拉压不同模量凹腔陶瓷导流块动力固有模态特性研究
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摘要
为了研究拉压不同模量(以下简称双模量)凹腔陶瓷导流块的动力特性,将陶瓷导流块等效成一根双模量材料简支Euler梁,从而得出凹腔火焰稳定器在双模量材料下的振动情况,保证该结构在高温状态下稳定。以双模量简支Euler梁为研究对象,通过二次开发,实现了Ansys平台分析具有该类材料属性结构动力特性的功能。将得到的前三阶固有频率与文献中推得的频率计算公式所得的固有频率进行了分析对比,得到的误差除了第一阶外都大于5%,发现文献所得结果有缺陷。将得到的各阶频率及振型曲线与已知的经典弹性理论的频率与振型曲线进行对比,说明材料的双模量属性对固有频率的影响很大,对振型曲线并没有影响。通过振型及材料属性分布图能直观地观察到材料的拉压区域,说明材料的拉压区域不能仅分为两个区域,振型阶次越高分区也越复杂。
In order to study the dynamic characteristics of the ceramic diversion block with different modules in tension and compression(the following is referred as bi-modulus),the ceramic diversion block was equivalent to a simply supported Euler beam with bi-modulus,thus,the vibration of the cavity flame stabilizer with bi-modulus material was obtained to ensure that the structure is stable at high temperature. Taking simply supported Euler beam as a research project,the function of analyzing dynamic characteristics of materials which have these material properties has come true in Ansys by secondary development. After comparing the initial three frequencies which were gained from finite element method and the analytical formula in a literature respectively,errors were gained. Except for the first-order frequency,errors are all more than 5%,so the analytical formula in literature has some flaws. Comparing the frequency and vibration mode curve of each order with these which were gained in classical elastic theory,it shows that the bi-modulus property of material has a great influence on the natural frequency and has no effect on the vibration mode curve. The tensile and compressive zones of the material can be visually observed through the vibration mode curves and material property distribution diagrams,indicating that the zones of tension and compression of the material cannot be divided into only two. The higher the vibration mode,the more complex the zone is.
In order to study the dynamic characteristics of the ceramic diversion block with different modules in tension and compression(the following is referred as bi-modulus),the ceramic diversion block was equivalent to a simply supported Euler beam with bi-modulus,thus,the vibration of the cavity flame stabilizer with bi-modulus material was obtained to ensure that the structure is stable at high temperature. Taking simply supported Euler beam as a research project,the function of analyzing dynamic characteristics of materials which have these material properties has come true in Ansys by secondary development. After comparing the initial three frequencies which were gained from finite element method and the analytical formula in a literature respectively,errors were gained. Except for the first-order frequency,errors are all more than 5%,so the analytical formula in literature has some flaws. Comparing the frequency and vibration mode curve of each order with these which were gained in classical elastic theory,it shows that the bi-modulus property of material has a great influence on the natural frequency and has no effect on the vibration mode curve. The tensile and compressive zones of the material can be visually observed through the vibration mode curves and material property distribution diagrams,indicating that the zones of tension and compression of the material cannot be divided into only two. The higher the vibration mode,the more complex the zone is.
引文
[1]蔡尊,王振国,孙明波,等.超声速气流中凹腔主动喷注的强迫点火过程实验研究[J].推进技术,2014,35(12):1661-1668.(CAI Zun,WANG Zhen-guo,SUN Ming-bo,et al. Experimental Study of Forced Ignition Process with Active Cavity Injection in a Supersonic Flow[J]. Journal of Propulsion Technology,2014,35(12):1661-1668.)
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[3]杜玲,李范春,马雪松,等.凹腔火焰稳定器组件界面的适配性研究[J].推进技术,2016,37(12):2359-2365.(DU Ling,LI Fan-chun,MA Xue-song,et al. Suitability Investigation about Components Interface of Flame Holder with Cavity[J]. Journal of Propulsion Technology,2016,37(12):2359-2365.)
[4] Timoshenko. Strength of Materials,PartⅡ:Advanced Theory and Problems[M]. Princeton:Van Nostrand,1941.
[5] Ambartsumyan.不同模量理论[M].邬瑞锋,张允真,译.北京:中国铁道出版社,1986.
[6] Khan K,Patle B P,Nath Y. Effect of Bimodularity on Frequency Response of Cylindrical Panels Using Galerkin Time Domain Approach[J]. Indian Academy of Sci-ences,2010,35(6):721-737.
[7] Khan A H,Patel B P. Periodic Response of Bimodular Laminated Composite Cylindrical Panels with and Without Geometric Nonlinearity[J]. International Journal of Non-Linear Mechanics,2014,67:209-217.
[8] Xie W H,Peng Z J,Meng S H,et al. GWFMM Model for Bi-Modulus Orthotropic Materials:Application to Mechanical Analysis of 4D-C/C Composites[J]. Composite Strctures,2016,150:132-138.
[9] Radostin A,Nazarov V,Kiyashko S. Propagation of Nonlinear Acoustic Waves in Bimodular Media with Linear Dissipation[J]. Wave Motion,2013,50(2):191-196.
