薄板结构的吸振控制研究
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摘要
实际受激振动系统多是弹性结构，如楼板、舰船甲板和飞机壁板等，这些结构的振动和辐射噪声往往给工作环境和产品性能等带来不利的影响，对其振动和噪声进行控制的研究是一项很有工程意义的课题。被动式动力吸振器结构简单，安装方便，不需耗能，是一种有效的振动控制装置，本文研究运用被动式动力吸振器控制弹性结构振动的一般性问题，以期为弹性结构吸振控制的工程实施提供理论指导和设计方法。
文中以简支矩形薄板模拟弹性主振系，首先研究了多点简谐集中力和力偶作用下，结构附加多个动力吸振器的动力学模型，推导了系统中的传递功率流，并为了使研究结果具有一般性，将结构导纳和功率流作了无量纲化处理，在此基础上，以控制频率范围内输入主振系的净功率流最大值最小化为优化设计方法，探讨了多种情形下动力吸振器的优化设计问题，分析了各相关因素对吸振器参数和控制效果的影响，得出结论：在质量比较小时，外激励形式和主振系结构形式对吸振器参数的影响较小；通过增大质量比来提高控制效果在质量比较大时不理想；吸振器参数对板的损耗因子不敏感，实际工程中不需要知道精确的损耗因子值；吸振器的安装位置对控制效果影响较大，要尽量将吸振器安装于结构上响应较大的点。
考虑到随机振动在工程中的普遍性，文中还研究了动力吸振器对薄板随机振动的抑制问题。运用结构导纳理论推导了系统的传递函数，将板上各点的位移响应方差在空间域内积分，得到总体位移响应的评价指标，定义为薄板总体位移方差，通过数值分析，得出将吸振器调谐到第一阶模态共振频率，合理选择阻尼参数，可以在整个宽频带内取得有效的抑制随机振动的作用。
针对传统质量-弹簧-阻尼式动力吸振器设计和加工上的不便性，文中还提出了一种简便、有效的高阻尼均直梁式动力吸振器，通过对梁板耦合结构的功率流传递特性的研究，探讨了梁式动力吸振器的优化设计方法，数值仿真结果显示，梁式动力吸振器不但结构简单，质量比小，而且吸振频带宽，吸振效果好，并且增加梁的损耗因子，有利于抑制输入系统的总功率流峰值和输入主振系的净功率流。
The structures excited in practice are mostly elastic structures, and the vibration and noise of those structures are sometimes disadvantageous to working environment and product capability, so the study of control of vibration and noise for them is very meaningful. The passive dynamic vibration absorber is a kind of very effective device for suppressing vibration, which is simple in structure, easy to fit, and not consuming power. The Suppression of vibration of elastic structures using dynamic vibration absorbers is studied in this paper, for providing the theory basis and design method for the vibration-absorption control of elastic structures.
A simply supported rectangular thin plate is simulated as the main vibration system in this paper. The dynamic model of the main system with multiple dynamic vibration absorbers under multiple harmonic fixed force and force-coupling is studied by means of power flow method, and in order to make the results have general meaning, the structure mobility and power flow in the system are expressed in dimensionless fashion. Based on this, regarding the maximum of the net power flow input the main vibration system over the control frequency range as the objective function, discussed is the optimal design of dynamic vibration absorbers in multiple cases. Furthermore, by analyzing the influence of interrelated factors on the structure parameters and the control effect of dynamic vibration absorbers, some conclusions are attained as follows: the influence of the exciting form and main structure form on the parameters of dynamic vibration absorbers is not apparent when the mass ratio is small; increasing the mass ratio can enhance the control effect, but it is not economical when the mass ratio is biggish; the exact loss factor of the main vibration system is not necessary in practical engineering; dynamic vibration absorbers should be fit in the positions of large response to attain good control effect.
Because random vibration is widespread in practice, the suppression of random vibration of a plate using a dynamic vibration absorber is also studied in this paper. The system transfer function is deduced by means of the theories of structure mobility. And based on this, the displacement response variance is integrated in the space field to attain the evaluation index of total response, which is named as the total displacement response variance. The results of the numerical simulation demonstrate that the dynamic vibration absorber is effective in suppressing random vibration in the whole broadband frequency region when it is tuned to the first resonance and has appropriate damping coefficient.
