本文選題：廣義Hamilton變分原理　切入點：限制失穩(wěn)　出處：《應用力學學報》2016年05期 　論文類型：期刊論文

【摘要】：應用廣義Hamilton變分原理,建立了任意位置限位器約束下繞軸線自轉簡支梁的非線性模型。取簡支梁前兩階模態(tài)為Ritz基分析系統(tǒng)的穩(wěn)定性,獲得了限位器無摩擦情形下系統(tǒng)的限制失穩(wěn)臨界值、分岔模式、后屈曲解以及致穩(wěn)限位器的最佳配置位置。擴充Ritz基對失穩(wěn)臨界值和限位器最佳配置位置的收斂性進行了驗證;進一步分析了限位器夾緊力摩擦效應對系統(tǒng)穩(wěn)定性的影響規(guī)律。研究表明:在限位器約束下,繞軸線自轉簡支梁存在臨界轉速,當轉速超過臨界轉速時,梁的撓度和軸向位移分別發(fā)生叉式分岔和跨臨界分岔而失去穩(wěn)定性;限位器夾緊力摩擦效應將提升失穩(wěn)臨界值,使失穩(wěn)后的系統(tǒng)在轉速返回時出現明顯的滯后效應,以比失穩(wěn)臨界值更低的轉速回到原平衡位置;繞軸線自轉簡支梁系統(tǒng)致穩(wěn)限位器的最佳配置位置在梁長的中間。這些結果對提升繞軸線自轉簡支梁的局部限制失穩(wěn)性能的認識和指導限位器的配置具有實際意義。
[Abstract]:Based on the generalized Hamilton variational principle, a nonlinear model of a simply supported beam with rotation around an axis is established under the constraint of an arbitrary position limiter. The first two modes of the simply supported beam are taken as the stability of the Ritz basis analysis system. The limit instability critical value, bifurcation mode, post-buckling solution and the optimal configuration position of the stabilizer are obtained under the condition of no friction. The convergence of the instability critical value and the optimal configuration position of the limiter is verified by the extended Ritz basis. The influence of clamping force friction effect on the stability of the system is further analyzed. The results show that there is a critical speed of the simply supported beam rotating around the axis under the constraint of the limiter, and when the rotational speed exceeds the critical speed, The deflection and axial displacement of the beam are forked bifurcation and transcritical bifurcation, respectively, and the friction effect of clamping force of the limiter will increase the critical value of instability and make the system after the instability appear obvious hysteresis effect when the rotational speed returns. Return to the original equilibrium position at a speed lower than the critical value of instability; The optimal position of the stability limiter is in the middle of the beam length. These results are of practical significance to the understanding of the local limited instability performance of the rotating simply supported beam around the axis and the configuration of the locator.
【作者單位】： 中國工程物理研究院總體工程研究所;
【基金】：國家自然科學基金(11402244) 中物院發(fā)展基金(2015B0201024) 中國工程物理研究院重點學科項目“計算固體力學”資助
【分類號】：O317

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本文編號：1580374