摘要
粘弹性隔振器在航天领域具有广泛的应用,但由于粘弹性材料的高度非线性,在粘弹性隔振器动力学性能建模、设计及计算等方面一直存在困难。为此,本文对粘弹性隔振器动力学性能涉及的关键问题进行全面而深入的理论与实验研究,包括粘弹性材料的温度谱模型、时温叠加方法,结构等强度力学模型及修正模态应变能法,温升计算方法。
粘弹性隔振器的关键要素之一是粘弹性材料。基于频率谱五参数分数微分模型和温频镜像关系数学形式,提出了粘弹性材料的动力学性能六参数分数微分温度谱模型(Six-Parameter Fractional Derivative Model,简称SPFDM)。SPFDM能直接利用动态机械分析实验结果,对于损耗模量和损耗因子具有对称性或非对称性的情形均适用。SPFDM的参数具有明确的物理含义,推导了温度谱模型参数的初值公式,并给出了参数辨识步骤。
粘弹性材料的动力学性能不仅与温度有关,还与频率有关,通常以时温叠加平移得到的主曲线表征。为获得更准确的时温叠加曲线,提出了一个基于广义Maxwell模型的时温平移方法(Generalized Maxwell Model Based Shifting,简称GMMBS)。与传统基于重叠窗口的时温叠加方法相比,GMMBS不需要首先判断重叠窗口的大小及存在性,能利用所有的实验数据中包含的有用信息来计算平移因子。
在粘弹性材料研究的基础上,首先建立了关于隔振器支架结构的等强度力学模型,然后提出了计算隔振器动力学参数的ZMSE (Zhang Modal Strain Energy,简称ZMSE)模态应变能法。关于隔振器支架结构,基于小变形假设、莫尔定理及等强度梁理论,建立了隔振器结构参数与性能参数的等强度力学模型。等强度力学模型能够由隔振器的结构参数直接预测性能参数,并且可按需要的安全系数设计具有等强度特性的隔振器。关于粘弹性隔振器动力学参数,在分析了模态应变能法和已有修正方法的原理及其相互关系的基础上,提出了一种基于损耗因子幅值的修正模态应变能法ZMSE。ZMSE的修正因子随粘弹性隔振器对应模态阶次损耗因子幅值变化。以可等价为粘弹性夹层梁/板的四参数原型系统和新型高阻尼航天载荷隔振器作为算例,通过与已有方法的对比分析了所提ZMSE的准确性。
粘弹性隔振器在振动过程中,会导致粘弹性材料温度升高,尤其是当粘弹性材料具有高阻尼特性时,热动力耦合现象明显。针对一般的任意激励,基于五参数分数微分本构模型,建立了热动力学耦合的控制微分方程,并推出了差分形式。针对工程上常见的稳态谐波激励,控制微分方程通过傅立叶变换可显著简化,文中建立了相应的温升计算方法。
对粘弹性隔振器动力学性能提出的相关理论与方法还需要充分的实验进行验证。针对为多种粘弹性材料,进行了大量的动态机械分析实验。定频变温实验验证了SPFDM温度谱模型的准确性,并揭示了当材料存在次级转变区时,温度谱模型在该区域的误差可能较大。变频变温实验用以验证GMMBS时温叠加方法的准确性,同时发现粘弹性材料在变频、变温下的力学性能除了水平向平移关系外,还可能存在较小的纵向平移。针对一种新型等强度高阻尼粘弹性隔振器,正弦、随机实验表明,ZMSE模态应变能法计算的隔振器动力学参数预测准确,隔振器具有设计的刚度和优良的阻尼性能,在中高频范围内能有效抑制振动能量的传递。温升实验结果表明,热动力耦合温升计算理论结果与实验温升曲线趋势基本相同；对于高阻尼粘弹性隔振器,温升幅值十分显著,在设计时应计入温升对隔振器性能的影响,使隔振器发挥最大的隔振性能。
Although viscoelastic isolators have been widely used in aerospace and other engineering fields, due to the high nonlinear properties of viscoelastic materials, it remains difficult in some aspects about dynamic performance, such as modeling, design and calculation, etc. Therefore, in this thesis, the involved key problems of viscoelastic isolators'dynamic performance have been investigated by comprehensive theoretical and experimental study, including viscoelastic temperature spectrum model, time-temperature superposition method, vibration isolators'support structure design and dynamics performance calculating method, temperature rise calculation.
Viscoelastic materials are one of the most important elements of viscoelastic isolators. Based on the Five-Parameter Fractional Derivative Model of frequency spectrum and mathematic temperature-frequency mirror relationship, Six-Parameter Fractional Derivative Model of the temperature spectrum, hereinafter referred to as SPFDM, has been proposed. SPFDM can directly use the experimental results of dynamic mechanical analysis, is applicable to loss modulus and the loss factor with both symmetry and asymmetry. SPFDM' parameters have clear physical meaning, whose initial values can be deteminated by some deduced formulas. Parameter identification steps are also given.
Viscoelastic materials'dynamic performance depends not only on temperature, but also on frequency, is commonly characterized with the master curve obtained by the time-temperature superposition. To obtain more accurate Time-Temperature shift, a Generalized Maxwell Model Based Shifting method, hereinafter referred to as GMMBS, has been put forward. Compared with those traditional methods based on the overlapping window, GMMBS doesn't need first judgment of the size and existence of the overlapping window, can use all the experimental data which contains useful information to calculate the shift factor.
Based on viscoelastic materials' research, the equal strength mechanical model and new mode strain energy method have been established for viscoelastic isolators'bracket and whole dynamic parameters, respectively. Based on the assumption of small deformation, Mohr's law, equal strength theory, the equal strength mechanical model is suggested for isolators'bracket. The model can directly predict isolators'performance parameters, and can help to design isolators'bracket with the needed safety factor. Based on the analysis of the principle and the correction of existed modal strain energy methods, Zhang Modal Strain Energy, hereinafter referred to as ZMSE, have been proposed, of which the correction factor depends on the amplitude of the loss factor. Taking the four-parameter prototype system, which is equivalent to viscoelastic laminated beam/board, and a new type isolator as an example, ZMSE's accuracy is discussed through the comparison with the existing methods.
In vibration process, viscoelastic isolators'temperature will rise due to energy dissipation, especially when the viscoelastic materials have high damping characteristics. For the general input, the thermal dynamic coupling differential equations are established based on the Five-Parameter Fractional Derivative Model, and the corresponding difference form is introduced too. For the steady-state harmonic input, which is very common in engineering application, the established differential equations can be significantly simplified by Fourier transformation. The calculation method of the temperature rise has also been deduced for the steady-state case.
The proposed theories and methods above for viscoelastic isolators'dynamic performance still need to be fully verified by experiments. With the condition of fixed frequency and temperature, experiments have verified the accuracy of the SPFDM, and reveal that the SPFDM's error may be relatively big when there is a subprime transition region. With the condition of variable frequency and temperature, experiments have proven the accuracy of the GMMBS, and reveal that there may be both vertical shift and horizontal shift for the dynamic performance of viscoelastic materials. Sine and random experiments show that the ZMSE can calculate the dynamic parameters of the isolators with reasonable accuracy. The isolator with desired stiffness and damping can effectively restrain the vibration energy transfer in the wide bandwidth. Experiments of the temperature rise show that the thermal dynamic coupling calculation method is basically accurate. For those high damping viscoelastic isolators, the amplitude of the temperature rise is notable, which is necessary to be considered in the design of isolators in order to maximize the performance of vibration isolation.
引文
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