定激励下板梁振动功率流最小响应的研究
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摘要
本论文以实验室承担的工程项目为背景,采用理论分析、模拟仿真相结合方法,以振动功率流大小为指标,研究了板构件在不同边界条件下、简支弹性梁构件的振动特性,具有一定的理论意义和重要实用价值。
板梁结构大量运用于机械工程结构中,本文分析了其振动响应特性,找出在定激励作用下的最小振动响应,进行了较深入的理论研究,并具有明确的应用对象(内燃叉车)。
对板梁结构各个结构参数影响板梁结构的振动特性进行了分析,编制了数值优化程序,以功率流峰值最大值最小的优化策略对三种不同的边界条件的板结构进行了激励点位置寻优；对比三种不同边界板结构模型的优化结果,得到三边固定一边自由板结构振动功率流峰值最小,两边固定两边自由板模型功率流峰值最大的结论。为工程上的设计提供理论参考指导。本文的研究工作包括以下内容：
首先研究振动功率流的基本原理、基本概念、计算方法,然后基于振动理论,研究定激励作用下板的振动的分析方法,利用结构动力学、机械导纳的有关理论和处理方法,从功率流的基本概念和基本原理出发推导出了在定激励作用下两边固定两边自由板、四边固定板、三边固定一边自由板功率流表达式,并对在激励点位置、板长、板宽、板厚等参数变化时进行了数值计算,以上理论研究为叉车类车架结构的动态响应分析提供了一种方法,为这类结构的动特性改进与设计提供了理论依据。得到具有工程意义的一般性结论：
(1)这三种边界条件的板厚度的增加,板的功率流峰值是一致减小的。所以在工程设计时,只要工程设计允许时就可以尽可能加大厚度；(2)这三种边界条件的板损耗因子增大时,功率流峰值减小,在工程设计时,若要减小振动功率峰值,要选大的损耗因子；(3)这三种边界条件的板长值由小变大时,功率流峰值一致变小,在工程设计时,尽可能选择大的板长值；(4)这三种边界条件的板宽取小值时,功率流峰值小,在工程设计时,选择小的板宽度值是有利的。小宽度板的模态有一些没有被激励起来,所以振动能量很小。在工程设计时,若能让大多数模态不被激发就是振动能量最小的,可实际工程大量运用薄壁结构件,我们要合理的结构设计,来避免模态的激发；(5)对于四边固定板、两边固定两边自由板,其边界对称,激励点在中心时的振动功率流峰值大于激励点不在中心时的情况。尽管在中心时被激发的模态数少,但此时模态一旦被激发,峰值能量就较大,激励点不在中心时,尽管激励出了较多的模态,可此时的模态峰值较小。在工程设计时,若是激励点在板中心时,一定要考察出此时是否激励出模态。对于两边固定两边自由板、三边固定一边自由板,不仅是激励点要避开中心点激励,还要避开自由边上的激励：(6)这三种边界条件的板,在工程设计时,都需要考虑激励点避开板的中心,在宽度方向上激励点位置不同,峰值出现大小交替,所以,工程设计时,必须通过仔细计算才能找到使得峰值最小位置点；(7)当激励点位置相同时,三种边界条件板各有优劣,取决于点的具体位置,工程设计时,要具体计算来确定用何种边界条件。
针对具有工程意义的简支弹性梁结构,进行了理论分析,得出了具有工程意义的结果：(1)梁越长振动功率流峰值越小；(2)壁厚值需要适当选择；(3)梁损耗因子增大,功率流峰值一致减小,在工程设计时若主要考虑减小功率峰值,就可取较大值的损耗因子,但损耗因子增大,会使得阻尼材料的重量增加；(4)梁截面积不变,-而截面高增加,功率流峰值在减小,所以在工程设计时,当梁截面积为定值时,尽量加大截面高度减小截面宽度；(5)激励点从中间向两端移动变化时候,功率流的峰值变小,激励点尽量选择在离两端近一些。(6)得到设计简支-弹性支承梁系统的顺序是,首先根据结构需要和强度要求设计梁的基本参数,根据系统支承的稳定性及减振的需要来设计弹性支承的刚度范围,利用频率方程数值方法确定固有频率,然后根据本文总结的规律计算最终确定其刚度、梁的长、宽、高、壁厚。
最后运用大型商业软件ANSYS对板模型、梁模型进行了模拟分析,得到了与理论分析相一致的结论,这也印证了理论分析的正确性。
我们知道,内燃叉车的主体结构是钢板焊接而成的车架,动力装置支承在车架上,内燃叉车的振动始终困扰着生产企业,制约着内燃叉车NVH性能的改善。本文的研究结果正好可很好的应用于内燃叉车的结构设计上,有利于设计出理想NVH性能的叉车,会迅速推动企业效益的增长。
This Paper is based on the background of the projects undertaken by the laboratory. By theoretical analysis and numerical calculation method, the paper took the vibration power flow as an objective function, studied the plate with different boundary conditions, and simply supported elastic beam vibration characteristics. The results have the important theory significance and the practical value.