[10] Katicha S W,Flintsch G W. Bimodular Analysis of Hot-Mix Asphalt[J]. Road Materials and Pavement Design,2010,11(4):917-946.
[11]杜玲,李范春,郭雪莲,等.基于应力球张量法的不同模量陶瓷梁有限元分析[J].推进技术,2015,36(8):1229-1235.(DU Ling,LI Fan-chun,GUO Xuelian,et al. Finite Element Analysis of Ceramic Beam with Different Modulus Based on Stress Balls Tensor Method[J]. Journal of Propulsion Technology,2015,36(8):1229-1235.)
[12]杜玲,李范春.受均布载荷的双模量陶瓷简支梁的有限元计算[J].推进技术,2016,37(7):1356-1363.(DU Ling,LI Fan-chun. Finite Element Calculation of Simply Supported Beam with Biomodulus Ceramic Subjected to Uniform Load[J]. Journal of Propulsion Technology,2016,37(7):1356-1363.)
[13]张洪武,张亮,高强.拉压不同模量材料的参变量变分原理和有限元方法[J].工程力学,2012,29(8):22-27.
[14]姚文娟,叶志明.不同拉压模量连续梁的解析解[J].力学季刊,2011,32(1):68-73.
[15]王铭慧,赵永刚.拉压弹性模量不等材料简支梁的线性振动问题[J].甘肃科学学报,2014,26(5):10-13.
[16]姚熊亮.结构动力学[M].哈尔滨:哈尔滨工程大学出版社,2007.
[17]刘相斌,宋宏伟.不同模量弯曲梁的自由振动[J].大连民族学院学报,2007,9(5):104-107.
[2]蔡尊,王振国,李西鹏,等.基于超声速气流中凹腔主动喷注的强迫点火方案研究[J].推进技术,2015,36(8):1186-1192.(CAI Zun,WANG Zhenguo,LI Xi-peng,et al. Investigation of Forced Ignition Scheme Based on Active Cavity Injection in a Supersonic Flow[J]. Journal of Propulsion Technology,2015,36(8):1186-1192.)
[3]杜玲,李范春,马雪松,等.凹腔火焰稳定器组件界面的适配性研究[J].推进技术,2016,37(12):2359-2365.(DU Ling,LI Fan-chun,MA Xue-song,et al. Suitability Investigation about Components Interface of Flame Holder with Cavity[J]. Journal of Propulsion Technology,2016,37(12):2359-2365.)
[4] Timoshenko. Strength of Materials,PartⅡ:Advanced Theory and Problems[M]. Princeton:Van Nostrand,1941.
[5] Ambartsumyan.不同模量理论[M].邬瑞锋,张允真,译.北京:中国铁道出版社,1986.
[6] Khan K,Patle B P,Nath Y. Effect of Bimodularity on Frequency Response of Cylindrical Panels Using Galerkin Time Domain Approach[J]. Indian Academy of Sci-ences,2010,35(6):721-737.
[7] Khan A H,Patel B P. Periodic Response of Bimodular Laminated Composite Cylindrical Panels with and Without Geometric Nonlinearity[J]. International Journal of Non-Linear Mechanics,2014,67:209-217.
[8] Xie W H,Peng Z J,Meng S H,et al. GWFMM Model for Bi-Modulus Orthotropic Materials:Application to Mechanical Analysis of 4D-C/C Composites[J]. Composite Strctures,2016,150:132-138.
[9] Radostin A,Nazarov V,Kiyashko S. Propagation of Nonlinear Acoustic Waves in Bimodular Media with Linear Dissipation[J]. Wave Motion,2013,50(2):191-196.
[10] Katicha S W,Flintsch G W. Bimodular Analysis of Hot-Mix Asphalt[J]. Road Materials and Pavement Design,2010,11(4):917-946.
[11]杜玲,李范春,郭雪莲,等.基于应力球张量法的不同模量陶瓷梁有限元分析[J].推进技术,2015,36(8):1229-1235.(DU Ling,LI Fan-chun,GUO Xuelian,et al. Finite Element Analysis of Ceramic Beam with Different Modulus Based on Stress Balls Tensor Method[J]. Journal of Propulsion Technology,2015,36(8):1229-1235.)
[12]杜玲,李范春.受均布载荷的双模量陶瓷简支梁的有限元计算[J].推进技术,2016,37(7):1356-1363.(DU Ling,LI Fan-chun. Finite Element Calculation of Simply Supported Beam with Biomodulus Ceramic Subjected to Uniform Load[J]. Journal of Propulsion Technology,2016,37(7):1356-1363.)
[13]张洪武,张亮,高强.拉压不同模量材料的参变量变分原理和有限元方法[J].工程力学,2012,29(8):22-27.
[14]姚文娟,叶志明.不同拉压模量连续梁的解析解[J].力学季刊,2011,32(1):68-73.
[15]王铭慧,赵永刚.拉压弹性模量不等材料简支梁的线性振动问题[J].甘肃科学学报,2014,26(5):10-13.
[16]姚熊亮.结构动力学[M].哈尔滨:哈尔滨工程大学出版社,2007.
[17]刘相斌,宋宏伟.不同模量弯曲梁的自由振动[J].大连民族学院学报,2007,9(5):104-107.
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