scholarly journals Abnormal stresses in underground pipeline due to static and dynamic reversal of several foundation blocks

2020 ◽  
pp. 53-60
Author(s):  
M.I. Vaskovskyi ◽  
A. B. Struk ◽  
M. V. Makoviichuk ◽  
I. P. Shatskyi
Keyword(s):  
Equivalent Stress ◽  
Normal Pressure ◽  
Forced Oscillations ◽  
Underground Pipeline ◽  
Harmonic Oscillations ◽  
Time Harmonic ◽  
Block Foundation ◽  
Solid Foundation ◽  
Ultimate Equilibrium ◽  
Linear Setting

The article discusses the issues of forecasting the strength of underground pipelines laid in seismically active areas through sections composed of relatively rigid moving blocks. In such dangerous areas, in addition to the normal pressure load of the transported product, the pipe is subjected to additional effects from the movements of the fragments of the block foundation. As the literature data show, the problems of the influence of the interaction of faults on the stress state of the pipeline have not yet been studied. The aim of the study is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged foundation caused by static or time-harmonic reciprocal turns of the blocks around the axis of the pipe on both sides of several faults. Static equilibrium and harmonic oscillations of the pipeline are investigated in a linear setting, modelling it with a rod with an annular cross section. The inertia of the transported product is not taken into account. To consider the issues of the ultimate equilibrium of the pipe, the momentless theory of shells and the energy theory of strength are used. The soil backfill is considered as Winkler’s elastic layer. Multiple damages to the solid foundation are presented in the form of several faults on which there is a rupture of the angle of rotation around the axis of the pipe. We formulated boundary value problems for differential equations of static torsion and torsional harmonic oscillations with discontinuous right-hand sides. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetrical reversal of the foundation blocks, the distributions of the torsion angle and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations of the system, are investigated.

scholarly journals STATIC STRAINING AND LONGITUDINAL OSCILLATIONS OF UNDERGROUND PIPELINE BUILT ON BLOCK FOUNDATION

2021 ◽  
pp. 123-133
Author(s):  
A. B. Struk ◽  
M. I. Vaskovskyi ◽  
I. P. Shatskyi ◽  
M. V. Makoviichuk
Keyword(s):  
Steady State ◽  
Stress State ◽  
Differential Equations ◽  
Analytical Solutions ◽  
Equivalent Stress ◽  
Forced Oscillations ◽  
Underground Pipeline ◽  
Underground Pipelines ◽  
Block Foundation ◽  
Static Tensile

The article considers the issues of forecasting the strength of underground pipelines, which are operated on seismically active sections of the route, composed of relatively rigid mobile blocks. According to the literature, the problems of the influence of the interaction of base faults on the stress state of the pipeline have not been studied to date. The aim of the work is to develop a model for the analysis of abnormal stresses in the underground pipeline on a damaged basis caused by static or time-harmonious mutual movement of its blocks along the axis of the pipe in the presence of several faults. Boundary value problems for differential equations of static tensile-compression and steady-state longitudinal oscillations of a tubular rod with discontinuous right-hand sides are formulated. Based on the analytical solutions of these problems for the cases of antisymmetric and symmetric displacement of the foundation blocks, the distributions of axial displacement and equivalent stress in the pipe, depending on the distance between faults and the frequency of forced oscillations, are investigated.

Harmonic Oscillations of Nonlinear Two-Degree-of-Freedom Systems

1955 ◽  
Vol 22 (1) ◽  
pp. 107-110
Author(s):  
T. C. Huang
Keyword(s):  
Nonlinear System ◽  
Degrees Of Freedom ◽  
Forced Oscillations ◽  
Viscous Damping ◽  
Free Oscillations ◽  
Response Curves ◽  
Harmonic Oscillations ◽  
Restoring Force ◽  
Nonlinear Restoring Force ◽  
Two Degree Of Freedom

Abstract In this paper an investigation is made of equations governing the oscillations of a nonlinear system in two degrees of freedom. Analyses of harmonic oscillations are illustrated for the cases of (1) the forced oscillations with nonlinear restoring force, damping neglected; (2) the free oscillations with nonlinear restoring force, damping neglected; and (3) the forced oscillations with nonlinear restoring force, small viscous damping considered. Amplitudes of oscillations and frequency equations are derived based on the mathematically justified perturbation method. Response curves are then plotted.

scholarly journals Discrete-continuous simulation and analysis of forced oscillations of (heavy) rope of crane loading mechanism in its process

2020 ◽  
Vol 11 (3) ◽  
pp. 181-186
Author(s):  
Yu. V. Chovnyuk ◽  
◽  
I. M. Sivak ◽  
Keyword(s):  
Internal Friction ◽  
Cross Sections ◽  
Integrodifferential Equation ◽  
Forced Oscillations ◽  
Harmonic Oscillations ◽  
Continuous Simulation ◽  
Considerable Length ◽  
Rope System ◽  
Oscillatory Processes

The analysis of forced oscillations and waveformations of heavy ropes of hoisting mechanisms of cranes in the processes of starting the latter is carried out. The main parameters of the resulting waveforms in the ropes for different ways of lifting the load ("with a pickup", "by weight") are determined. The influence of gravity on the rope and the longitudinal oscillations arising in it, as well as on the longitudinal waveforms arising inside it are investigated. The rope of the lifting mechanism, in this case, is considered as a tensile rod. The laws of motion of cross-sections of ropes are established, according to which the forces arising in ropes are minimized during the startup of hoisting mechanisms of cranes. The application of the integrodifferential equation, which adequately describes the oscillations of the rope system of cargo cranes, and also takes into account the frequencyindependent internal friction in these systems, which accompanies the oscillatory processes in the ropes during transient reagents for their differentiation by different ways of lifting loads. The parameters of the established harmonic oscillations of the rope system of cranes for long-term lifting of the load and taking into account the inertial properties of the rope (considerable length), as well as the magnitude of the static movement of the rope (for different ways of lifting loads) are determined.

