Pmm Journal of Applied Mathematics and Mechanics最新文献_第2页

Numerical-analytical method for investigating the stability of motion of bodies of revolution in soft soil media 软土介质中旋转体运动稳定性研究的数值解析方法

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.016

V.G. Bazhenov, V.L. Kotov

{"title":"Numerical-analytical method for investigating the stability of motion of bodies of revolution in soft soil media","authors":"V.G. Bazhenov, V.L. Kotov","doi":"10.1016/j.jappmathmech.2018.03.016","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.016","url":null,"abstract":"<div><p>A method is presented of investigating the stability of rectilinear<span><span> motion of a body of revolution in a compressible soil medium with nonlinear physical-mechanical properties of the soil and two-dimensional effects of flow taken into account. The parameters of the axisymmetric<span> process are calculated numerically, whereas the perturbed motion – the radial displacement and rotation relative to the centre of mass – is determined analytically. In the particular case of a conical projectile and linear pressure distribution along the generatrix, an estimate is obtained of the critical position of the centre of mass as a function of the </span></span>taper angle<span><span>, the mass and velocity of the body, the coefficient of friction, and the </span>hydrodynamic parameters of the soil medium. Unlike the usually implemented situation of constant pressure postulated by the local interaction models, a displacement of the critical position of the centre of mass by up to 20% of the length of the cone has been found, which leads to a substantial decrease in the margin of stability in a restricted sense. Here, the force parameters and the kinematic parameters of motion of the cone on the boundary of the stability region differ both qualitatively and quantitatively. The stability of motion of bodies in soil media with a nonlinear pressure distribution over the contact surface has not previously been investigated.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 473-479"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.016","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90013049","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Contact problem of electroelasticity for a piecewise homogeneous piezoelectric plate with an elastic coating 具有弹性涂层的片状均匀压电板的电弹性接触问题

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.08.015

N.N. Shavlakadze

引用次数: 5

On stability in a case of oscillations of a pendulum with a mobile point mass 具有可动质点的摆摆振荡情况下的稳定性

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.12.003

A.P. Markeev

引用次数: 4

The stability of capillary waves of finite amplitude 有限振幅毛细管波的稳定性

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.12.009

A.G. Petrov

引用次数: 2

On periodic motions of a gyrostat satellite with a large inner (gyrostatic) angular momentum 具有大内角动量的陀螺卫星的周期运动

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.12.007

V.V. Sazonov, A.V. Troitskaya

{"title":"On periodic motions of a gyrostat satellite with a large inner (gyrostatic) angular momentum","authors":"V.V. Sazonov, A.V. Troitskaya","doi":"10.1016/j.jappmathmech.2017.12.007","DOIUrl":"10.1016/j.jappmathmech.2017.12.007","url":null,"abstract":"<div><p>Rotational motion<span> of an axially symmetric gyrostat satellite under the action of its gravitational torque in a circular orbit is considered. Periodic motions of the symmetry axis<span><span><span><span> of the satellite relative to the orbital coordinate system are investigated. In absolute space, these motions appear as a slow precession about the normal to the orbital plane. Such motions are described by an </span>autonomous system<span> of fourth-order differential equations. The gyrostatic angular momentum is assumed to be large, which allows us to introduce a large parameter into the equations of motion. Solutions that are a rest in absolute space, with the symmetry axis forming a nonzero angle with the orbital plane, serve as the generating solutions. The period of the found solutions depends on this angle. Earlier, the limit case of such periodic motions when the symmetry axis of the satellite lies in the orbital plane in the generating solutions was investigated. The limit solutions describe small oscillations of the symmetry axis of the satellite in absolute space, and their period is equal to half the orbital period. To prove the existence of the new motions, we reduce the </span></span>boundary value problem configuring the periodic solutions to a system of integral equations, which is solved by the method of </span>successive approximations. This reduction is carried out according to the same scheme as in the degenerate case, but the necessary solutions of the integral equations are constructed differently. The result obtained explains the appearance of the limit solutions although the latter cannot be constructed within the framework of the considered general case.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 4","pages":"Pages 295-304"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.12.007","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80007714","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

The local transport relations in a rarefied gas 稀薄气体中的局部输运关系

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.08.008

V.S. Galkin, S.V. Rusakov

引用次数: 0

Application of the theory of reversible discontinuities to the investigation of equations describing waves in tubes with elastic walls 可逆不连续理论在弹性壁管波方程研究中的应用

