-
文中借鉴参考文献[9]中的热机械分析法,并根据美国材料与试验协会(American Society for Testing and Materials, ASTM) E381标准[10]进行复合材料热膨胀系数测试,试件尺寸如图3所示。
采用汉硕高新材料(天津)有限公司生产的TU/SYT49S-130碳纤维复合材料预浸料单向带作为弹载光学系统支撑结构的主要原材料,该预浸料主要由T700级碳纤维和环氧树脂组成。该单向带固化后的单层厚度为0.125 mm,由于试件厚度为6 mm (如图3所示),因此铺层数为48层。所有试件长度方向为0°铺层方向,铺层方式有三种,如表1所示。试件采用热压罐工艺制备,固化工艺曲线如图4所示。试件的实物图如图5所示。
表 1 试验矩阵
Table 1. Test matrix
Group number Layers Quantity A [048] 10 B [9048] 6 C [(0/45/90/−45)6]S 10 -
利用热膨胀仪(DIL402型,如图6所示)测定试件沿长度方向线热膨胀系数,温度测试范围为30~80 ℃,加热速率设为6 ℃/min,试验结果在表2中列出。通过A组和B组的试验结果可以得到TU/SYT49S-130碳纤维复合材料沿纤维方向和垂直于纤维方向的线热膨胀系数分别为1.397×10−6/℃和37.95×10−6/℃。表2中C组试验结果用于验证下一节给出的热膨胀变形有限元仿真方法。
表 2 试件长度方向热膨胀系数测试结果
Table 2. Test results of thermal expansion coefficient along the length direction of test piece
Group number Coefficient of thermal
expansion×10−6/℃Average×
10−6/℃Coefficient of
variationA1 1.286 1.397 0.117 A2 1.359 A3 1.153 A4 1.509 续表 2
Continued Tab.2Group number Coefficient of thermal
expansion×10−6/℃Average×
10−6/℃Coefficient of
variationA5 1.616 1.397 0.117 A6 1.601 A7 1.328 A8 1.196 A9 1.542 A10 1.383 B1 38.546 37.95 0.059 B2 36.729 B3 39.558 B4 38.998 B5 39.875 B6 34.006 C1 4.125 4.141 0.101 C2 4.102 C3 4.156 C4 3.939 C5 4.564 C6 3.970 C7 3.674 C8 3.537 C9 4.391 C10 4.957 -
为了模拟弹载光学系统复合材料支撑结构的热膨胀变形,基于上节测定的沿纤维方向和垂直于纤维方向的线热膨胀系数和汉硕高新材料(天津)有限公司提供的其他材料参数(如表3所示),利用有限元软件ABAQUS分别建立铺层方式为[048]、[9048]、[(0/45/90/-45)6]S的碳纤维复合材料层合板热膨胀变形仿真分析模型,采用连续壳单元SC8R。仿真得到的热膨胀变形云图如图7(a)~(c)所示,在30~80 ℃的升温区间内,沿长度方向(x轴方向)的最大热膨胀变形量分别为1.899×10−3 mm、4.817×10−2 mm和5.526×10−3 mm。
表 3 TU/SYT49S-130材料属性
Table 3. Material parameters of TU/SYT49S-130
Parameter Value Longitudinal elastic modulus/GPa 135 Transverse elastic modulus/GPa 8.35 Poisson's ratio 0.3 Density/g·cm−3 1.04 Shear modulus/GPa 5.31 将[048]、[9048]、[(0/45/90/-45)6]S铺层层合板沿长度方向热膨胀变形仿真结果分别代入热膨胀系数计算公式(1)[10]中,可以得到三种铺层方式的层合板沿长度方向的线热膨胀系数分别为1.52×10−6/℃、38.54×10−6/℃和4.42×10−6/℃,与表2给出的三组试验平均值比较,相对误差分别为8.6%、1.6%和6.7%。
$$ \alpha {\text{ = }}\frac{{\Delta L}}{{L \times \Delta T}} $$ (1) 式中:α为线热膨胀系数;ΔL为沿长度方向的热膨胀变形量;L为初始长度;ΔT为温差。
图8所示为三种铺层方式的试验与仿真分析的热膨胀应变随温度变化曲线图,可以看出,复合材料层合板的线热膨胀应变量随温度的升高而增加,并且在试验温度范围内基本呈线性关系。三组的试验数据与仿真数据的相关系数都为0.99,总体吻合度较好,并且线热膨胀系数的试验结果平均值与仿真结果的相对误差均在10%以内,说明文中建立的有限元仿真分析模型能够有效预测复合材料结构热膨胀变形。
图 8 热膨胀变形试验与仿真分析得到的应变-温度曲线
Figure 8. Strain-temperature curves obtained from thermal expansion deformation test and simulation analysis
从试验和仿真结果看,[9048]铺层的层合板线热膨胀系数是 [048]铺层的层合板的近30倍,这是因为[048]层合板沿长度方向的线热膨胀系数主要受碳纤维纵向热膨胀系数的影响,而[9048]层合板沿长度方向的线热膨胀系数主要受环氧树脂基体热膨胀系数的影响[9]。而环氧树脂基体的热膨胀系数要远大于碳纤维纵向的热膨胀系数,如表4所示[11]。[(0/45/90/−45)6]S铺层的层合板是多向铺层,沿长度方向的线热膨胀系数受碳纤维和环氧树脂基体的共同影响,因此[(0/45/90/−45)6]S层合板的线热膨胀系数位于[048]和[9048]之间。
-
弹载光学系统碳纤维复合材料支撑结构的优化设计思路如图9所示。