A large number of plate beam structure used in mechanical engineering, its vibration response characteristics need to be researched. In order to identify the Minimum vibration response under the Action of Determine Excitation, a more in-depth research of theory is needed. This paper investigated the vibration characteristics of the plate beam structure, and those researched results have clear application object.
By theoretical analysis and numerical calculation, the paper studied the plate structure vibration characteristics.That different structure parameters how to affect the plate structure vibration characteristics was analysed.The conclusions of designing plate structure with good vibration characteristics were drawed. It provides reference for designing the structure. A numerical optimization program was programmed with minimization peak power optimization strategy.For three different boundary conditions plate structure was optimized.After the comparison of three kinds of different boundary plate structure model of the optimized results, draw a coclution that the three fixed edges plate vibration power flow peak is minimum and the two fixed edges plate vibration power flow peak is maximum. It provides a theoretical reference guide for engineering design.
The paper contents are as follows:
Firstly the basic concepts, basic principles and calculation method of power flow was studied. Then, based on vibration theory, the paper studied plate vibration analysis methods under the action of determine excitation. Regards plate structure as the research object, using structural dynamics, mechanical admittance theory and processing method, From the power flow of the basic concept and the basic principle, the paper deduced the different power flow equations and numerical calculation result of the plates, such as two edges fixed and the other two edges free plate, quadrilateral fix plate, three edges fixed plate,under the action of determine excitation, with different conditions, such as the excitation point position, length, width, thickness and other parameters. The study on the plate structure dynamic response analysis provides a method for designing these dynamic characteristics and provides a theoretical basis for the design improvement. Some general conclusions of engineering significance were drawed.
Some general conclusions of engineering significance as follows:
For the three kind of boundary conditions of the plate,
(1) As the thickness of the plate is increased, power flow peak is reduced.So,when a Mechanism structure is designed, as long as under the condition of the engineering design allows,the thicker the plate is,the less the power flow peak is.(2) As the Plate loss factor is increased, power flow peak is reduced. So, when a Mechanism structure is designed, we should choose the big loss factor.(3) The Plate longth increased and power flow peak reduced.So, when a Mechanism structure is designed, we should choose the longer Plate.(4) As the Plate width is increased, power flow peak is reduced, when a Mechanism structure is designed, we should choose the narrower Plate.Some modal in narrower plate was not excited, so the vibration energy was very small. The vibration is very small when the some modal are not excited. Plate structure is widly used in Practical engineering, so we should design to avoid the excited modal.(5) As Quadrilateral fixed plate and two sides fixed two sides free plate were conserned, they are Symmetric boundary; the vibration power flow peak caused by excitation point in the center of the plate is greater than those caused by the excitation point in the corner of the plate.Although the number of modal excited by in the center were a few, those mode once are excited, peak energy is larger than those that excited by incentive point not in the center, although many modal was incentived, the peak is smaller. When a Mechanism structure is designed, we should pay attention to whether those modal were excited by the incentive point in the center of the board. As three sides fixed plate and two sides fixed two sides free plate are conserned, the position of exciting point is not only to avoid the plate center, but also to avoid the free edge of it.(6) When a Mechanism structure is designed, we should pay attention not to putting the incentive point in the center of the plate. With the different incentive point position the peak changed from big to small alternately, we must calculate carefully to find the minimum peak.(7) When the excitation point position is same, each of the three kinds of boundary conditions plate has advantages and disadvantages, depending on the incentive location. When a Mechanism structure is designed, we should choose the boundary conditions by calculation.
