结构共振疲劳试验及裂纹构件的振动疲劳耦合分析
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摘要
工程中,任何结构都存在不同程度的损伤,多数以裂纹模式存在。受外部激励作用,结构可能同时产生振动和疲劳现象,两者之间相互耦合,从而引起新的科学问题。本文以典型结构件的共振疲劳试验结论为理论分析的依据,基于局部柔度理论,透过振动分析与疲劳裂纹扩展理论研究裂纹梁和裂纹板的振动疲劳耦合效应,探讨裂纹扩展下的结构振动行为与振动对疲劳裂纹扩展的影响。主要研究内容和学术贡献如下:
试验方面,设计了激振器激励的振动疲劳试验系统,提出了共振频带激励的结构寿命测试方法。以典型结构件为对象,完成了不同工况下的结构共振疲劳试验。透过试验现象观察和试验数据分析,发现了影响结构振动疲劳寿命的诸多因素,并讨论了各因素与振动疲劳寿命之间的内在联系。
理论方面,基于断裂力学和能量原理,推导了横向裂纹梁的局部柔度模型,计算了典型加载时常见形式裂纹均匀梁的局部柔度系数。以裂纹梁为对象,提出了裂纹梁的振动疲劳寿命分析方法,着重考虑结构响应特性随疲劳裂纹扩展的变化。分析时,通过复弹性模量引入阻尼损耗因子,Paris方程模拟裂纹扩展,同步分析方法考虑振动与疲劳的耦合效应。分析后发现,激励频率、阻尼以及模态等对疲劳裂纹扩展具有重要影响,共振疲劳裂纹扩展的阻尼效应十分明显,第一阶共振疲劳破坏尤为严重。然后,考虑裂纹呼吸行为对振动与疲劳的作用,利用双线性弹簧模型描述裂纹呼吸行为,通过Galerkin方法把裂纹梁简化为单自由度系统,基于刚度时变性建立裂纹梁的参数振动方程,结合Coulomb干摩擦模型和能量耗散理论推导摩擦阻尼损耗因子,应用广义Forman方程模拟裂纹扩展。研究表明,裂纹闭合使梁的固有频率下降速度减缓,缩短振动疲劳寿命,呼吸行为引发参数振动,导致振动不稳定,摩擦阻尼对共振疲劳寿命影响显著。以裂纹板为对象,建立了裂纹板的振动模型,并讨论振动参数对板疲劳裂纹扩展的影响。理论推导时,把结构裂纹等效为附加外载荷,由力学平衡原理推导含裂纹项的板振动方程,通过Rice和Levy得到的应力关系式形成裂纹项,经Galerkin法把双边悬臂裂纹板简化为单自由度系统,再根据Berger方法考虑面内载荷得到含二、三次非线性项的振动方程。结果显示,结构尺寸、疲劳裂纹及激励力等参数对裂纹板的振动行为具有明显的影响,阻尼、激励幅值和激励频率等对疲劳裂纹扩展寿命的作用不容忽视。
最后,推广理论研究成果,提出一种简易的考虑耦合影响的结构振动疲劳寿命分析方法。通过典型试验件的共振疲劳寿命计算验证分析方法的合理性。结果表明,该寿命分析方法简单易行,给工程结构的振动疲劳寿命分析提供了一种思路。
There are different modes of damage in any engineering structures, and most of them are cracks. Problems of vibration and fatigue are often produced by external force simultaneously. New scientific problems are produced due to coupling effect of vibration and fatigue. Based on the results of fatigue testing for the resonating structure, the cracked beam and the cracked plate are employed for coupling research of vibration and fatigue through vibration analysis and fatigue crack growth calculation in view of local complicane model. The vibration behaviors change as crack growth and the influence of vibration on fatigue crack propagation are discussed. The results and the main contributions are as following.
In experiment, vibration-exciter-based fatigue testing system is designed and a fatigue testing method of the resonance controlled structure is proposed. Experiments are carried out for the typical components under different working conditions. Influences of dynamic characteristis on the structure fatigue life are discoveried through investigation of experimental phenomena and datas. The internal connecting link of vibration and fatigue crack growth is discussed.
