提出了一种新型数值方法——拟小波方法研究梁的动力稳定性.给出了求解梁动力响应的拟小波算法,采用拟小波数值格式离散振动方程中的空间导数,四阶Runge - Kutta(RK4)法离数时间导数.通过判断动力响应的稳定性而得到梁的动力失稳区.用拟小波方法计算了受到周期性轴向力作用时两端简支和固支梁的动力失稳区,并讨论了周期性轴向力中恒定项对动力失稳区的影响.将拟小波方法计算的动力失稳区与现有解析解进行对比,发现两种计算结果吻合得很好,从而验证了采用拟小波方法研究梁动力稳定性的可行性和有效性.同时研究结果表明随着轴向力中恒定项的增加,动力失稳区由高频区移向低频区.%A novel numerical method-quasi-wavelet method is proposed for studying the dynamic stability of beams. The quasi-wavelet algorithm to solve dynamic responses of beams is stated. The quasi-wavelet numerical scheme is used to discrete the spatial derivatives in the equation of vibration, while the fourth-order Runge-Kutta( RK4 ) method is adopted to deal with the temporal discretization. The dynamic instability regions are obtained by judging the stability of dynamic responses of beams. The dynamic instability regions of simply supported-simply supported and clamped-clamped beams subjected to periodic axial forces are calculated by quasi-wavelet method. And the effect of the constant term in the periodic axial force on the instability region is also discussed. Comparing the dynamic instability regions obtained by quasi-wavelet method with existing analytical results, it is found that the two kinds of results are coincident with each other well, which verifies the feasibility and effectiveness of quasi-wavelet method to the study of dynamic stability of beams. Meanwhile the result also shows the instability region shifts from high frequencies to low frequencies with the increase of the constant term in the periodic axial force.
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