【摘要】：研究了軸向運(yùn)動粘彈性Rayleigh梁參激振動的穩(wěn)定性。根據(jù)廣義哈密頓原理建立軸向運(yùn)動Rayleigh梁橫向振動的控制方程,同時考慮軸力的變化。采用多尺度方法直接求解控制方程,推導(dǎo)出主共振和組合共振的可解性條件;利用Routh-Hurwitz穩(wěn)定性判據(jù)導(dǎo)出了穩(wěn)定性邊界方程;進(jìn)而確定梁兩端簡支和固支邊界條件下,因共振而產(chǎn)生的失穩(wěn)區(qū)域。數(shù)值算例給出了兩端簡支和固支邊界條件下彎曲剛度,支撐剛度,粘彈性系數(shù)以及平均速度對前兩階主共振及組合共振穩(wěn)定性區(qū)域的影響。
[Abstract]:The stability of parametric vibration of viscoelastic Rayleigh beams with axial motion is studied. Based on the generalized Hamiltonian principle, the governing equations of lateral vibration of axially moving Rayleigh beams are established, and the variation of axial forces is considered. The solvability conditions of main resonance and combined resonance are derived by using multi-scale method, the stability boundary equation is derived by using Routh-Hurwitz stability criterion, and the boundary conditions of simple support and fixed support at both ends of beam are determined. A region of instability resulting from resonance. Numerical examples show the effects of bending stiffness, bracing stiffness, viscoelastic coefficient and average velocity on the first two order principal resonance and combined resonance stability region under the boundary conditions of simple support and fixed support.
【作者單位】： 上海應(yīng)用技術(shù)大學(xué);廣州明珞汽車裝備有限公司;
【基金】：國家自然科學(xué)基金項(xiàng)目(11202136)
【分類號】：TB535

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