К вопросу о влиянии неоднородного диэлектрического покрытия на характеристики металлической поверхности

Within the framework of the quantum-statistical functional and the Ritz method, the the problem of finding the surface energy per unit area and work function electrons of a metal flat surface with a inhomogeneous dielectric coating, taken into account in the approximation of a continuous medium. For a uniform coating, the calculated values are insensitive to the selection one-parameter functions for an electronic profile, but sensitive to the gradient series of kinetic energy non-interacting electrons. Calculations are performed for Al, Na and the comparison with the calculations by the Kohn-Shem method is made. Analytically the connection between the theory of the Ritz method for inhomogeneous coatings and calculations by the Kohn-Shem method work function of electrons for metal-dielectric nanosandwiches. As it turned out, the influence inhomogeneous coating on the characteristics of the metal surface can be scaled down to a uniform coverage case. The possibility of using the obtained results in various experimental situations are discussed.

Local stability of concrete arch bridge based on Ritz method

In order to minimize the self-weight and prevent local buckling failure of thin-walled box concrete arch bridges at the same time, the limit values of width-thickness ratios are deduced based on Ritz method and equivalent strut theory of arch bridge. A new method of determining sectional forms based on the limit values of width-thickness ratios is put forward. Based on Mupeng bridge, the theoretical results are verified by finite element software ANSYS. Results show that the limits of width-thickness ratios are related to concrete grade, equivalent calculation length and radius of gyration, the allowable minimum thickness of Mupeng bridge is 15 cm to avoid local buckling. The limit values of width-thickness ratios deduced in this paper are reasonable and this new method of determining sectional forms is simple and rational to apply in engineering. A scientific engineering calculation method on arch ring design is put forward and it can provide a theoretical basis for the design of thin-walled box concrete arch bridges constructed by cantilever pouring.

Vibrations of a Cylindrical Sandwich Shell with a Honeycomb Core Made Using FDM technology

Presented is a model of the dynamic deformation of a three-layer cylindrical shell with a honeycomb core, manufactured by fused deposition modeling (FDM), and skins reinforced with oriented carbon nano-tubes (CNT). A ULTEM 9085 thermoplastic-based honeycomb core is considered. To analyze the stress-strain state of the honeycomb core, a finite element homogenization procedure was used. As a result of this procedure, the dynamic response of the honeycomb core is modeled by a homogeneous orthotropic material, whose mechanical properties correspond to those of the core. The proposed model is based on the high-order theory, extended for the analysis of sandwich structures. The skin displacement projections are expanded along the transverse coordinate up to quadratic terms. The honeycomb core displacement projections are expanded along the transverse coordinate up to cubic terms. To ensure the integrity of the structure, shell displacement continuity conditions at the junction of the layers are used. The investigation of linear vibrations of the shell is carried out using the Rayleigh-Ritz method. For its application, the potential and kinetic energies of the structure are derived. Considered are the natural frequencies and modes of vibrations of a one-side clamped cylindrical sandwich shell. The dependence of the forms and frequencies of vibrations on the honeycomb core thickness and the direction of reinforcement of the shell skins have been investigated. It was found that the eigenforms of a sandwich shell are characterized by a smaller number of waves in the circumferential direction, as well as a much earlier appearance of axisymmetric forms. This means that when analyzing the resonant vibrations of a sandwich shell, it is necessary to take into account axisymmetric shapes. Changing the direction of reinforcement of the skins with CNTs makes it possible to significantly influence the frequencies of the natural vibrations of the shell, which are characterized by a nonzero number of waves in the circumferential direction. It was found that this parameter does not affect the frequencies of the axisymmetric shapes of the shell under consideration.

APPLICATION OF THE MAPLE PACKAGE FOR CALCULATING THE RIBBED PLATE FOR STRENGTH, TAKING INTO ACCOUNT THE DISCRETE LOCATION OF THE RIBS

This paper presents an analytical calculation of the stress-strain state of a ribbed plate supported by a cross system of stiffeners. The calculation was carried out by the Ritz method using the Maple mathematical package

Flexural Analysis of Thick Isotropic Rectangular Plates Using Orthogonal Polynomial Displacement Functions

This paper analysed the flexural behaviour of SSSS thick isotropic rectangular plates under transverse load using the Ritz method. It is assumed that the line that is normal to the mid-surface of the plate before bending does not remain the same after bending and consequently a shear deformation function f (z) is introduced. A polynomial shear deformation function f (z) was derived for this research. The total potential energy which was established by combining the strain energy and external work was subjected to direct variation to determine the governing equations for the in – plane and out-plane displacement coefficients. Numerical results for the present study were obtained for the thick isotropic SSSS rectangular plates and comparison of the results of this research and previous work done in literature showed good convergence. However, It was also observed that the result obtained in this present study are significantly upper bound as compared with the results of other researchers who employed the higher order shear deformation theory (HSDT), first order shear deformation theory (FSDT) and classical plate theory (CPT) theories for the in – plane and out of plane displacements at span – depth ratio of 4. Also, at a span - depth ratio of and above, there was approximately no difference in the values obtained for the out of plane displacements and in-plane displacements between the CPT and the theory used in this study.

Rigid-Flexible Coupled Dynamics and PD-Robust Control Design for the Spacecraft with Rotating Solar Panels

The dynamical model for the spacecraft with multiple solar panels and the cooperative controller for such spacecraft are studied in this paper. The spacecraft consists of a rigid platform and two groups of flexible solar panels, where solar panels could be driven to rotate by the connecting shaft. The flexible solar panel involves the use of the orthogonal polynomial in two directions to describe its elastic deformation. By using the Rayleigh–Ritz method, the characteristic equation is derived to obtain natural frequencies and modal shapes of the whole spacecraft. Then the discrete rigid-flexible coupled dynamical equation of the spacecraft is obtained by using the Hamiltonian principle. The equation involves the coupling of the attitude maneuver, solar panels’ driving and vibration suppression. These dynamical behaviors are addressed by the rigid-flexible coupled mode for the first time in this paper. Based on the dynamical equation, the cooperative control scheme is designed by combing the proportional-differential and robust control method. Numerical results show the accuracy of the present modelling method and the validation of the control strategy. The modal analysis implies the complex rigid-flexible coupled characteristic between the central platform and flexible solar panels. The proposed control scheme can maintain the attitude stability while solar panels are being driven, as well as the vibration suppression of flexible solar panels.