In theory, to begin with the local compliance model of the cracked beam is given in view of the fracture mechanics and energy principle. Local compliance expression of the uniformity cantilever beam subjected to a typical loading with common mode crack is given. In addition, a new analytical method of the vibration fatigue life for the cracked beam is proposed with the structural response changes as crack growth. In this analysis, the damping loss factor is introduced by complex elastic modulus, and the crack growth is analyzed by employing a Paris equation, and the coupling effect of vibration and crack growth is considered by vibration analysis and fatigue crack growth calculation cycle by cycle. It can be shown that the influences of frequency, damping and mode on vibration fatigue life are very obvious. Due to the influence of damping, the resonance fatigue crack growth rate decrease, and the first resonance has more contribution to fatigue crack growth than that of other mode vibration. What is more, the influence of the crack breathing behavior on vibration and fatigue are studied. During the coupling analysis, the breathing crack is depicted by the double linear spring model, and the cracked beam is simplied to single-degree-of-freedom system by Galerkin’s method, and the parametric vibration equation is deduced by employing the varying stiffnes, and the friction damping loss factor is given based on the Coulomb friction model and the energy dissipation theory, and the crack propagation is analyzed by employing a modified Forman equation. Results indicate that the closing effect of the breathing crack adds average stiffness, and influences of parametric resonance on the vibration fatigue can’t be ignored, and the friction damping has important influence on the life of vibration fatigue crack growth. Finally, an analytical model of the vibrating cracked plate is derived and the coupling effects of vibration and fatigue are investigated. In analysis, the crack is equivalented by an additional external force, and equation of the vibrating cracked plate is derived by using mechanical equilibrium principle, and the crack terms are obtained by using stress relational expression introduced by Rice and Levy. Galerkin’s method is applied to reformulate the vibration equation of the bilateral cantilver cracked plate into single-degree-of-freedom system. Nonlinearity is introduced by formulations introduced by applying Berger’s method. Results are presented in terms of natural frequency versus structural dimensions and crack length, and the structural vibration response of the cracked plate is calculated of cracked plate, and the influences of damping and exciting force on the life of vibration fatigue are discussed.
Finally, a simple analytical method of the structural vibration fatigue life with coupling effect is proposed based on the theoretical research production, and the rationality of the analytical method is verified by the simulation results of the typical experimental component. Results indicate that this analytical method of the vibration fatigue life is simple, and it is a good idea for fatigue life analysis of engineering structures.
试验方面,设计了激振器激励的振动疲劳试验系统,提出了共振频带激励的结构寿命测试方法。以典型结构件为对象,完成了不同工况下的结构共振疲劳试验。透过试验现象观察和试验数据分析,发现了影响结构振动疲劳寿命的诸多因素,并讨论了各因素与振动疲劳寿命之间的内在联系。
理论方面,基于断裂力学和能量原理,推导了横向裂纹梁的局部柔度模型,计算了典型加载时常见形式裂纹均匀梁的局部柔度系数。以裂纹梁为对象,提出了裂纹梁的振动疲劳寿命分析方法,着重考虑结构响应特性随疲劳裂纹扩展的变化。分析时,通过复弹性模量引入阻尼损耗因子,Paris方程模拟裂纹扩展,同步分析方法考虑振动与疲劳的耦合效应。分析后发现,激励频率、阻尼以及模态等对疲劳裂纹扩展具有重要影响,共振疲劳裂纹扩展的阻尼效应十分明显,第一阶共振疲劳破坏尤为严重。然后,考虑裂纹呼吸行为对振动与疲劳的作用,利用双线性弹簧模型描述裂纹呼吸行为,通过Galerkin方法把裂纹梁简化为单自由度系统,基于刚度时变性建立裂纹梁的参数振动方程,结合Coulomb干摩擦模型和能量耗散理论推导摩擦阻尼损耗因子,应用广义Forman方程模拟裂纹扩展。研究表明,裂纹闭合使梁的固有频率下降速度减缓,缩短振动疲劳寿命,呼吸行为引发参数振动,导致振动不稳定,摩擦阻尼对共振疲劳寿命影响显著。以裂纹板为对象,建立了裂纹板的振动模型,并讨论振动参数对板疲劳裂纹扩展的影响。理论推导时,把结构裂纹等效为附加外载荷,由力学平衡原理推导含裂纹项的板振动方程,通过Rice和Levy得到的应力关系式形成裂纹项,经Galerkin法把双边悬臂裂纹板简化为单自由度系统,再根据Berger方法考虑面内载荷得到含二、三次非线性项的振动方程。结果显示,结构尺寸、疲劳裂纹及激励力等参数对裂纹板的振动行为具有明显的影响,阻尼、激励幅值和激励频率等对疲劳裂纹扩展寿命的作用不容忽视。
最后,推广理论研究成果,提出一种简易的考虑耦合影响的结构振动疲劳寿命分析方法。通过典型试验件的共振疲劳寿命计算验证分析方法的合理性。结果表明,该寿命分析方法简单易行,给工程结构的振动疲劳寿命分析提供了一种思路。