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.009

I.B. Bakholdin

{"title":"Application of the theory of reversible discontinuities to the investigation of equations describing waves in tubes with elastic walls","authors":"I.B. Bakholdin","doi":"10.1016/j.jappmathmech.2018.03.009","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.009","url":null,"abstract":"<div><p>Equations which describe the propagation of waves in tubes with elastic walls are investigated, methods for calculating them are developed, and solutions containing reversible discontinuity structures are analysed in the case of a fluid-filled tube. The model of a tube with elastic walls constructed on the basis of the complete model of a membrane and the non-linear theory of elasticity<span><span> is generalized. The viscosity and compressibility of the material, the possibility of filling the tube with a gas, and the </span>flexural rigidity<span><span> of the tube walls are taken into account. The problem of the decay of an arbitrary discontinuity is solved numerically in the case of a fluid-filled tube. The results obtained correspond to the previously developed theory of reversible discontinuities. Simplified hyperbolic equations of long waves, as well as equations for small-amplitude waves which do not take into account longitudinal elastic waves and are similar to the Boussinesq equations, are derived for cases when a tube is filled with a liquid and a gas. The possibility of overturning of the waves is analysed. A procedure for correcting the </span>numerical schemes by adding terms with high-order derivatives to the equations is developed, and the order of approximation of the numerical scheme remains unchanged, enabling the performance of calculations with low schematic dissipation.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 409-419"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.009","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91724955","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Variational formulation of dynamic problems for a nonlinear Cosserat medium 非线性Cosserat介质动力学问题的变分公式

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.07.007

E.V. Zdanchuk, V.V. Kuroyedov, V.V. Lalin, I.I. Lalina, E.A. Provatorova

引用次数: 2

Modelling of the non-axisymmetric bulging of elastoplastic shells of revolution under combined axisymmetric loadings 轴对称复合载荷作用下转弹塑性弹壳非轴对称胀形的建模

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.010

A.A. Artem’eva, V.G. Bazhenov, E.V. Nagornykh, D.A. Kazakov, T.V. Kuzmicheva

{"title":"Modelling of the non-axisymmetric bulging of elastoplastic shells of revolution under combined axisymmetric loadings","authors":"A.A. Artem’eva, V.G. Bazhenov, E.V. Nagornykh, D.A. Kazakov, T.V. Kuzmicheva","doi":"10.1016/j.jappmathmech.2018.03.010","DOIUrl":"10.1016/j.jappmathmech.2018.03.010","url":null,"abstract":"<div><p><span>A method for the numerical investigation of the non-linear unsteady non-axisymmetric bulging of elastoplastic shells of revolution under complex combined axisymmetric loadings and large subcritical strains is presented. The method enables the limit states and stability of the </span>deformation processes of shells of revolution relative to axisymmetric and non-axisymmetric forms to be evaluated over a broad range of loading rates from quasistatic to dynamic. Its efficiency is substantiated by theoretical calculations and an experimental analysis of the stability of elastoplastic deformation processes of tubular metal samples during combined loadings by tension, internal pressure and torsion. The investigations performed show that preliminary loading alters the initial geometry of the shell and produces deformation anisotropy with great strengthening of the material in the direction of the principal axis of deformation. Torsion of an unloaded shell results in complex loading, which is especially apparent in the initial instant of application of the load and does not have an appreciable influence on the critical parameters of the non-axisymmetric loss of stability. ©2017</p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 5","pages":"Pages 420-428"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.010","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85398837","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

On methods for increasing the margin of stability of motion of optimum bodies 提高最优体运动稳定裕度的方法

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.015

G. Ye. Yakunina

{"title":"On methods for increasing the margin of stability of motion of optimum bodies","authors":"G. Ye. Yakunina","doi":"10.1016/j.jappmathmech.2018.03.015","DOIUrl":"https://doi.org/10.1016/j.jappmathmech.2018.03.015","url":null,"abstract":"<div><p>The possibilities of increasing the margin of stability of motion of optimum bodies having minimum drag or maximum penetration depth during high-velocity motion in a dense medium are investigated. It is assumed that the stresses generated by the medium acting on a surface element of the body are described within the framework of the local interaction model by binomial formulae<span> quadratic in the velocity. A study has been performed for the case when the body shape is taken to be prescribed and when it is possible to vary it without departing from the class of optimum bodies. It is shown that for a fixed shape the simplest ways to increase the margin of stability of motion of the body are to decrease its mass or to move the centre of mass of the body closer to its vertex. It is possible to increase the margin of stability of motion of the body without decreasing its mass and without breaching the homogeneity of the body if it is equipped with fins. A method has been developed for constructing homogeneous optimum bodies with fins, whose bow (nose or leading part) is an optimum cone (OC) and whose stern (aft part) is constructed from segments of an OC and planes tangent<span> to an OC of shorter length. It is shown that for prescribed mass, length, and base area of the body it is always possible to construct a homogeneous optimum body with positive margin of stability of motion. A test of the analytical results was carried out, based on a numerical solution of the Cauchy problem for the system of equations of motion of the body, constructed without simplifying restrictions on the shape of the body or the nature of its motion.</span></span></p></div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 6","pages":"Pages 463-472"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2018.03.015","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91672357","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0