标题： 二维准静态弹性接触问题中从连续解到跳跃解的转变：制动噪音起始背后的数学原理 显示英文标题

标题： Transition from Continuous to Jumping Solutions in 2D Quasi-static Elastic Contact Problems with Coulomb Friction: the Mathematics Underlying the Onset of Brake Squeal

摘要： 我们在一个非常一般的设定中表述了具有库仑摩擦的准静态弹性接触问题，其中载荷和解在时间上可能有跳跃。 利用我们最近论文[4]中的思想，我们给出了摩擦系数大小的一个最优条件，在该条件下，我们证明了在最一般的二维问题情况下，对于任意绝对连续的载荷，存在一个绝对连续的解。 我们提供了例子说明，当该条件被违反时，即使载荷随时间绝对连续变化，解也可能出现自发的时间跳跃。 我们认为，准静态问题中解的这些自发时间跳跃揭示了过程从准静态性质向动态性质的转变，被解释为干摩擦弹性动力接触问题中摩擦诱发振动开始的数学特征。 显示英文摘要

摘要： We formulate the quasi-static elastic contact problem with Coulomb friction in a very general setting, with possible jumps in time for both the load and the solution. Exploiting ideas originating in our recent paper [4], we exhibit an optimal condition on the magnitude of the friction coefficient under which we prove the existence of an absolutely continuous solution for arbitrary absolutely continuous loads in the case of the most general 2D problem. We provide examples showing that, when the condition is violated, spontaneous jumps in time of the solution may occur, even when the load varies absolutely continuously in time. We argue that these spontaneous jumps in time of the solution in the quasi-static problem reveal a transition of the process from a quasi-static nature to a dynamic nature, interpreted as the mathematical signature of the onset of friction-induced vibrations in the elastodynamic contact problem with dry friction.