首先以钛合金支撑结构为原准,在CATIA中建立复合材料支撑结构初始几何模型,如图10所示,然后导入Hypermesh中建立二维复合材料有限元模型,如图11所示,其中可以将支撑结构分为中心主体(图11中绿色部分)和两侧支撑板(图11中灰色部分)两个部分。然后利用Optistruct求解器对复合材料支撑结构整体进行三级优化:铺层形状优化、铺层厚度优化和铺层顺序优化。每步优化完成后,对二维复合材料模型进行热膨胀仿真,可以根据仿真结果初步判断是否达到减少轴向热膨胀变形85%以上的设计要求,若没有达到,便需要根据铺层形状和铺层厚度的优化结果,在CATIA中对支撑结构中心主体和两侧支撑板的厚度以及减轻孔的形状、位置进行调整,然后重新导入Hypermesh中利用Optistruct进行优化。
当优化后的二维复合材料模型热膨胀变形满足设计要求,以二维模型为依据在CATIA中建立新的支撑结构三维几何模型,并导入ABAQUS中建立支撑结构三维有限元模型,进行热膨胀变形仿真以及质量和模态分析,如果仍然满足设计要求,便可结束优化。
-
在Hypermesh中导入的支撑结构CATIA三维几何模型进行抽中面处理,即将三维模型转为二维模型,然后赋予TU/SYT49S-130碳纤维复合材料属性,并划分单元类型为CQUAD4和CTRIA3混合,共14935个单元。因为0°与±30°的铺层组合具有较小热膨胀系数 [12-13],所以对支撑结构主体和两侧支撑板分别设定初始铺层方式为[0/±30],单层厚度为2 mm和1.5 mm。根据弹载光学系统支撑结构实际约束条件,对支撑结构四周长圆孔和后端部的四个圆孔施加完全固定约束,如图11中红色约束。对支撑结构整体施加50 ℃温升载荷。
文中弹载光学系统复合材料支撑结构的优化设计共进行了五次迭代,每一次迭代中都会分步进行铺层形状、铺层厚度以及铺层顺序的优化,并且在每一步优化完成后会对二维复合材料支撑结构模型进行热膨胀计算。表5列出了五次迭代中,每步优化后复合材料支撑结构相对钛合金结构的热膨胀变形减小比例。
表 5 二维复合材料支撑结构相对钛合金结构热膨胀变形的减小比例
Table 5. Reduction ratio of thermal expansion deformation of two-dimensional composite support structure compared with titanium alloy structure
Iteration order Ply shape optimization Ply thickness optimization Ply sequence optimization 1 45.8% 54.4% 59.4% 2 70.7% 72.2% 74.2% 3 71.7% 73.7% 76.0% 4 80.3% 82.1% 84.1% 5 88.2% 89.4% 89.8% -
Optistruct复合材料铺层优化第一阶段是铺层形状优化,该阶段以单元厚度作为优化对象[14],以整体结构轴向热膨胀量最小为优化目标,研究材料的分布情况,并施加复合材料支撑结构整体质量不超过钛合金结构和基频不低于钛合金结构的整体约束。
除了结构的整体约束,还需要根据复合材料制备方法施加一部分工艺约束:(1)在满足支撑结构动态特性和质量约束的前提下,为确保复合材料结构主体和两侧支撑板不会因为过厚导致结构在拐角处因为压力不足而使内部出现缺陷 [11],亦不会因为过薄导致结构发生明显的翘曲变形[15-16]致使后期装配出现困难,根据钛合金结构主体和两侧支撑板的厚度(分别为5 mm和4 mm),设定复合材料结构主体的铺层厚度应在4~8 mm之间,两侧支撑板厚度应在3~5 mm之间;(2)根据供应商提供的碳纤维复合材料单层预浸料固化后的厚度,设定单个铺层的最小厚度为0.125 mm;(3)为了满足复合材料结构均衡铺层要求,减小结构翘曲[15],需使+30°与−30°的总铺层厚度相同。
表6中列出了五次迭代过程中复合材料支撑结构的铺层形状优化结果。结果中的不同颜色代表不同的铺层厚度,红色区域的厚度较大,蓝色区域的厚度较小。由此,可以根据颜色分布考虑结构整体布局,保留红色区域,在蓝色区域布置面积、形状合适的减轻孔。
表 6 五次迭代中的复合材料支撑结构铺层形状优化结果
Table 6. Optimization results of ply shape of composite support structure in five iterations
Iteration order CATIA model before
optimizationOptimization result
of ply shapeThermal expansion
deformation/mmReduction relative to thermal
expansion of titanium alloy1 1.17×10−2 45.8% 2 6.32×10−3 70.7% 3 6.12×10−3 71.7% 4 4.25×10−3 80.3% 5 2.54×10−3 88.2% -
Optistruct复合材料铺层优化第二阶段是铺层厚度优化,该阶段整体优化目标和约束条件与第一阶段相同,在此基础上,为避免拉-剪、拉-弯耦合而引起固化后的翘曲变形,需施加层合板铺层对称的工艺约束[17]。
第一阶段优化结束后,每一种角度的铺层会被切分为多层形状相同的铺层束,一般默认切分为四层,而第二阶段就将铺层束的厚度作为优化对象,经过优化后可以计算出铺层束的最优厚度[14]。从前文可知,TU/SYT49S-130单层预浸料固化后的厚度为0.125 mm,那么优化后的铺层束厚度除以0.125就是该铺层束最终的总层数。最后将每个铺层束的厚度和层数相加即可得到层合板的总厚度和总层数。
表7中列出了五次迭代过程中复合材料支撑结构的铺层厚度优化结果。铺层厚度优化在铺层形状优化结果的基础上,相比于钛合金结构,将复合材料支撑结构前端的轴向热膨胀变形分别进一步减小了8.6%、1.5%、2.0%、1.8%和1.2%。
表 7 五次迭代中的复合材料支撑结构铺层厚度优化结果
Table 7. Optimization results of ply thickness of composite support structure in five iterations
Iteration order Thickness after optimization/mm Number of plies after optimization Thermal expansion
deformation/mmReduction relative to thermal
