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首页> 外文期刊>WSEAS Transactions on Applied and Theoretical Mechanics >The Impact Induced 3:1 Internal Resonance in Nonlinear Doubly Curved Shallow Panels with Rectangular Platform
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The Impact Induced 3:1 Internal Resonance in Nonlinear Doubly Curved Shallow Panels with Rectangular Platform

机译：具有矩形平台的非线性双曲浅面板的碰撞诱导3：1内部共振

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摘要

Geometrically non-linear vibrations of doubly curved shallow panels with rectangular platform under the low-velocity impact by an elastic sphere are investigated. It is assumed that the target is simply supported and partial differential equations are obtained in terms of its transverse displacement and Airy's stress function. The local bearing of the target and impactor's materials is neglected with respect to the shell deflection in the contact region. The equations of motion are reduced to a set of infinite nonlinear ordinary differential equations of the second order in time and with cubic and quadratic nonlinearities in terms of the generalized displacements. The internal resonance three-to-one induced during the process of impact is investigated by the method of multiple time scales. The time dependence of the contact force is determined.
机译：研究了弹性球体在低速冲击下矩形平台双曲浅面板的几何非线性振动。假定简单地支撑目标，并根据其横向位移和艾里应力函数获得了偏微分方程。对于靶子和冲击器材料的局部支承，在接触区域中的壳体挠度方面可以忽略。运动方程在时间上被简化为一组无限次的二阶非线性常微分方程，并且在广义位移方面具有三次和二次非线性。采用多种时间尺度的方法研究了撞击过程中三对一的内部共振。确定了接触力的时间依赖性。

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