The instability of an elastic planet with a liquid core

具有液体内核的行星在自身引力作用下的弹性变形及稳定性分析

Considering a spherical planet with a liquid core surrounded by a solid shell,we developed a quasi-static model to investigate the deformation of the double-layered planet with self-gravity and obtained the boundary value problem about radial equilibrium,which is solved by the numerical methods.The effects of governing parameters about geometry,density and bulk modulus on the deformation of the planet with self-gravity were discussed.In addition,we also developed the incremental equation theory to investigate the stability of the double-layered planet under its own gravity.It is concluded that instability is more likely to occur on the planet with smaller liquid cores when the outer radius and density of the planets are constant.Although we only study special double-layered planets,these methods can be conveniently extended to complex multi-layered planets.

以一个由液体内核和超弹性固体外壳组成的球形行星为研究对象,建立准静态理论模型分析其在自身重力作用下的变形行为.基于有限变形理论得到行星球对称变形的非线性方程及边界条件,并采用数值方法求解该边值问题,分析几何、密度以及体积模量等参数对其变形行为的影响.在此基础上,通过增量变形理论研究微小扰动情况下行星的稳定性。研究表明,对于固体壳外径和密度不变的行星,液体核心越小,失稳越容易发生。本文建立的理论方法可以拓展到复杂多层行星变形及稳定性的研究中.