expansion of titanium alloyMain body Side plate Main body Side plate 1 8.0 4.5 64 36 9.86×10−3 54.4% 2 7.25 4.75 58 38 6.01×10−3 72.2% 3 7.25 4.75 58 38 5.69×10−3 73.7% 4 7.75 4.75 62 38 3.87×10−3 82.1% 5 5.75 3.5 46 28 2.29×10−3 89.4% -
Optistruct复合材料铺层优化第三阶段是铺层顺序优化,该阶段是为了确定真实铺层的上下叠放次序[14],在整体优化目标与约束条件不变的情况下,需要额外定义一些工艺约束来确定铺层顺序的最优解:(1)参考文献[3]中提出,当0°方向的铺层在外侧时,可以得到更低热膨胀系数的层合板,因此添加层合板表面铺层为0°的约束;(2)为避免产生树脂基体纵向开裂以及层间应力提高,应设置同一铺层角的连续铺层数不能超过四层[17]。
表8中列出了五次迭代过程中,复合材料支撑结构的铺层顺序优化结果。铺层顺序优化在铺层厚度优化结果的基础上,相比于钛合金结构,将复合材料支撑结构前端的轴向热膨胀变形分别进一步减小了5.0%、2.0%、2.3%、2.0%和0.4%。
表 8 五次迭代中的复合材料支撑结构铺层顺序优化结果
Table 8. Optimization results of ply sequence of composite support structure in five iterations
Iteration
orderPly sequence before optimization Ply sequence after optimization Thermal expansion deformation/mm Reduction relative to thermal expansion of titanium alloy Main body Side plate Main body Side plate 1 [012/3010/−3010]S [04/308/−308]S [03/−30/302/0/−30/30/−303/
302/−30/30/−30/0/−30/03/
−30/30/03/302/−30/30/0]S[0/302/−30/302/−302/302/
−302/02/30/−30/0/−302/30]S8.76×10−3 59.4% 2 [013/308/−308]S [05/307/−307]S [0/302/0/−30/302/0/30/−30/0/30/02/−30/0/30/−30/0/30/02/
−30/0/−30/−302/0]S[0/−302/0/30/0/−30/0/
−302/30/−30/303/0/−30/302]S5.57×10−3 74.2% 3 [09/3010/−3010]S [05/307/−307]S [0/303/−30/02/−302/30/04/
−30/02/30/−303/304/−302/
30/−30]S[0/−302/302/−30/303/
−30/30/02/−30/0/−302/0/30]S5.18×10−3 76.0% 4 [017/307/−307]S [05/307/−307]S [0/−30/02/303/02/−30/03/30/
04/302/03/−304/02/−30/30]S[02/302/0/−30/30/−302/304/−30/02/−303]S 3.44×10−3 84.1% 5 [07/308/−308]S [04/305/−305]S [0/−30/30/−302/30/02/30/0/
−30/304/−303/0/−30/0/30/0]S[0/303/0/30/02/−303/30/−302]S 2.20×10−3 89.8% -
上节中,最后一次铺层顺序优化结束后,已经实现了二维复合材料支撑结构的轴向前端热膨胀变形相较于钛合金支撑结构减小85%以上的设计要求,但是因为二维支撑结构模型没有考虑厚度方向热膨胀的影响,所以需要再对复合材料支撑结构的三维模型进行热膨胀变形分析,进一步确定优化完成后的复合材料支撑结构是否能够满足设计要求。
以上节最后优化得到的支撑结构各部分铺层方式为基础,利用第2节中经过试验验证的碳纤维复合材料结构热膨胀变形ABAQUS有限元仿真方法对支撑结构进行分析计算。有限元模型如图12所示,共有245136个连续壳单元。
图13所示为计算得到的复合材料支撑结构热膨胀变形云图,其中支撑结构轴向前端最大位移为2.63×10−3 mm,相较于钛合金支撑结构,热膨胀变形减小了87.8%,满足设计要求。
-
利用ABAQUS计算得到优化完成的碳纤维复合材料支撑结构重134 g,相较于重364 g的钛合金支撑结构,质量减小了63.2%,与复合材料相较于钛合金具有更小密度的特性相符,不仅满足复合材料支撑结构质量不超过钛合金支撑结构的设计要求,而且支撑结构质量呈现大幅减小。
表9中分别列出了复合材料支撑结构和钛合金支撑结构前三阶的模态分析结果。结果表明,复合材料支撑结构的前三阶频率相较于钛合金支撑结构分别提高了24.4%、5.5%、21.5%,与复合材料相较于钛合金具有更高比刚度的特性相符,满足复合材料支撑结构基频不低于钛合金支撑结构的设计要求。
表 9 模态分析结果
Table 9. Results of modal analysis
Order Composite support structure Titanium alloy support structure First Vibration mode diagram Frequency/Hz 1 312.5 1 054.9 Second Vibration mode diagram Frequency/Hz 1 361.7 1 290.4 Third Vibration mode diagram Frequency/Hz 2 334.6 1 921.1
Low thermal expansion optimization of composite support structure for missile-borne optical system
-
