热环境下干摩擦支承边界系统的振动特性研究
发布时间：2018-07-17 08:34
【摘要】：从工程实际中提炼出一种热环境下含间隙的机械构件的力学模型，根据不同的接触边界，建立了三种不同的横向振动微分方程。分析了梁内部由于变温作用产生的温度应力，讨论了梁由于变温作用发生失稳的临界温度。考虑干摩擦和温度应力同时影响下的梁的运动，导出相应的固有频率以及固有振型的解析表达式，，验证了振型正交性。根据解析解以及由Matlab编写的有限元程序解答，讨论了不同边界接触形式下变温对固有频率的非线性影响。建立了右端相对滑动情况下梁的无量纲模态坐标方程，讨论了变温对实际模态坐标与无量纲模态坐标之间的转化关系的影响。采用谐波平衡法以及半周期稳态解法，分析了系统的非粘结稳态振动以及解存在的条件，当给定实际简谐激励，包括实际激励幅值和实际激励频率时，给出了确定系统能够产生非粘结运动的变温范围的方法。分析了系统的双stop粘滑运动，求解出三分之一倍频激励下双stop粘滑运动解析解，分析了解的存在条件，给出了确定系统能够产生三分之一倍频激励下双stop粘滑运动的变温范围的方法。采用中心差分法数值验证了非粘结振动以及双stop粘滑运动的解析解。
[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.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113.1
本文编号：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.
【学位授予单位】：南京航空航天大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：TH113.1
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