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超聲速氣流下黏彈性?shī)A層壁板非線性顫振分析

Nonlinear analysis of viscoelastic sandwich panel's vibration under supersonic airflow

  • 摘要: 基于Kelvin-Voigt黏彈性本構(gòu)模型、von-Karmen薄板大變形理論和三階氣動(dòng)力活塞理論建立了三維黏彈性?shī)A層壁板的氣動(dòng)彈性顫振方程。使用Galerkin截?cái)喾椒ǎ瑢?duì)超聲速氣流下，四邊簡(jiǎn)支黏彈性?shī)A層壁板顫振的非線性特性進(jìn)行了研究。對(duì)于非線性一階截?cái)喾匠蹋芯苛怂钠胶恻c(diǎn)及穩(wěn)定性隨來(lái)流速度的變化情況，得到了系統(tǒng)發(fā)生靜態(tài)分叉時(shí)的臨界速度；對(duì)于非線性二階截?cái)喾匠蹋褂脭?shù)值仿真分析方法，得到了系統(tǒng)發(fā)生Hopf分叉時(shí)的臨界速度，并利用響應(yīng)、相圖等手段研究得到黏彈性?shī)A層板隨來(lái)流速度變化的動(dòng)力學(xué)特性。

     

    Abstract: Based on the Kelvin-Voigt constitutive law, the governing equations for the fluRer vibration of the viscoelastic sandwich panel are established with consideration of the yon-Karmen thin plate large deflection and the nonlinear piston theory. By using the method of the Galerkin tnmcation, the nonlinear dynamical characteristics of the viscoelastic sandwich panel under the supersonic flow and with the simple suppoas on four sides are analyzed. For the equation of the first-order Galerkin truncation, the equilibrium of the system and its stability are studied, the critical flow of the static bifurcation is obtained; for the equation of the second-order Galerkin truncation, the critical flow of the Hopf bifurcation is obtained by applying the Hopf bifurcation criterion, the dynamical behavior with the varying flow conditions is observed by employing the diagram of the response and phase portrait.

     

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