Research into the Strength of an Open Wagon with Double Sidewalls Filled with Aluminium Foam

The research is concerned with the use of double walls filled with aluminium foam for an open wagon in order to decrease the dynamic stresses during the operational modes. The research presents the strength calculation for the bearing structure of an open wagon with consideration of the engineering solutions proposed. It was found that the maximum equivalent stresses appeared in the bottom section of the centre sill behind the back support; they amounted to about 315 MPa and did not exceed the allowable values. The maximum displacements were detected in the middle section of the centre sill and amounted to 9.6 mm. The maximum deformations were 1.17 × 10−2. The research also presents the strength calculation for a weld joint in the maximum loaded zones of the bearing structure of an open wagon and gives the results of a modal analysis of the bearing structure of the improved open wagon. It was found that the critical oscillation frequencies did not exceed the allowable values. The results of the research may be useful for those who are concerned about designing innovative rolling stock units and improving the operational efficiency of railway transport.

Locomotion of Self-Excited Vibrating and Rotating Objects in Granular Environments

Many reptiles, known as ‘sand swimmers’, adapt to their specific environments by vibrating or rotating their body. To understand these type of interactions of active objects with granular media, we study a simplified model of a self-excited spherical object (SO) immersed in the granular bed, using three-dimensional discrete element method (DEM) simulations. Modelling the vibration by an oscillatory motion, we simulate the longitudinal locomotion of the SO in three modes: transverse vibration, rotation around different axes, and a combination of both. We find that the mode of oscillation in y direction coupled with rotation around x-axis is optimal in the sense that the SO rises fastest, with periodic oscillations, in the z direction while remaining stable at the initial x position. We analyze the physical mechanisms governing the meandering up or down and show that the large oscillations are caused by an asynchronous changes between the directions of oscillation and rotation. We also observed that the SO’s rising rate is sensitive to three parameters: the oscillation amplitude, the oscillation frequency, f, and the rotation angular velocity, Ω. We report the following results. 1. When the frequencies of the rotation and transverse motion are synchronised, SO rises when Ω<0 and sinks when Ω>0; the average rising/sinking rate is proportional to |Ω|. 2. The rising rate increases linearly with the oscillation amplitude. 3. There exists a critical oscillation frequency, above and below which the rising mechanisms are different. Our study reveals the range of parameters that idealized ‘swimmers’ need to use to optimize performance in granular environments.

Oscillation and non-oscillation of half-linear differential equations with coeffcients determined by functions having mean values

The paper belongs to the qualitative theory of half-linear equations which are located between linear and non-linear equations and, at the same time, between ordinary and partial differential equations. We analyse the oscillation and non-oscillation of second-order half-linear differential equations whose coefficients are given by the products of functions having mean values and power functions. We prove that the studied very general equations are conditionally oscillatory. In addition, we find the critical oscillation constant.

Critical Oscillation Constant for Euler Type Half-Linear Differential Equation Having Multi-Different Periodic Coefficients

We compute explicitly the oscillation constant for Euler type half-linear second-order differential equation having multi-different periodic coefficients.