摘要: 为了减小弹载光学系统支撑结构在服役温度下的热膨胀变形,选用纤维方向热膨胀系数小、可设计性强、比重小的碳纤维复合材料代替钛合金作为支撑结构主体材料。首先测定复合材料沿纤维方向和垂直纤维方向的线热膨胀系数,并在此基础上建立复合材料层合结构热膨胀仿真分析方法,然后以轴向前端热膨胀变形量最小为目标、质量与基频为约束进行复合材料支撑结构优化设计,通过有限元数值仿真验证设计方法的有效性。结果表明:碳纤维复合材料支撑结构相较于钛合金支撑结构在50 ℃的均匀温升区间内轴向前端热膨胀变形减小87.8%,质量减小63.2%,基频提升了24.4%,满足了支撑结构对超低热膨胀、轻量化和动态特性的要求。Abstract:
Objective In order to reduce the thermal expansion deformation of the support structure of the missile-borne optical system at service temperature, the carbon fiber reinforced composite with low thermal expansion coefficient in the fiber direction, strong designability and small specific gravity is used to replace titanium alloy as the main material of the support structure, and the composite support structure is designed by optimization. The optimized carbon fiber reinforced composite support structure shall meet the following requirements: (1) The main geometric size and the interface position shall remain unchanged; (2) Under the condition of 50 ℃ temperature rise, the axial thermal expansion deformation is reduced by more than 85% compared to the titanium alloy support structure; (3) The weight is lighter than titanium alloy support structure; (4) The fundamental frequency shall not be lower than the titanium alloy support structure. Methods Firstly, according to the ASTM (American Society for Testing and Materials) E381 standard, the linear thermal expansion coefficients of the carbon fiber reinforced composite along the fiber direction and perpendicular to the fiber direction are measured using a thermal dilatometer (Fig.6) for two kinds of particular layup. On this basis, a thermal expansion simulation model for the composite structures is established in ABAQUS, and the feasibility of the model is validated by comparing with test results. Then, taking the axial thermal expansion deformation as the optimization objective, the Optistruct software is used to optimize the layer shape, layer thickness, and layer sequence step by step for the two-dimensional carbon fiber composite support structure until the axial thermal expansion deformation meets the design requirements. Based on the optimized two-dimensional model, considering the influence of thermal expansion deformation in the thickness direction, a three-dimensional finite element model of the composite support structure is established in ABAQUS to conduct the analyses of thermal expansion, weight and vibration mode. Results and Discussions From the thermal expansion coefficient tests, the linear thermal expansion coefficients of carbon fiber reinforced composites along the fiber direction and perpendicular to the fiber direction are obtained as 1.397×10−6/℃ and 37.95×10−6/℃ respectively (Tab.2). The thermal expansion deformation obtained from the simulation (Fig.7-8) for the laminates with three kinds of layup is in good