身管横向固有振动的半解析解法

为了获得更加精确的身管横向固有振动解，将身管简化成多段考虑截面剪切变形和转动惯量的变截面Timoshenko梁，由此建立了身管的横向振动方程。应用Chebyshev正交多项式将身管的横向振动展开，合并边界条件和各段梁的连接条件可获得一组身管横向固有振动方程组，求解该方程组即可获得变截面身管的固有振动特性。数值算例表明：该方法求解高效，具有良好精度、能适应各种边界条件。

Semi-analytic Solution of Nature Frequency of Transverse Vibration of a Barrel

To obtain more accurate result of transverse natural vibration of barrel, a barrel was simplified to several segments of Timoshenko beams with variable cross-sections in consideration of the shear distortion and the moment of inertia, establishing the transverse vibration equations. The Chebyshev orthogonal polynomial was applied to deploy the differential equations. As a result, a set of transverse nature vibration equations of the barrel was obtained by assembling the boundary and collection equations. The natural vibration characteristic of barrel with variable cross-section was got by solving the equations. The results of numerical examples show that the method is effective, accurate, and could adapt to various boundary conditions.