Two-dimensional water waves in the presence of a freely floating body: trapped modes and conditions for their absence

2015 ◽  
Vol 779 ◽  
pp. 684-700 ◽  
Author(s):  
Nikolay Kuznetsov
Keyword(s):  
Water Waves ◽  
Small Amplitude ◽  
Floating Body ◽  
Two Dimensional ◽  
Trapped Modes ◽  
Constant Depth ◽  
Time Harmonic ◽  
Equipartition Of Energy ◽  
Linear Setting ◽  
Inverse Procedure

The coupled motion is investigated for a mechanical system consisting of water and a body freely floating in it. Water occupies either a half-space or a layer of constant depth into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes. Under the assumption that the motion is of small amplitude near equilibrium, a linear setting is applicable, and for the time-harmonic oscillations it reduces to a spectral problem with the frequency of oscillations as the spectral parameter. Within this framework, it is shown that the total energy of the water motion is finite and the equipartition of energy holds for the whole system. On this basis two results are obtained. First, the so-called semi-inverse procedure is applied for the construction of a family of two-dimensional bodies trapping the heave mode. Second, it is proved that no wave modes can be trapped provided that their frequencies exceed a bound depending on the cylinder properties, whereas its geometry is subject to some restrictions and, in some cases, certain restrictions are imposed on the type of mode.

On the coupled time-harmonic motion of a freely floating body and water covered by brash ice

2016 ◽  
Vol 795 ◽  
pp. 174-186 ◽  
Author(s):  
Nikolay Kuznetsov ◽  
Oleg Motygin
Keyword(s):  
Small Amplitude ◽  
Finite Interval ◽  
Finite Energy ◽  
Floating Body ◽  
Coupled Motion ◽  
Time Harmonic ◽  
All Solutions ◽  
Equipartition Of Energy ◽  
Linear Setting ◽  
Inverse Procedure

A mechanical system consisting of water covered by brash ice and a body freely floating near equilibrium is considered. The water occupies a half-space into which an infinitely long surface-piercing cylinder is immersed, thus allowing us to study two-dimensional modes of the coupled motion, which is assumed to be of small amplitude. The corresponding linear setting for time-harmonic oscillations reduces to a spectral problem whose parameter is the frequency. A constant that characterises the brash ice divides the set of frequencies into two subsets and the results obtained for each of these subsets are essentially different. For frequencies belonging to a finite interval adjacent to zero, the total energy of motion is finite and the equipartition of energy holds for the whole system. For every frequency from this interval, a family of motionless bodies trapping waves is constructed by virtue of the semi-inverse procedure. For sufficiently large frequencies outside of this interval, all solutions of finite energy are trivial.

IMPEDANCE AND ADMITTANCE OF MECHANICAL SYSTEMS

2020 ◽  
Vol 5 ◽  
pp. 3-11 ◽  
Author(s):  
I.P. POPOV
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Mechanical Systems ◽  
Forced Oscillations ◽  
Calculation Algorithm ◽  
Harmonic Oscillations ◽  
Oscillation Modes ◽  
Steady State Oscillation ◽  
Algebraic Operations ◽  
Phase Relationships

It is noted that the traditional calculation of mechanisms in forced oscillations is often a difficult task. Most often, calculators are interested in steady-state oscillation modes. The aim of the work is to significantly simplify the calculations by replacing the need to solve differential equations with algebraic methods. A similar approach is widely used in electrical engineering. The use of a symbolic (complex) description of mechanical systems under forced harmonic oscillations (in the steady state) made it possible to abandon the extremely cumbersome and time-consuming calculation algorithm associated with solving differential equations and replace it with simple and clear algebraic operations. Due to this, the calculation time is reduced significantly. Vector diagrams, not being a necessary component of the study of mechanical systems, have significant methodological significance, since they show quantitative and phase relationships between the parameters of systems.

Oscillations of a rigid sphere embedded in an infinite elastic solid

1967 ◽  
Vol 63 (4) ◽  
pp. 1207-1227 ◽  
Author(s):  
P. Chadwick ◽  
E. A. Trowbridge
Keyword(s):  
Small Amplitude ◽  
Elastic Solid ◽  
Time Dependent ◽  
Forced Oscillations ◽  
Graphical Form ◽  
Rigid Sphere ◽  
Impulsive Force ◽  
Free Oscillations ◽  
Time Harmonic ◽  
Two Parameters

AbstractIn this paper, which is a continuation of (1), we study steady (i.e. time-harmonic) and transient rectilinear oscillations of small amplitude of a rigid sphere embedded in an infinite elastic solid. Two types of transient motions are considered, forced oscillations in which the sphere is subject to a prescribed time-dependent force, and free oscillations in which the sphere is set in motion by an impulsive force. For each mode of vibration of the sphere the character of the solution is determined by two parameters, the density contrast between the sphere and its surroundings and a parameter related to the Poisson's ratio of the elastic solid. Numerical results referring to transient rectilinear oscillations are presented in graphical form.

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