agreement with the test results (Tab.2). It is shown that the established simulation model can effectively predict the thermal expansion deformation of the composite structures. After five optimization iterations, compared to the titanium alloy support structure, the carbon fiber reinforced composite support structure meets the design requirements with 87.8% reduction in the axial thermal expansion deformation within a temperature rise range of 50 ℃ (Fig.13), with 63.2% reduction in the weight and 24.4% increase in the fundamental frequency (Tab.9). Conclusions Compared to titanium alloy, carbon fiber reinforced composite not only has lower density and greater specific stiffness, but also can achieve low thermal expansion deformation in one direction through reasonable design. Therefore, using carbon fiber reinforced composite instead of titanium alloy as the main material for the support structure of missile-borne optical systems can significantly reduce the axial thermal expansion deformation of the support structure through optimal design, while also achieving structural lightweight and improving structural stiffness. -
Key words:
- composite /
- low thermal expansion /
- optimal design /
- optical system /
- support structure
-
表 1 试验矩阵
Table 1. Test matrix
Group number Layers Quantity A [048] 10 B [9048] 6 C [(0/45/90/−45)6]S 10 表 2 试件长度方向热膨胀系数测试结果
Table 2. Test results of thermal expansion coefficient along the length direction of test piece
Group number Coefficient of thermal
expansion×10−6/℃Average×
10−6/℃Coefficient of
variationA1 1.286 1.397 0.117 A2 1.359 A3 1.153 A4 1.509 续表 2
Continued Tab.2Group number Coefficient of thermal
expansion×10−6/℃Average×
10−6/℃Coefficient of
variationA5 1.616 1.397 0.117 A6 1.601 A7 1.328 A8 1.196 A9 1.542 A10 1.383 B1 38.546 37.95 0.059 B2 36.729 B3 39.558 B4 38.998 B5 39.875 B6 34.006 C1 4.125 4.141 0.101 C2 4.102 C3 4.156 C4 3.939 C5 4.564 C6 3.970 C7 3.674 C8 3.537 C9 4.391 C10 4.957 表 3 TU/SYT49S-130材料属性
Table 3. Material parameters of TU/SYT49S-130
Parameter Value Longitudinal elastic modulus/GPa 135 Transverse elastic modulus/GPa 8.35 Poisson's ratio 0.3 Density/g·cm−3 1.04 Shear modulus/GPa 5.31 Parameter T700 carbon fiber (longitudinal) Epoxy resin Coefficient of thermal expansion/℃−1 −0.381×10−6 56.8×10−6 表 5 二维复合材料支撑结构相对钛合金结构热膨胀变形的减小比例
Table 5. Reduction ratio of thermal expansion deformation of two-dimensional composite support structure compared with titanium alloy structure
Iteration order Ply shape optimization Ply thickness optimization Ply sequence optimization 1 45.8% 54.4% 59.4% 2 70.7% 72.2% 74.2% 3 71.7% 73.7% 76.0% 4 80.3% 82.1% 84.1% 5 88.2% 89.4% 89.8% 表 6 五次迭代中的复合材料支撑结构铺层形状优化结果
Table 6. Optimization results of ply shape of composite support structure in five iterations
