Calculation of the strength of reinforced concrete columns under repeated longitudinal impact

This paper reports the results of experiments with reinforced concrete column models subjected to repeated longitudinal impact loading using a pile driver. The strength of the column models is analyzed by comparing experimental data with results of mathematical modeling. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 1, pp. 181–190, January–February, 2008.     

Wave motion in a thick cylindrical rod undergoing longitudinal impact

The paper presents a new formulation and the comprehensive analytical solution to longitudinal impact of thick elastic rods. In contrast to previously published works, the solution is derived based on the exact three-dimensional theory without using the classic Skalak’s decomposition. This new direct approach makes the analytical solution more transparent and much easier to obtain. The resulting formulas for basic mechanical quantities are derived using the residue theorem and their evaluation is made in such a way that the accuracy of presented results is significantly higher than those previously published. Based on these results, the transient wave phenomena occurring in the rods are discussed in detail. Additionally, the solution in time domain is obtained also by semi-analytical approach making use of numerical inverse Laplace transform. It is shown that the selected FFT based algorithm is accurate and robust enough, such that the analysis of wave motion in spatial and time domain can be done effectively preserving the results precision. Presented solution can be used as a benchmark for verification of numerical and experimental methods applied to elastodynamics problems.     

Thin rod under longitudinal dynamic compression

The paper contains a short survey of the papers on the static and dynamic longitudinal compression of a thin rod initiated by Morozov and and carried out in 2009–2016 with his direct participation. We consider linear and nonlinear problems related to the propagation of longitudinal waves in a rod and the transverse vibrations generated by these waves; parametric resonances; beating due to energy exchange between longitudinal and transverse vibrations; the rod shape evolution as the load exceeds the Euler critical value; the possibility of buckling of the rod rectilinear shape under a load less than the Euler load; and the rod dynamics at the initial stage of motion. The prospects of further investigations related to the complication of the models are considered, in particular, the problem of longitudinal impact by a body on a rod and the transverse vibrations generated by it.     

Calculation of the longitudinal velocity in the linear problem of a vibrator in a subsonic boundary layer

The linear problem is considered of a localized vibrator mounted on a flat plate in a subsonic boundary layer. The plate and the vibrator are assumed to be heat-insulated, and the dimensions of the vibrator and the frequency of the oscillations are such that the flow may be described by means of the equations of a boundary layer with self-induced pressure. The amplitude of the oscillations of the vibrator and the perturbations of the flow parameters corresponding to it are assumed to be small, and this makes it possible to linearize these equations. Integral transformations are used to construct a solution for values of the time greatly exceeding the period of the oscillations of the vibrator. The profiles of the perturbations of the longitudinal velocity are calculated in dependence on the transverse coordinate for various values of the longitudinal coordinate. A comparison is made with the profiles of the perturbations of the longitudinal velocity which have been obtained experimentally.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 61–67, May–June, 1987.     

Influence of the connecting condition on the dynamic buckling of longitudinal impact for an elastic rod

The stress wave propagation law and dynamic buckling critical velocity are formulated and solved by considering a general axial connecting boundary for a slender elastic straight rod impacted by a rigid body. The influence of connecting stiffness on the critical velocity is investigated with varied impactor mass and buckling time. The influences of rod length and rod mass on the critical velocity are also discussed. It is found that greater connecting stiffness leads to larger stress amplitude, and further results in lower critical velocity. It is particularly noteworthy that when the connecting stiffness is less than a certain value,dynamic buckling only occurs before stress wave reflects off the connecting end. It is also shown that longer rod with larger slenderness ratio is easier to buckle, and the critical velocity for a larger-mass rod is higher than that for a lighter rod with the same geometry.     

Mechanism by which a frictionally confined rod loses stability under initial velocity and position perturbations

We present a theory to reveal for the first time the distinct mechanisms by which a compressed rod confined in a channel buckles in the presence of dry friction. Contrary to the case of a frictionless contact, with friction the system can bear substantially enhanced compressive load without buckling after its stiffness turns negative, and the onset of instability is strongly affected by the amount of perturbation set by the environment. Our theory, confirmed by simulations, shows that friction enhances stability by opening a wide stable zone in the perturbation space. Buckling is initiated when the applied compressive force is such that the boundary of the stable zone touches a point set by the environment, at a much higher critical load. Furthermore, our analysis shows that friction has a strong effect on the buckling mode; an increase in friction is found to lead to higher buckling modes.     

Group theoretic analysis and similarity solution for a nonlinear viscous rod subjected to time dependent velocity impact

Unidirectional wave motion in a nonlinear viscous rod obeying Norton's law in creep, subjected to time dependent velocity impact is considered. From the basic equations of the problem and the four parameter dimensional group of transformations, absolute invariants of the group are constructed to obtain similarity transformations. Similarity representation of the original system of partial differentiation equations is formulated as a system of nonlinear ordinary differential equations with auxiliary conditions. Closed form solutions are obtained for a linear rod, for a nonlinear rod subjected to constant velocity impact and a weekly nonlinear rod. Nonlinear case is solved by a numerical approach based on the quasilinearization method.     

Calculation of cell face velocity of non-staggered grid system

In this paper,the cell face velocities in the discretization of the continuity equation,the momentum equation,and the scalar equation of a non-staggered grid system are calculated and discussed.Both the momentum interpolation and the linear interpolation are adopted to evaluate the coefficients in the discretized momentum and scalar equations.Their performances are compared.When the linear interpolation is used to calculate the coefficients,the mass residual term in the coefficients must be dropped to maintain the accuracy and convergence rate of the solution.     

Calculation of the pressure at the critical point when a shock wave is incident on a body moving with supersonic velocity

The interaction of a shock wave with a blunted body moving with supersonic velocity is considered. It is shown that under certain conditions the reflection pressure at the critical point of the body can be determined on the basis of one-dimensional theory of shock waves. The error due to the application of this theory is investigated. Equations are obtained for the maximum error as asymptotically large values of the number M of the unperturbed stream incident on the body. Conditions under which secondary reflections of the discontinuities at the critical points are possible are analyzed.Moscow. Translated from Izvestiya Akademii Nauk SSSR. Mekhanika Zhidkosti i Gaza, No. 6, pp. 94–101, November–December, 1972.     

控制棒驱动机构步跃提升碰撞的动力学建模

控制棒驱动机构(CRDM)在步跃提升时,钩爪部件会与承压壳体上的提升磁极发生面面碰撞。本文基于混合坐标法建立控制棒驱动机构有限元离散的刚-柔耦合动力学方程,用罚函数法计算了钩爪部件与承压壳体之间的碰撞力和应力分布情况。结果表明,刚柔耦合多体方法在仿真小变形碰撞时可以提高计算效率,同时又能达到与有限元方法同等的精度。进一步对碰撞模型不同区域的网格疏密和尺寸大小做了定量分析,得到了降低有限元网格数量的方法,可为工程中碰撞模型的网格划分提供参考。     

Calculation of the fundamental frequencies of a rotating long vertical rod

A method is proposed for calculation of the complex eigenvalues of a boundary-value problem that describes the rotation of a long vertical partially compressed rod subject to the action of dead weight and torque. The solution of the problem is sought for two sections of the rod in the form of asymptotic expansions in a small parameter, which are then joined at a certain point. The results obtained are discussed and compared with the results of other studies. The method may be used for analysis of the rotation of a long vertical pipe in deep-well drilling. Central Scientific and Research Institute of Geological Exploration, Moscow, Russia. Translated from Prikladnaya Mekhanika, Vol. 36, No. 3, pp. 137–143. March, 2000.