确定弹性系统临界力的振动法

Vibration Method of Determining Critical Force in Elastic System

两端铰支杆在纵、横载荷作用下自由振动频率与临界力的关系式为ω~2=ω_0~2[1-(ρ/ρ_0)]。利用能量原理证明杆件在其他约束时也符合上述关系。同时证明上述关系亦适用于板和扁壳等工程中的常见结构。从而得到确定弹性系统临界力振动法的一般表达式。

Based on the relationship between free vibrational frequency and critical force ω=ω_0~2(1-ρ/ρ_0) for two-end-pinned rod with a vertical or horizontal force ap- Plied and with energy theory, it is found that the formula is also suitable for other con- straint conditions of rod. Meanwhile, further studies show that the formula gets good result in common engrneering structures such as flat and shallow shell etc.