Iteration order CATIA model before
optimizationOptimization result
of ply shapeThermal expansion
deformation/mmReduction relative to thermal
expansion of titanium alloy1 1.17×10−2 45.8% 2 6.32×10−3 70.7% 3 6.12×10−3 71.7% 4 4.25×10−3 80.3% 5 2.54×10−3 88.2% 表 7 五次迭代中的复合材料支撑结构铺层厚度优化结果
Table 7. Optimization results of ply thickness of composite support structure in five iterations
Iteration order Thickness after optimization/mm Number of plies after optimization Thermal expansion
deformation/mmReduction relative to thermal
expansion of titanium alloyMain body Side plate Main body Side plate 1 8.0 4.5 64 36 9.86×10−3 54.4% 2 7.25 4.75 58 38 6.01×10−3 72.2% 3 7.25 4.75 58 38 5.69×10−3 73.7% 4 7.75 4.75 62 38 3.87×10−3 82.1% 5 5.75 3.5 46 28 2.29×10−3 89.4% 表 8 五次迭代中的复合材料支撑结构铺层顺序优化结果
Table 8. Optimization results of ply sequence of composite support structure in five iterations
Iteration
orderPly sequence before optimization Ply sequence after optimization Thermal expansion deformation/mm Reduction relative to thermal expansion of titanium alloy Main body Side plate Main body Side plate 1 [012/3010/−3010]S [04/308/−308]S [03/−30/302/0/−30/30/−303/
302/−30/30/−30/0/−30/03/
−30/30/03/302/−30/30/0]S[0/302/−30/302/−302/302/
−302/02/30/−30/0/−302/30]S8.76×10−3 59.4% 2 [013/308/−308]S [05/307/−307]S [0/302/0/−30/302/0/30/−30/0/30/02/−30/0/30/−30/0/30/02/
−30/0/−30/−302/0]S[0/−302/0/30/0/−30/0/
−302/30/−30/303/0/−30/302]S5.57×10−3 74.2% 3 [09/3010/−3010]S [05/307/−307]S [0/303/−30/02/−302/30/04/
−30/02/30/−303/304/−302/
30/−30]S[0/−302/302/−30/303/
−30/30/02/−30/0/−302/0/30]S5.18×10−3 76.0% 4 [017/307/−307]S [05/307/−307]S [0/−30/02/303/02/−30/03/30/
04/302/03/−304/02/−30/30]S[02/302/0/−30/30/−302/304/−30/02/−303]S 3.44×10−3 84.1% 5 [07/308/−308]S [04/305/−305]S [0/−30/30/−302/30/02/30/0/
−30/304/−303/0/−30/0/30/0]S[0/303/0/30/02/−303/30/−302]S 2.20×10−3 89.8% 表 9 模态分析结果
Table 9. Results of modal analysis
Order Composite support structure Titanium alloy support structure First Vibration mode diagram Frequency/Hz 1 312.5 1 054.9 Second Vibration mode diagram Frequency/Hz 1 361.7 1 290.4 Third Vibration mode diagram Frequency/Hz 2 334.6 1 921.1 -
[1] Xu Wei, Zhao Junwei, Yuan Benli, et al. Experiment and simulation on aircraft thermal protection and utilization integrated system [J]. Journal of Aerospace Power, 2022, 37(3): 555-563. (in Chinese) doi: 10.13224/j.cnki.jasp.20210161 [2] Chen Xianzhi, Ren Gang, Luo Zhenbao, et al. Research on application technology of advanced photoelectric seeker [J]. Infrared and Laser Engineering, 2021, 50(9): 20210531. (in Chinese) doi: 10.3788/IRLA20210531 [3] Zhong Weihong, Zhang Zuoguang, Song Huancheng. Study on thermal expansion coefficient and design for