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首页> 外文会议>International Conference on Mathematical, Computational and Statistical Sciences >Low-Velocity Impact Response of Non-Linear Doubly Curved Shallow Shells with Rectangular Base under 3:1 Internal Resonance
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Low-Velocity Impact Response of Non-Linear Doubly Curved Shallow Shells with Rectangular Base under 3:1 Internal Resonance

机译：非线性双弯曲浅壳的低速冲击响应，矩形底座3：1内谐振

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摘要

Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular base under the low-velocity impact by an elastic sphere are investigated. It is assumed that the shell is simply supported and partial differential equations are obtained in terms of shell's transverse displacement and Airy's stress function. The local bearing of the shell 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. Assuming that only two natural modes of vibrations, which are coupled by a three-to-one internal resonance, dominate during the process of impact and applying the method of multiple time scales, the set of equations is obtained, which allows one to find the time dependence of the contact force and to determine the contact duration and the maximal contact force.
机译：大振幅（几何非线性）双弯曲扁壳与下低速冲击矩形基部通过弹性球的振动进行了研究。据推测，所述外壳简单地支撑并在壳的横向位移和艾里的应力功能方面获得了偏微分方程。外壳和冲击的材料的局部轴承被忽略相对于在接触区域中的外壳偏转。运动方程在广义位移而言被减少到一组所述第二顺序在时间和与立方和二次非线性无限非线性常微分方程的。假定冲击的过程中的振动，这是由一个三到一内部谐振耦合，支配的只有两个自然模式和应用多个时间尺度的方法，得到该组方程，它允许一个找到的接触力的时间依赖性，并确定接触持续时间和最大接触力。

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