The paper aims at derivation of the asymptotic model for surface wave propagating in a pre-stressed incompressible elastic halfspace, subject to prescribed surface loading. The approach relies on the slow-time perturbation procedure, extending the previously known hyperbolic-elliptic formulations for surface waves in compressible linearly elastic solids. Within the derived model, the decay away from the surface is governed by a pseudo-static elliptic equation, whereas wave propagation is described by a hyperbolic equation on the surface. The effect of pre-stress, namely, the principal Cauchy stress σ 2 , is investigated. Finally, an illustrative example of the Lamb problem is considered, demonstrating the efficiency of the approach.
A generalized dynamic model taking into account coupled vibrations of a rotor-fluid-foundation system, linear eccentricity, damping, and rolling bearing nonlinearity is developed. The nonlinear equations of motion are formulated and analysed. Forced and free vibrations of the system are investigated. Peculiarities of the dynamic behaviour are revealed, including properties of vibration frequencies and amplitudes. The obtained results have the potential to be implemented in the optimal design of modern industrial devices.
In this paper, we study various variants of Verhulst-like ordinary differential equations (ODE) and ordinary difference equations (O Δ E). Usually Verhulst ODE serves as an example of a deterministic system and discrete logistic equation is a classic example of a simple system with very complicated (chaotic) behavior. In our paper we present examples of deterministic discretization and chaotic continualization. Continualization procedure is based on Padé approximants. To correctly characterize the dynamics of obtained ODE we measured such characteristic parameters of chaotic dynamical systems as the Lyapunov exponents and the Lyapunov dimensions. Discretization and continualization lead to a change in the symmetry of the mathematical model (i.e., group properties of the original ODE and O Δ E). This aspect of the problem is the aim of further research.
The dynamics of the horizontal drill string considering frictional forces between the column and the borehole is investigated. A model of longitudinal vibrations of columns proposed in T.G. Ritto et al. is considered. The investigated model has a nonlinear character, and is modelled by the lumped parameters method. The drill-string is discretized with 100 nodes of lumped masses. Displacement of the bit, bit speed and also the ratio between the output power (obtained from the bit-rock interaction) and the input power is defined by the authors. The frictional force between the column and the borehole is relevant and uncertain. The frictional coefficient is modelled as a random field with exponential autocorrelation function. The obtained results are qualitatively and quantitatively consistent with the results of Ritto, where the dynamic model calculations are carried out by the finite element method.
The paper is dedicated to applied problems of dynamic stability of deformable systems. Dynamics of boring columns for shallow drilling (up to 500 m) applied in oil-gas extractive industry is considered. The purpose is investigation of influence of the drill rod's material properties of amplitude-frequency characteristic and stability of movement. Deformation of the drill rod is assumed finite. A model of a compressed-torsioned drill rod is considered within the nonlinear theory of finite deformations of V.V. Novozhilov. Dynamic of elastic movement for steel and dural drill rods applied in the extractive industry, resonant vibration modes and instability zone are investigated. The resonant vibrations of drill rods on the basic and higher (third) frequencies and their stability are calculated.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.