach.

Accuracy Characteristics of the Parametric Burg Method for Spatial Signal Processing in a Nonuniform Array Antenna

Introduction. In the case of a nonuniform (NU) design of the antenna elements (AEs) of the receiving antenna array (AA), the antenna pattern (AP) features sidelobes (SL) with a significantly higher noise level than acceptable values. Under low signal-to-noise ratios (SNR), this noise leads to angular coordinate measuring errors thus worsening the statistical accuracy characteristics (ACs) of the signal. It is of relevance to construct the ACs of angular coordinates when a modified parametric Burg method (BM) is applied to spatial reflected signal processing in a transportable decametre range radar (DRR) with a nonuniform array (NUA) and linear accuracy characteristics. Aim. To analyse the statistical ACs of angular coordinate objects when using a modified BM for spatial reflected signal processing in a DRR with a linear NUA, in which AEs are located with a random step in the range from λ/2 to several λ, where λ is the operating carrier wavelength.Materials and methods. Statistical ACs were constructed by computer modelling in the MatLab software, the reliability of which was confirmed by conventional discrete Fourier transform methods, as well as by comparing the obtained ACs with asymptotic bounds, including Cramer-Rao bounds.Results. The possibility and conditions of using a modified parametric BM for estimating the azimuthal coordinates of reflected radar signals were determined for the case of a nonuniform design of the over-the-horizon DRR receiving AA AEs. Statistical ACs were obtained and compared with the asymptotically optimal ACs of the maximum likelihood estimations corresponding to the uniform AE design.Conclusion. The obtained results confirm the suboptimality of the BM modified for signal processing in the NUA at a random AE spacing step in the range from λ/2 to 2λ, making it applicable for use in transportable DRRs.

FASS: a turbulence profiler based on a fast, low-noise camera

The measurement of the atmospheric optical turbulence with a new scintillation profiler is described and demonstrated. The instrument, FASS (Full Aperture Scintillation Sensor), uses new fast and low-noise detectors to record and process sequences of scintillation images. Statistical processing of these data is based on the calculation of power spectra of intensity in annular pupil zones over the angular coordinate. The angular power spectra are used to measure the optical turbulence intensity of 14 layers located at logarithmically-spaced distances from 0.3 km to 25 km. The reference functions relating turbulence strength to the angular power spectra are computed by numerical simulation. Measurement of the ground-later turbulence and total seeing with FASS is possible when the detector is conjugated to a negative (below ground) distance. Results of measurement campaigns at Paranal are reported, documenting a good agreement of turbulence profiles measured by FASS with two other instruments, SCIDAR and MASS.

Influence of boundary constraints on the appearance of asymmetrical equilibrium states in circular plates under normal pressure

Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of material heterogeneity and boundary on the buckling load is examined. It is shown that if the outer edge of a plate is elastically restrained against radial deflection, the buckling load for unsymmetrical buckling is larger than for a plate with a movable edge. The elasticity modulus decrease away from the center of a plate leads to sufficient lowering of the buckling pressure if the outer edge can move freely in the radial direction.

Study on numerical analysis of dynamic parameters of mobile walking robot

A dynamic model of a walking robot is proposed for moving along surfaces of different topologies and orientations to the horizon. The principal difference between walking robot mechanisms is that they are made in the form of flexible pedipulators. Actually the pedipulators are a set of spherical rings with a hydraulic or pneumatic drive. The patented design (Patent UA No 117065, publ. 2018.06.11) of the robot's feet is anthropomorphic and allows the robot to work in the angular coordinate system inherent in the human walking machine. The proposed mathematical model allows us to calculate the dynamic parameters (forces and moments) and compare these parameters with the allowable technological load that a walking robot can perform without losing adhesion with the displacement surface.

Angular superresolution of signals using virtual antenna arrays

We analysed existing publications concerning virtual antenna arrays and determined the limitations of using them in radar systems for the case of prior uncertainty regarding angular positions of signal sources. The paper shows that it is possible to increase angular coordinate resolution for the case of prior uncertainty regarding angular positions of signal sources by employing a virtual antenna array at typical signal-to-noise ratios used in radar signal processing. We provide results of simulating the signals numerically, which confirm our analytical calculations.