There are different modes of damage in any engineering structures, and most of them are cracks. Problems of vibration and fatigue are often produced by external force simultaneously. New scientific problems are produced due to coupling effect of vibration and fatigue. Based on the results of fatigue testing for the resonating structure, the cracked beam and the cracked plate are employed for coupling research of vibration and fatigue through vibration analysis and fatigue crack growth calculation in view of local complicane model. The vibration behaviors change as crack growth and the influence of vibration on fatigue crack propagation are discussed. The results and the main contributions are as following.
In experiment, vibration-exciter-based fatigue testing system is designed and a fatigue testing method of the resonance controlled structure is proposed. Experiments are carried out for the typical components under different working conditions. Influences of dynamic characteristis on the structure fatigue life are discoveried through investigation of experimental phenomena and datas. The internal connecting link of vibration and fatigue crack growth is discussed.
In theory, to begin with the local compliance model of the cracked beam is given in view of the fracture mechanics and energy principle. Local compliance expression of the uniformity cantilever beam subjected to a typical loading with common mode crack is given. In addition, a new analytical method of the vibration fatigue life for the cracked beam is proposed with the structural response changes as crack growth. In this analysis, the damping loss factor is introduced by complex elastic modulus, and the crack growth is analyzed by employing a Paris equation, and the coupling effect of vibration and crack growth is considered by vibration analysis and fatigue crack growth calculation cycle by cycle. It can be shown that the influences of frequency, damping and mode on vibration fatigue life are very obvious. Due to the influence of damping, the resonance fatigue crack growth rate decrease, and the first resonance has more contribution to fatigue crack growth than that of other mode vibration. What is more, the influence of the crack breathing behavior on vibration and fatigue are studied. During the coupling analysis, the breathing crack is depicted by the double linear spring model, and the cracked beam is simplied to single-degree-of-freedom system by Galerkin’s method, and the parametric vibration equation is deduced by employing the varying stiffnes, and the friction damping loss factor is given based on the Coulomb friction model and the energy dissipation theory, and the crack propagation is analyzed by employing a modified Forman equation. Results indicate that the closing effect of the breathing crack adds average stiffness, and influences of parametric resonance on the vibration fatigue can’t be ignored, and the friction damping has important influence on the life of vibration fatigue crack growth. Finally, an analytical model of the vibrating cracked plate is derived and the coupling effects of vibration and fatigue are investigated. In analysis, the crack is equivalented by an additional external force, and equation of the vibrating cracked plate is derived by using mechanical equilibrium principle, and the crack terms are obtained by using stress relational expression introduced by Rice and Levy. Galerkin’s method is applied to reformulate the vibration equation of the bilateral cantilver cracked plate into single-degree-of-freedom system. Nonlinearity is introduced by formulations introduced by applying Berger’s method. Results are presented in terms of natural frequency versus structural dimensions and crack length, and the structural vibration response of the cracked plate is calculated of cracked plate, and the influences of damping and exciting force on the life of vibration fatigue are discussed.
Finally, a simple analytical method of the structural vibration fatigue life with coupling effect is proposed based on the theoretical research production, and the rationality of the analytical method is verified by the simulation results of the typical experimental component. Results indicate that this analytical method of the vibration fatigue life is simple, and it is a good idea for fatigue life analysis of engineering structures.
引文
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