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Numerical solutions for point masses sliding over analytical surfaces: Part 2

Theoretical & Applied Mechanics Letters 2019年第2期9卷 96-105页

作者： stefano tinti Glauco Gallotti Department of Physics and Astronomy University of Bologna

This paper is the second of two companion papers addressing the dynamics of two coupled masses sliding on analytical surfaces and interacting with one another. The motion occurs under the effect of gravity, the reaction force of the surface and basal friction. The interaction force maintains the masses at a fixed distance and lies on the line connecting them. The equations of motion form a system of ordinary differential equations that are solved through a fourth-order Runge–Kutta numerical scheme. In the first paper we considered an approximate method holding when the line joining the masses is almost tangent to the surface at the instant mass positions. In this second paper we provide a general solution. Firstly, we present special cases in which the system has exact solutions. Second, we consider a series of numerical examples where the interest is focused on the trajectories of the masses and on the intensity and changes of the interaction force.

关键词： Two-point system Rigid-body motion Sliding downslopes

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Numerical solutions for point masses sliding over analytical surfaces: Part 1

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Theoretical & Applied Mechanics Letters 2019年第2期9卷 84-95页

作者： Glauco Gallotti stefano tinti Department of Physics and Astronomy University of Bologna

In this study, we introduce a system of differential equations describing the motion of a single point mass or of two interacting point masses on a surface, that is solved by a fourth-order explicit Runge–Kutta(RK4) scheme. The forces acting on the masses are gravity, the reaction force of the surface, friction, and, in case of two masses, their mutual interaction force. This latter is introduced by imposing that the geometrical distance between the coupled masses is constant. The solution is computed under the assumption that the point masses strictly slide on the surface, without leaping or rolling. To avoid complications stemming from numerical errors related to real topographies that are only known over discrete grids, we restrict our attention to simulations on analytical continuous surfaces. This study sets the basis for a generalization to more complex systems of masses, such as chains or matrices of blocks that are often used to model complex processes such as landslides and rockfalls. The results shown in this paper provide a background for a companion paper in which the system of equations is generalized, and different geometries are presented.

关键词： Point-mass sliding Two point-mass systems Analytical surfaces Numerical methods Runge-Kutta method

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公元前2．5万年西南亚得里亚海陆缘Gondola滑坡引发海啸的可能性

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海洋地质 2009年第1期25卷 46-47页

作者： stefano tinti Gianluca Pagnoni Alberto Annigliato Fabio Trincardi Filippo Zaniboni Federica Foglini Fabiano Gamberi Daniel Minisini 杨丽娟（译）闫章存（校对）博洛尼亚大学意大利海洋研究所意大利埃尼公司意大利不详

亚得里亚海西南陆缘，从陆架外缘到陆坡底部150km范围内，有多处边坡失稳的证据。上陆坡显示有多个陡峭的滑坡后壁，它们出现在向盆内缓倾的更新世海退序列的压实沉积单元中。在海底，Gondola滑坡是最明显的滑坡堆积，断块大，明显的滑... 详细信息

亚得里亚海西南陆缘，从陆架外缘到陆坡底部150km范围内，有多处边坡失稳的证据。上陆坡显示有多个陡峭的滑坡后壁，它们出现在向盆内缓倾的更新世海退序列的压实沉积单元中。在海底，Gondola滑坡是最明显的滑坡堆积，断块大，明显的滑痕（10km×2．5km）延伸到了陆架外缘（现今的深度约为180km，但滑塌时的古深度约为50m），约4．5km3的滑体移动的最大距离达到了50km。

关键词：亚得里亚海滑坡堆积陆缘海啸边坡失稳沉积单元

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