As the beam structure is corncerned, by analyzing in theory, we obtained a series of practical engineering significance results.
(1)The longer of the beam structure is, the less of the power flow is.(2) Wall thickness needs to appropriate select.(3) As the Beam loss factor is increased, power flow peak is reduced. So, when a Mechanism structure is designed, we should choose the big loss factor.(4) The hight increased with the power peak decreased under the condition of constant beam cross section. So, when a Mechanism structure is designed, we should choose the big hight and small width. When incentive point position is shifting from the middle of the beam to two ends of it, power flow peak is varying with from bigger to smaller. The incentive point postion should be putted the two ends or its vicinity. The order of design pivot-elastic supported beam is designing its basic parameters, and then according to the sturucture to support the stability and vibration needs, design elastic supporting rigidity range. After using the frequency equation numerical method to determine the natural frequency, based on the summary of the law, we compute its stiffness, longth, width, hight, wall thickness.
Finally applying the commercial software ANSYS to board model, to beam model is simulated and analyzed. Obtained consistent with the theoretical analysis conclusion, this has also verified the correctness of theoretical analysis.
The main structure of present forklift is welded steel frame; power device is supported on the frame.
Forklift vibration has plagued enterprises, restricting the performance improvement of forklift NVH. On the results of this study can be well applied to the structural design of the forklifts, and quickly promote forklift ideal NVH performance and the enterprise efficiency growth.
板梁结构大量运用于机械工程结构中,本文分析了其振动响应特性,找出在定激励作用下的最小振动响应,进行了较深入的理论研究,并具有明确的应用对象(内燃叉车)。
对板梁结构各个结构参数影响板梁结构的振动特性进行了分析,编制了数值优化程序,以功率流峰值最大值最小的优化策略对三种不同的边界条件的板结构进行了激励点位置寻优；对比三种不同边界板结构模型的优化结果,得到三边固定一边自由板结构振动功率流峰值最小,两边固定两边自由板模型功率流峰值最大的结论。为工程上的设计提供理论参考指导。本文的研究工作包括以下内容：
首先研究振动功率流的基本原理、基本概念、计算方法,然后基于振动理论,研究定激励作用下板的振动的分析方法,利用结构动力学、机械导纳的有关理论和处理方法,从功率流的基本概念和基本原理出发推导出了在定激励作用下两边固定两边自由板、四边固定板、三边固定一边自由板功率流表达式,并对在激励点位置、板长、板宽、板厚等参数变化时进行了数值计算,以上理论研究为叉车类车架结构的动态响应分析提供了一种方法,为这类结构的动特性改进与设计提供了理论依据。得到具有工程意义的一般性结论：
