集中荷载作用下双层弹性悬臂梁动力学分析

Dynamic Analysis of Two-layered Elastic Cantilever Beam under the Action of Concentrated Load

通过研究动集中载荷对双层弹性悬臂梁的动力学影响,旨在探讨悬臂式电磁发射装置的轨道及壁板的受力及振动规律。采用双层弹性基础梁理论,对悬臂式双层弹性基础梁在动集中载荷作用下的受力和振动情况进行了分析,将电磁发射装置的轨道及壁板简化为双层弹性悬臂梁力学模型,采用Dirac函数表示运动状态下电枢作用在轨道上的集中力,得出了内梁和外梁的动力学微分方程,应用模态函数正交性,求得了内外梁弯矩和应力的解析解。通过算例,分析了内梁和外梁的动力响应,并在相同条件下应用ANSYS进行了数值模拟,最后将解析解与数值解进行了比较,解析解的可靠性得到验证。将电磁发射装置简化为双层弹性悬臂梁要比单层弹性悬臂梁更加接近实际工况。研究成果有助于电磁发射装置的理论研究,可供相关工程设计参考。

The dynamic effect of the moving concentrated load on the two-layered elastic cantilever is studied, which aims to investigate the force and vibration of the rails and wall panels of the cantilever electromagnetic device. The research is ba sed on the two-layered elastic cantilever beam theory, analyzes the stress and vibration of two-layered elastic cantilever beam subjected to moving concentrated load, taking the electromagnetic launch device rails and wall panels as a two-layered elastic foundation beam, establishing a mechanical model, using the Dirac function to express the action of concentrated force on the rails due to the armature’s movement, and establishing the dynamic differential equation of upper beam and lower beam. The analytical solution of bending moment and stress of upper and lower beam is obtained according to modal orthogonality. In a case of given motion parameters and structural parameters, the dynamic response of the upper beam and the lower beam are analyzed;then the numerical simulation is carried out under the same conditions by ANSYS. Finally, the practicability of analytical solution is verified by comparisons with the numerical solution. The two-layered elastic cantilever beam model, which is more applicable to the actual working condition than the single-layered elastic cantilever beam model. It will contribute to the theoretical research on the electromagnetic launch device and can be used for reference of the engineering design in related fields.