Pmm Journal of Applied Mathematics and Mechanics最新文献_第7页

The angular motion of oceanic vortex formations 海洋涡旋形成的角运动

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/J.JAPPMATHMECH.2018.03.007

É. K. Lavrovskii, V. Fominykh

引用次数: 0

Spring analogy of non-linear oscillations of a bubble in a liquid at resonance 共振时液体中气泡非线性振荡的弹簧类比

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.12.008

V.V. Vanovskii, A.G. Petrov

{"title":"Spring analogy of non-linear oscillations of a bubble in a liquid at resonance","authors":"V.V. Vanovskii, A.G. Petrov","doi":"10.1016/j.jappmathmech.2017.12.008","DOIUrl":"10.1016/j.jappmathmech.2017.12.008","url":null,"abstract":"<div>Two non-linear oscillatory systems are considered. The first is a point mass on a spring with vertical vibration of the suspension point with a frequency that coincides with the frequency of free vertical oscillations and is two times greater than the frequency of free horizontal oscillations. The friction force in the spring is taken into account. For an initial deviation of the point mass from the vertical, after a long enough time the energy of the vertical oscillations is almost completely transferred into the energy of horizontal oscillations. Using an averaging method, an asymptotic solution is constructed, describing the transient process setting up a periodic solution. Comparison of the analytical solution with the numerical one demonstrates its high accuracy. The second system is an axisymmetrical bubble in a liquid under the variable pressure. An analogy between this system and the previous one is established. Vibration of the suspension point of a spring pendulum corresponds to variable liquid pressure, and the vertical and horizontal oscillation modes of the swinging spring correspond to the radial and deformational oscillation modes of the bubble, and the ratio of the frequencies of these modes is also taken to be equal to two. The friction force in the spring corresponds to energy dissipation under radial oscillations of the bubble. In our calculations of energy dissipation, we take into account the liquid viscosity, thermal dissipation, and acoustic radiation due to liquid compressibility. During transfer of the energy of the radial oscillations, the amplitude of the resonant deformational mode of the bubble oscillations grows anomalously, which makes it possible for the bubble to break up with small energy dissipation under the action of a time-varying external pressure field.</div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 4","pages":"Pages 305-316"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.12.008","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79825895","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: 2

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. Bakholdin

引用次数: 3

Mathematical modelling of the active flow control by periodic excitation 周期激励主动流量控制的数学建模

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.08.011

Yu.B. Lifshitz, D. Degani

引用次数: 3

Algorithms for the orientation of a moving object with separation of the integration of fast and slow motions 基于快、慢运动分离积分的运动目标定位算法

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.07.002

C.E. Perelyaev, Yu.N. Chelnokov

{"title":"Algorithms for the orientation of a moving object with separation of the integration of fast and slow motions","authors":"C.E. Perelyaev, Yu.N. Chelnokov","doi":"10.1016/j.jappmathmech.2017.07.002","DOIUrl":"10.1016/j.jappmathmech.2017.07.002","url":null,"abstract":"<div>Equations and algorithms for determining the orientation of a moving object in inertial and normal geographic coordinate systems are considered with separation of the integration of the fast and slow motions into ultrafast, fast and slow cycles. Ultrafast cycle algorithms are constructed using a Riccati-type kinematic quaternion equation and the Picard method of successive approximations, and the increments in the integrals of the projections of the absolute angular velocity vector of the object onto the coordinate axes (quasicoordinates) associated with them are used as input information. The fast cycle algorithm realizes the calculation of the classical rotation quaternion of an object on a step of the fast cycle in an inertial system of coordinates. The slow cycle algorithm is used in calculating the orientation quaternion of an object in the normal geographic coordinate system and aircraft angles. Results of modelling different versions of the fast and ultrafast cycle algorithms for calculating the inertial orientation of an object are presented and discussed. The experience of the authors in developing algorithms for determining the orientation of moving objects using a strapdown inertial navigation system is described and results obtained by them earlier in this field are developed and extended.</div>","PeriodicalId":49686,"journal":{"name":"Pmm Journal of Applied Mathematics and Mechanics","volume":"81 1","pages":"Pages 11-20"},"PeriodicalIF":0.0,"publicationDate":"2017-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.jappmathmech.2017.07.002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88832851","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: 8

Contact problem for a hollow cylinder 空心圆筒的接触问题

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.020

D.A. Pozharskii

引用次数: 2

Holonomic systems on a rapidly oscillating platform 快速振荡平台上的完整系统

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2018.03.003

E.I. Kugushev, M.A. Levin, T.V. Popova

引用次数: 1

On reversibility in systems with a non-compact configuration space and non-negative potential energy 非紧位形空间和非负势能系统的可逆性

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.12.001

V.V. Kozlov

引用次数: 0

Irina Georgiyevna Goryacheva (on her birthday) 伊琳娜-格奥尔基耶芙娜-戈里亚切娃（生日当天）

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2017-01-01 DOI: 10.1016/j.jappmathmech.2017.08.009

引用次数: 0

Creep fracture of plates with variable bending moments in the presence of an aggressive medium 具有变弯矩的板在腐蚀性介质中发生蠕变断裂

Pmm Journal of Applied Mathematics and Mechanics Pub Date : 2016-01-01 DOI: 10.1016/j.jappmathmech.2016.06.006

A.M. Lokoshchenko, L.V. Fomin

引用次数: 3