(1)这三种边界条件的板厚度的增加,板的功率流峰值是一致减小的。所以在工程设计时,只要工程设计允许时就可以尽可能加大厚度；(2)这三种边界条件的板损耗因子增大时,功率流峰值减小,在工程设计时,若要减小振动功率峰值,要选大的损耗因子；(3)这三种边界条件的板长值由小变大时,功率流峰值一致变小,在工程设计时,尽可能选择大的板长值；(4)这三种边界条件的板宽取小值时,功率流峰值小,在工程设计时,选择小的板宽度值是有利的。小宽度板的模态有一些没有被激励起来,所以振动能量很小。在工程设计时,若能让大多数模态不被激发就是振动能量最小的,可实际工程大量运用薄壁结构件,我们要合理的结构设计,来避免模态的激发；(5)对于四边固定板、两边固定两边自由板,其边界对称,激励点在中心时的振动功率流峰值大于激励点不在中心时的情况。尽管在中心时被激发的模态数少,但此时模态一旦被激发,峰值能量就较大,激励点不在中心时,尽管激励出了较多的模态,可此时的模态峰值较小。在工程设计时,若是激励点在板中心时,一定要考察出此时是否激励出模态。对于两边固定两边自由板、三边固定一边自由板,不仅是激励点要避开中心点激励,还要避开自由边上的激励：(6)这三种边界条件的板,在工程设计时,都需要考虑激励点避开板的中心,在宽度方向上激励点位置不同,峰值出现大小交替,所以,工程设计时,必须通过仔细计算才能找到使得峰值最小位置点；(7)当激励点位置相同时,三种边界条件板各有优劣,取决于点的具体位置,工程设计时,要具体计算来确定用何种边界条件。
针对具有工程意义的简支弹性梁结构,进行了理论分析,得出了具有工程意义的结果：(1)梁越长振动功率流峰值越小；(2)壁厚值需要适当选择；(3)梁损耗因子增大,功率流峰值一致减小,在工程设计时若主要考虑减小功率峰值,就可取较大值的损耗因子,但损耗因子增大,会使得阻尼材料的重量增加；(4)梁截面积不变,-而截面高增加,功率流峰值在减小,所以在工程设计时,当梁截面积为定值时,尽量加大截面高度减小截面宽度；(5)激励点从中间向两端移动变化时候,功率流的峰值变小,激励点尽量选择在离两端近一些。(6)得到设计简支-弹性支承梁系统的顺序是,首先根据结构需要和强度要求设计梁的基本参数,根据系统支承的稳定性及减振的需要来设计弹性支承的刚度范围,利用频率方程数值方法确定固有频率,然后根据本文总结的规律计算最终确定其刚度、梁的长、宽、高、壁厚。
最后运用大型商业软件ANSYS对板模型、梁模型进行了模拟分析,得到了与理论分析相一致的结论,这也印证了理论分析的正确性。
我们知道,内燃叉车的主体结构是钢板焊接而成的车架,动力装置支承在车架上,内燃叉车的振动始终困扰着生产企业,制约着内燃叉车NVH性能的改善。本文的研究结果正好可很好的应用于内燃叉车的结构设计上,有利于设计出理想NVH性能的叉车,会迅速推动企业效益的增长。
This Paper is based on the background of the projects undertaken by the laboratory. By theoretical analysis and numerical calculation method, the paper took the vibration power flow as an objective function, studied the plate with different boundary conditions, and simply supported elastic beam vibration characteristics. The results have the important theory significance and the practical value.
A large number of plate beam structure used in mechanical engineering, its vibration response characteristics need to be researched. In order to identify the Minimum vibration response under the Action of Determine Excitation, a more in-depth research of theory is needed. This paper investigated the vibration characteristics of the plate beam structure, and those researched results have clear application object.
By theoretical analysis and numerical calculation, the paper studied the plate structure vibration characteristics.That different structure parameters how to affect the plate structure vibration characteristics was analysed.The conclusions of designing plate structure with good vibration characteristics were drawed. It provides reference for designing the structure. A numerical optimization program was programmed with minimization peak power optimization strategy.For three different boundary conditions plate structure was optimized.After the comparison of three kinds of different boundary plate structure model of the optimized results, draw a coclution that the three fixed edges plate vibration power flow peak is minimum and the two fixed edges plate vibration power flow peak is maximum. It provides a theoretical reference guide for engineering design.