A kind of broadband uniform beam-type dynamic vibration absorber for elastic structures is brought forward for the complexity of the traditional dynamic vibration absorber. Based on the power flow characteristic of the beam-plate coupled structure,
文中以简支矩形薄板模拟弹性主振系，首先研究了多点简谐集中力和力偶作用下，结构附加多个动力吸振器的动力学模型，推导了系统中的传递功率流，并为了使研究结果具有一般性，将结构导纳和功率流作了无量纲化处理，在此基础上，以控制频率范围内输入主振系的净功率流最大值最小化为优化设计方法，探讨了多种情形下动力吸振器的优化设计问题，分析了各相关因素对吸振器参数和控制效果的影响，得出结论：在质量比较小时，外激励形式和主振系结构形式对吸振器参数的影响较小；通过增大质量比来提高控制效果在质量比较大时不理想；吸振器参数对板的损耗因子不敏感，实际工程中不需要知道精确的损耗因子值；吸振器的安装位置对控制效果影响较大，要尽量将吸振器安装于结构上响应较大的点。
考虑到随机振动在工程中的普遍性，文中还研究了动力吸振器对薄板随机振动的抑制问题。运用结构导纳理论推导了系统的传递函数，将板上各点的位移响应方差在空间域内积分，得到总体位移响应的评价指标，定义为薄板总体位移方差，通过数值分析，得出将吸振器调谐到第一阶模态共振频率，合理选择阻尼参数，可以在整个宽频带内取得有效的抑制随机振动的作用。
针对传统质量-弹簧-阻尼式动力吸振器设计和加工上的不便性，文中还提出了一种简便、有效的高阻尼均直梁式动力吸振器，通过对梁板耦合结构的功率流传递特性的研究，探讨了梁式动力吸振器的优化设计方法，数值仿真结果显示，梁式动力吸振器不但结构简单，质量比小，而且吸振频带宽，吸振效果好，并且增加梁的损耗因子，有利于抑制输入系统的总功率流峰值和输入主振系的净功率流。
The structures excited in practice are mostly elastic structures, and the vibration and noise of those structures are sometimes disadvantageous to working environment and product capability, so the study of control of vibration and noise for them is very meaningful. The passive dynamic vibration absorber is a kind of very effective device for suppressing vibration, which is simple in structure, easy to fit, and not consuming power. The Suppression of vibration of elastic structures using dynamic vibration absorbers is studied in this paper, for providing the theory basis and design method for the vibration-absorption control of elastic structures.
A simply supported rectangular thin plate is simulated as the main vibration system in this paper. The dynamic model of the main system with multiple dynamic vibration absorbers under multiple harmonic fixed force and force-coupling is studied by means of power flow method, and in order to make the results have general meaning, the structure mobility and power flow in the system are expressed in dimensionless fashion. Based on this, regarding the maximum of the net power flow input the main vibration system over the control frequency range as the objective function, discussed is the optimal design of dynamic vibration absorbers in multiple cases. Furthermore, by analyzing the influence of interrelated factors on the structure parameters and the control effect of dynamic vibration absorbers, some conclusions are attained as follows: the influence of the exciting form and main structure form on the parameters of dynamic vibration absorbers is not apparent when the mass ratio is small; increasing the mass ratio can enhance the control effect, but it is not economical when the mass ratio is biggish; the exact loss factor of the main vibration system is not necessary in practical engineering; dynamic vibration absorbers should be fit in the positions of large response to attain good control effect.
Because random vibration is widespread in practice, the suppression of random vibration of a plate using a dynamic vibration absorber is also studied in this paper. The system transfer function is deduced by means of the theories of structure mobility. And based on this, the displacement response variance is integrated in the space field to attain the evaluation index of total response, which is named as the total displacement response variance. The results of the numerical simulation demonstrate that the dynamic vibration absorber is effective in suppressing random vibration in the whole broadband frequency region when it is tuned to the first resonance and has appropriate damping coefficient.
A kind of broadband uniform beam-type dynamic vibration absorber for elastic structures is brought forward for the complexity of the traditional dynamic vibration absorber. Based on the power flow characteristic of the beam-plate coupled structure,
引文
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