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头部无触点旋转冲击,例如颈伤,在数学上被摸拟为绕对称轴作加速旋转的装有纯弹性材料的刚性球壳。我们在本文中得到了波传播的精确解。并借助于拉普拉斯变换方法求解了外壳表面受有矩形角度冲击问题的无量纲基本方程。此外利用方程的双曲特性得出了无量纲应力并通过移位理论得到反演。本文还给出了应力分布和应变能量密度分布以及应力的格林函数,即外输加入的角加速度取狄拉克δ-函数的形式.用卷积积分计算出壳内弹性材料对任何一般的加速度冲击的反应的特性曲线.对于单位冲击输入的各种情况的最大切应力的大小及定位作了比较.矩形冲击按其大小与加速度持续时间的乘积等于1而改变.本文证明了当加速度冲击的持续时间增加时最大的应力值从中心区域向球壳表面移动。对于外加的单位阶跃角加速度输入,应力最大值发生在无量纲时间为2时球壳表面。利用对应原理可以把这个解推广,用来确定含有粘弹性物质的球壳的反应.
Non-contact rotational shocks of the head, such as neck injuries, are mathematically simulated as rigid, spherical shells filled with purely elastic material for accelerated rotation about the axis of symmetry. We obtain the exact solution of wave propagation in this paper. Laplace transform method is used to solve the non-dimensional basic equations of rectangular shell on the surface. In addition, using the hyperbolic characteristic of the equation, dimensionless stress is obtained and the inversion is obtained by the displacement theory. In this paper, the Green’s function of stress distribution, strain energy density distribution and stress is also given, that is, the angular acceleration of external input is in the form of Dirac δ-function. Convolution integral is used to calculate the impact of shell elastic material on any general acceleration shock The magnitude of the maximum shear stress and the location of each impact input are compared with each other.The rectangular impact varies with the product of its magnitude and acceleration duration equal to 1. This paper demonstrates that when the acceleration shock is sustained As the time increases, the maximum stress moves from the center to the surface of the shell. For an additional unit-step angular acceleration input, the maximum stress occurs at the sphere shell surface with a dimensionless time of 2. The corresponding principle can be used to generalize this solution to determine the response of a spherical shell containing viscoelastic material.