The paper contents are as follows:
Firstly the basic concepts, basic principles and calculation method of power flow was studied. Then, based on vibration theory, the paper studied plate vibration analysis methods under the action of determine excitation. Regards plate structure as the research object, using structural dynamics, mechanical admittance theory and processing method, From the power flow of the basic concept and the basic principle, the paper deduced the different power flow equations and numerical calculation result of the plates, such as two edges fixed and the other two edges free plate, quadrilateral fix plate, three edges fixed plate,under the action of determine excitation, with different conditions, such as the excitation point position, length, width, thickness and other parameters. The study on the plate structure dynamic response analysis provides a method for designing these dynamic characteristics and provides a theoretical basis for the design improvement. Some general conclusions of engineering significance were drawed.
Some general conclusions of engineering significance as follows:
For the three kind of boundary conditions of the plate,
(1) As the thickness of the plate is increased, power flow peak is reduced.So,when a Mechanism structure is designed, as long as under the condition of the engineering design allows,the thicker the plate is,the less the power flow peak is.(2) As the Plate loss factor is increased, power flow peak is reduced. So, when a Mechanism structure is designed, we should choose the big loss factor.(3) The Plate longth increased and power flow peak reduced.So, when a Mechanism structure is designed, we should choose the longer Plate.(4) As the Plate width is increased, power flow peak is reduced, when a Mechanism structure is designed, we should choose the narrower Plate.Some modal in narrower plate was not excited, so the vibration energy was very small. The vibration is very small when the some modal are not excited. Plate structure is widly used in Practical engineering, so we should design to avoid the excited modal.(5) As Quadrilateral fixed plate and two sides fixed two sides free plate were conserned, they are Symmetric boundary; the vibration power flow peak caused by excitation point in the center of the plate is greater than those caused by the excitation point in the corner of the plate.Although the number of modal excited by in the center were a few, those mode once are excited, peak energy is larger than those that excited by incentive point not in the center, although many modal was incentived, the peak is smaller. When a Mechanism structure is designed, we should pay attention to whether those modal were excited by the incentive point in the center of the board. As three sides fixed plate and two sides fixed two sides free plate are conserned, the position of exciting point is not only to avoid the plate center, but also to avoid the free edge of it.(6) When a Mechanism structure is designed, we should pay attention not to putting the incentive point in the center of the plate. With the different incentive point position the peak changed from big to small alternately, we must calculate carefully to find the minimum peak.(7) When the excitation point position is same, each of the three kinds of boundary conditions plate has advantages and disadvantages, depending on the incentive location. When a Mechanism structure is designed, we should choose the boundary conditions by calculation.
As the beam structure is corncerned, by analyzing in theory, we obtained a series of practical engineering significance results.
(1)The longer of the beam structure is, the less of the power flow is.(2) Wall thickness needs to appropriate select.(3) As the Beam loss factor is increased, power flow peak is reduced. So, when a Mechanism structure is designed, we should choose the big loss factor.(4) The hight increased with the power peak decreased under the condition of constant beam cross section. So, when a Mechanism structure is designed, we should choose the big hight and small width. When incentive point position is shifting from the middle of the beam to two ends of it, power flow peak is varying with from bigger to smaller. The incentive point postion should be putted the two ends or its vicinity. The order of design pivot-elastic supported beam is designing its basic parameters, and then according to the sturucture to support the stability and vibration needs, design elastic supporting rigidity range. After using the frequency equation numerical method to determine the natural frequency, based on the summary of the law, we compute its stiffness, longth, width, hight, wall thickness.
Finally applying the commercial software ANSYS to board model, to beam model is simulated and analyzed. Obtained consistent with the theoretical analysis conclusion, this has also verified the correctness of theoretical analysis.
The main structure of present forklift is welded steel frame; power device is supported on the frame.
Forklift vibration has plagued enterprises, restricting the performance improvement of forklift NVH. On the results of this study can be well applied to the structural design of the forklifts, and quickly promote forklift ideal NVH performance and the enterprise efficiency growth.
引文
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