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.

About the features of hypersonic flow past a yawed plate

The flow around the yawed plate in the regime of strong interaction is considered in the case when the pressure at its trailing edge is not constant, but changes along the transverse coordinate. It is shown that in the case of large transverse gradients of the induced pressure, the type of expansions of flow functions in the vicinity of the leading edge changes significantly and the third term of the expansions should be taken into account.

Lens Raster as a Source of Distortions in Integral Photography

Analysis of methods for recording and reproducing a three-dimensional image allows to distinguish two different approaches. The fi approach consists in formation of stereoscopic images, the second one provides the formation of an optical object model and includes particularly a group of integral photography methods .The use of integral photography methods for recording and reproducing volumetric images is relevant due to the lack of fl inherent for stereoscopic methods and relative simplicity of technical implementation. Lens raster used in this method is a possible source of image distortion. This paper aim is to determine the range of parameters of the lens system, namely, the allowable values of the pitch of the lens raster, providing distortions absence caused this raster.Types of possible distortions and sources of their occurrence are indicated. The requirements for the pitch of the lenticular raster are formulated, based on conditions of false information absence, absence of discontinuity of the image in depth and in the transverse direction, and invisibility of lens elements of the reproduction matrix.Studies shoed that the lenticular pitch is limited by the four inequalities, three of which limit the pitch value from below, and the fourth one from above. A set of conditions limiting the step of the lens matrix was analyzed. The boundaries of allowable step values depend on four groups of parameters: raster dimensions, location of the subjects, reproduction and observation parameters. Result of the method usage as a dependence of the allowable range of the pitch of the lenticular raster on transverse coordinate of the recorded point with fi values of other parameters is presented.

The matrix solution of the 4×4 problem by the Wentzel-KramersBrillouin method for a planar inhomogeneous anisotropic layer

Using methods of classical electrodynamics, we consider the oblique incidence of a plane electromagnetic wave on a twisted planar anisotropic inhomogeneous layer, in which the optical axis changes direction with respect to the plane of incidence. We consider the general case when all components of the permittivity tensor of the medium are nonzero functions of the transverse coordinate in the layer. Using the Wentzel-Kramers-Brillouin method, we obtain in the initial approximation a 4×4-matrix solution for the projections of the fields of an electromagnetic wave in an inhomogeneous anisotropic medium. The matrix reflection coefficients are calculated and shown to depend on the torsion angle of the medium.

Design of active disturbance rejection controller for compass-like biped walking

This article proposes an active disturbance rejection controller design scheme to stabilize the unstable limit cycle of a compass-like biped robot. The idea of transverse coordinate transformation is applied to form the control system based on angular momentum. With the linearization approximation, the limit cycle stabilization problem is simplified into the stabilization of an linear time-invariant system, which is known as transverse coordinate control. In order to solve the problem of poor adaptability caused by linearization approximation, we design an active disturbance rejection controller in the form of a serial system. With the active disturbance rejection controller, the system error can be estimated by extended state observer and compensated by nonlinear state error feedback, and the unstable limit cycle can be stabilized. The numerical simulations show that the control law enhances the performance of transverse coordinate control.

Lump and rogue waves for the variable-coefficient Kadomtsev–Petviashvili equation in a fluid

Under investigation in this paper is the variable-coefficient Kadomtsev–Petviashvili equation, which describes the long waves with small amplitude and slow dependence on the transverse coordinate in a single-layer shallow fluid. Employing the bilinear form and symbolic computation, we obtain the lump, mixed lump-stripe soliton and mixed rogue wave-stripe soliton solutions. Discussions indicate that the variable coefficients are related to both the lump soliton’s velocity and amplitude. Mixed lump-stripe soliton solutions display two different properties, fusion and fission. Mixed rogue wave-stripe soliton solutions show that a rogue wave arises from one of the stripe solitons and disappears into the other. When the time approaches 0, rogue wave’s energy reaches the maximum. Interactions between a lump soliton and one-stripe soliton, and between a rogue wave and a pair of stripe solitons, are shown graphically.

ANALYSIS OF POSSIBLE CAUSES AND MECHANISMS OF DESTRUCTION OF BUILDING STRUCTURES

In order to better understand the wave properties of the Timoshenko equation, the derivation of the refined equation from the equations of the plane elasticity problem for a long band is carried out. The simple iterations method is used for the derivation. It includes known methods: the semi-inverse method of Saint-Venant and Picard operator. In accordance with the semi-inverse method, a part of the unknowns is defined, which are interpreted as the values of the initial (zero) approximation. Proceeding from them, a sequential computation is carried out using a sequence of the four Picard operators in such a way that the outputs of the one operator are the inputs for the next. Calculating in this way all the unknowns in the zeroth approximation by the direct integration over the transverse coordinate, the values of the initial approximation are calculated in the first approximation. These quantities are small of the second order with respect to the dimensionless thickness. Expressions for the unknowns are obtained as power functions of the transverse coordinate and as a function of the deriva-tives along the longitudinal coordinate. By the Banach fixed point theorem, the computation process is asymptot-ically convergent one. After this, boundary conditions on the long sides are satisfied by means of the derivatives of the arbitrariness, depending only on the longitudinal coordinate. This gives us the ordinary differential equations for the determination of these arbitrary functions. In turn, the integration constants of the last equations can be found from the conditions on the short sides of the strip. The ordinary differential equations are split into equations for slowly varying and quickly varying quantities. The slowly changing values give the classical solu-tion of the beam oscillations. The quickly varying solutions give the perturbed solutions describing high-frequency oscillations and singularly perturbed wave solutions for time-concentrated effects. Some of these soluions are absent in the Timoshenko equation. It is assumed that the selected shear waves provoke in the buildings subjected to the rapid impacts (shock by airplane, explosions, and seismic movements of the base) the interruptions of interlayers between the floors and subsequent progressive collapse.

Mathematical modelling of particle aggregation and sedimentation in the inclined tubes

Sedimentation of the aggregating particles in the gravity field is widely used as an easy and cheap test of the suspension stability of different technical suspensions, blood and nanofluids. It was established the tube inclination makes the test much faster that is known as the Boycott effect. The dependence of the sedimentation rate on the angle of inclination is complex and poorly understood yet. In this paper the two phase model of the aggregating particles is generalized to the inclined tubes. The problem is formulated in the two-dimensional case that corresponds to the narrow rectangle vessels or gaps of the viscosimeters of the cone-cone type. In the suggestion of small angles of inclination the equations are averaged over the transverse coordinate and the obtained hyperbolic system of equations is solved by the method of characteristics. Numerical computations revealed the increase in the initial concentration of the particles, their aggregation rate, external uniform force and inclination angle accelerate the sedimentation while any increase in the fluid viscosity decelerates it that is physically relevant. Anyway, the behaviors of the acceleration are different. Based on the results, a novel method of estimation of the suspension stability is proposed.