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精确计算电磁炮发射轨道的受力变形,将发射轨道模拟为移动载荷作用下弹性基础上的简支梁,并应用欧拉梁理论建立了力学模型,利用伽辽金法和Sturn-Liouville展开,推导出了电磁炮发射轨道受正弦函数磁压力下控制方程的解析解.与通常用拉格朗日方程法计算轨道受力变形的方法相比,利用伽辽金法求解不需要计算梁的动能、应变能和耗散能.用Matlab软件做算例分析得到:梁的变形受阻尼系数、移动载荷的出口速度、弹性系数等因素影响显著,受轨道质量的影响很小.
The elastic orbit of the electromagnetic cannon’s launch orbit is accurately calculated and the launch orbit is modeled as a simply supported beam under the elastic load of moving load. The mechanical model is established by using the Eulerian beam theory. By using the Galerkin method and Sturn-Liouville expansion, The analytical solution of the control equations of the electromagnetic cannon orbit under the magnetic pressure of the sine function is deduced. Compared with the method of calculating the deformation of the orbit normally by the Lagrange method, the kinetic energy of the beam need not be calculated by Galerkin method , Strain energy and dissipative energy.An example analysis using Matlab software shows that the deformation of the beam is significantly affected by the damping coefficient, the exit velocity of the moving load, the elastic coefficient and other factors, and is less affected by the orbital quality.