熱環(huán)境下干摩擦支承邊界系統(tǒng)的振動特性研究
發(fā)布時間：2018-07-17 08:34
【摘要】：從工程實際中提煉出一種熱環(huán)境下含間隙的機械構件的力學模型，根據(jù)不同的接觸邊界，建立了三種不同的橫向振動微分方程。分析了梁內部由于變溫作用產生的溫度應力，討論了梁由于變溫作用發(fā)生失穩(wěn)的臨界溫度�？紤]干摩擦和溫度應力同時影響下的梁的運動，導出相應的固有頻率以及固有振型的解析表達式，，驗證了振型正交性。根據(jù)解析解以及由Matlab編寫的有限元程序解答，討論了不同邊界接觸形式下變溫對固有頻率的非線性影響。建立了右端相對滑動情況下梁的無量綱模態(tài)坐標方程，討論了變溫對實際模態(tài)坐標與無量綱模態(tài)坐標之間的轉化關系的影響。采用諧波平衡法以及半周期穩(wěn)態(tài)解法，分析了系統(tǒng)的非粘結穩(wěn)態(tài)振動以及解存在的條件，當給定實際簡諧激勵，包括實際激勵幅值和實際激勵頻率時，給出了確定系統(tǒng)能夠產生非粘結運動的變溫范圍的方法。分析了系統(tǒng)的雙stop粘滑運動，求解出三分之一倍頻激勵下雙stop粘滑運動解析解，分析了解的存在條件，給出了確定系統(tǒng)能夠產生三分之一倍頻激勵下雙stop粘滑運動的變溫范圍的方法。采用中心差分法數(shù)值驗證了非粘結振動以及雙stop粘滑運動的解析解。
[Abstract]:A mechanical model of mechanical members with gaps in thermal environment is extracted from engineering practice. According to different contact boundaries, three different differential equations of transverse vibration are established. The temperature stress in the beam due to the variable temperature is analyzed and the critical temperature of the instability of the beam due to the variable temperature is discussed. Considering the effects of both dry friction and thermal stress on the motion of the beam, the analytical expressions of the corresponding natural frequency and natural mode are derived, and the orthogonality of the modes is verified. According to the analytical solution and the finite element program solution written by Matlab, the nonlinear influence of temperature variation on natural frequency under different boundary contact forms is discussed. The dimensionless modal coordinate equation of the beam under the condition of relative sliding at the right end is established, and the influence of temperature on the transformation between the actual modal coordinate and the dimensionless modal coordinate is discussed. By using harmonic balance method and semi-periodic steady-state solution, the unbonded steady state vibration of the system and the conditions for the existence of the solution are analyzed. When the actual harmonic excitation is given, including the actual excitation amplitude and the actual excitation frequency, The method of determining the variable temperature range of the system which can produce unbonded motion is given. The double stop stick-slip motion of the system is analyzed, and the analytical solution of the double stop stick-slip motion under the excitation of 1/3 times frequency is obtained, and the existence conditions of the solution are analyzed. A method is given to determine the temperature range of the double stop stick-slip motion under the excitation of 1/3 times frequency. The central difference method is used to verify the analytical solutions of the unbonded vibration and the double stop stick-slip motion.
【學位授予單位】：南京航空航天大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH113.1
本文編號：2129822
[Abstract]:A mechanical model of mechanical members with gaps in thermal environment is extracted from engineering practice. According to different contact boundaries, three different differential equations of transverse vibration are established. The temperature stress in the beam due to the variable temperature is analyzed and the critical temperature of the instability of the beam due to the variable temperature is discussed. Considering the effects of both dry friction and thermal stress on the motion of the beam, the analytical expressions of the corresponding natural frequency and natural mode are derived, and the orthogonality of the modes is verified. According to the analytical solution and the finite element program solution written by Matlab, the nonlinear influence of temperature variation on natural frequency under different boundary contact forms is discussed. The dimensionless modal coordinate equation of the beam under the condition of relative sliding at the right end is established, and the influence of temperature on the transformation between the actual modal coordinate and the dimensionless modal coordinate is discussed. By using harmonic balance method and semi-periodic steady-state solution, the unbonded steady state vibration of the system and the conditions for the existence of the solution are analyzed. When the actual harmonic excitation is given, including the actual excitation amplitude and the actual excitation frequency, The method of determining the variable temperature range of the system which can produce unbonded motion is given. The double stop stick-slip motion of the system is analyzed, and the analytical solution of the double stop stick-slip motion under the excitation of 1/3 times frequency is obtained, and the existence conditions of the solution are analyzed. A method is given to determine the temperature range of the double stop stick-slip motion under the excitation of 1/3 times frequency. The central difference method is used to verify the analytical solutions of the unbonded vibration and the double stop stick-slip motion.
【學位授予單位】：南京航空航天大學
【學位級別】：碩士
【學位授予年份】：2012
【分類號】：TH113.1
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