zero-expansion of single andhybrid multi-directional composite [J]. Acta Aeronauticaet Astronautica Sinica, 1993, 14(11): 612-617. (in Chinese) doi: 10.3321/j.issn:1000-6893.1993.11.008 [4] Velea M N, Lache S. Thermal expansion of composite laminates Bulletin of the Transilvania University of Brasov. Engineering Sciences [J]. Series I, 2015, 8(1): 25. [5] Huang Longnan, Wang Xinbo, Zhang Dongxing. Design of hybrid composite laminates with zero in-plane 2D expansion [J]. Journal of Harbin Institute of Technology, 2009, 41(10): 91-94. (in Chinese) doi: 10.3321/j.issn:0367-6234.2009.10.018 [6] Cao Jun, Zhu Zhipeng. Optimization design of thermal expansion coefficient of laminates using genetic algorithms [J]. Fiber Reinforced Plastics/Composites, 2003(2): 33-35, 46. (in Chinese) doi: 10.3969/j.issn.1003-0999.2003.02.010 [7] 宋伟阳. 新型空间相机全碳支撑结构设计及整机力热稳定性研究 [D]. 中国科学院大学(中国科学院长春光学精密机械与物理研究所), 2022. Song Weiyang. A design of CFRP supported structure for a new space camera and research on mechanical and thermal stability of the camera [D]. Changchun: Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences (University of Chinese Academy of Sciences), 2022. (in Chinese) [8] Li Yanwei, Yin Longhai, Li Yulong, et al. New lightweight design method and application of main support structure in airborne infrared imaging system [J]. Infrared and Laser Engineering, 2022, 51(11): 20220232. (in Chinese) doi: 10.3788/IRLA20220232 [9] Qiu Xueqiong, Chen Lin. Test and theoretical method for coefficients of thermal expansion of carbon fiber reinforced composite laminate [J]. Composites Science and Engineering, 2021(7): 28-32, 104. (in Chinese) [10] ASTM International. Standard test method for linear thermal expansion of solid materials by thermomechanical analysis: ASTM E831-19[S]. United States: ASTM International, West Conshohocken, PA, 2014. [11] 湛利华. 树脂基复合材料构件制造技术[M]. 长沙: 中南大学出版社, 2018. [12] 王兴业, 朱文山, 王晓勇. 复合材料零膨胀系数层合板的设计—兼论铺层对层合板线膨胀系数的影响[J]. 宇航材料工艺, 1986(1): 39-44. [13] Zhang Jianke. Thermal expansion——One of thermophysical properties of carbon fiber/epoxy-resin composites [J]. Chinese Space Science and Technology, 1987(5): 45-50, 69. (in Chinese) [14] 方献军, 徐自立, 熊春明. OptiStruct及HyperStudy优化与工程应用[M]. 北京: 机械工业出版社, 2021. [15] Zhang Na, Yao Shuyan, Ma Ju, et al. Study on the shrinkage deformation of thin composite laminates during curing process [J]. Fiber Reinforced Plastics/Composites, 2009(4): 24-26, 31. (in Chinese) doi: 10.3969/j.issn.1003-0999.2009.04.007 [16] He Liang, Zhu Panxing, Xu Xiaowei, et al. A review on mechanism and control methods of residual stress and cured deformation of composite materials [J]. Composite Materials and Engineering, 2022(7): 121-128. (in Chinese) [17] 史晋蕾, 姚丽瑞. 航空复合材料技术[M]. 北京: 航空工业出版社, 2013.