Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430330
TIAN Yaping, YANG Jianghui, WANG Ruibang
Aimed at the coupling transition relationship between the periodic motion, the tooth surface impact, the non-meshing state and the dynamic load of straight bevel gear systems with backlash, the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle. Besides, the improved CPNF (continuous-Poincaré-Newton-Floquet) method was applied to solve the solution domain structure of the periodicity, impact, non-meshing and dynamic load characteristics of the system cells. The simulation results show that, there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure, including the saddle node bifurcation, the Hopf bifurcation, the period-doubling bifurcation, the catastrophe bifurcation and the period-3 bifurcation. The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient. The tooth surface non-meshing, the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion. Meanwhile, in the same domain, the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.
针对带间隙直齿锥齿轮系统的周期运动、齿面冲击、非啮合状态和动载荷之间的耦合过渡关系，基于单元映射原理建立了时变啮合刚度和频率比的二参数平面。此外，采用改进的CPNF (continuous- poincar - newton - floquet)方法求解了系统单元的周期性、冲击性、非啮合性和动载荷特性的解域结构。仿真结果表明，在2参数解域结构中存在丰富的3种齿面冲击共存的分岔模式，包括鞍节点分岔、Hopf分岔、倍周期分岔、突变分岔和3周期分岔。时变啮合刚度系数的增大会加剧齿面冲击和混沌。齿面不啮合、齿背啮合和动载荷系数在齿面碰撞和周期运动的影响下会发生突变。同时，在同一域内，齿面非啮合和齿背啮合随频率比的增大而减弱，随刚度系数的增大而增大。
{"title":"Parametric Solution Domain Structures for Bifurcation and Non-Meshing Dynamic Characteristics of Straight Bevel Gear Systems","authors":"TIAN Yaping, YANG Jianghui, WANG Ruibang","doi":"10.21656/1000-0887.430330","DOIUrl":"https://doi.org/10.21656/1000-0887.430330","url":null,"abstract":"Aimed at the coupling transition relationship between the periodic motion, the tooth surface impact, the non-meshing state and the dynamic load of straight bevel gear systems with backlash, the 2-parameter plane with respect to the time-varying meshing stiffness and the frequency ratio was built based on the cell mapping principle. Besides, the improved CPNF (continuous-Poincaré-Newton-Floquet) method was applied to solve the solution domain structure of the periodicity, impact, non-meshing and dynamic load characteristics of the system cells. The simulation results show that, there are plentiful bifurcation modes with 3 kinds of tooth surface impacts coexisting in the 2-parameter solution domain structure, including the saddle node bifurcation, the Hopf bifurcation, the period-doubling bifurcation, the catastrophe bifurcation and the period-3 bifurcation. The tooth surface impact and chaos will intensify due to increase of the time-varying meshing stiffness coefficient. The tooth surface non-meshing, the tooth back meshing and the dynamic load coefficient will exhibit mutations under the influences of the tooth impact and the periodic motion. Meanwhile, in the same domain, the tooth surface non-meshing and the tooth back meshing will weaken with the frequency ratio but heighten with the stiffness coefficient.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838753","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out. Like the shell sandwich structure in nature, the ring is composed of 3 well-bonded regions, of which the inner and outer regions are made of homogeneous anisotropic materials, and the intermediate transition region is made of a material with arbitrary-gradient properties along the radial direction. Based on the boundary conditions and the continuity conditions at the interface, the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method, then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution. The distributions of the stress and displacement fields in the sandwich ring structure were given. Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model. The effectiveness and accuracy of the integral equation method were verified through comparison of the numerical solutions with the exact ones for a special power function gradient variation form. The more general Voigt function model was adopted for the intermediate transition region, and the influences of the anisotropy degree, the gradient parameter, and the thickness on the stress and displacement fields were analyzed. The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sandwich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures.
{"title":"Elastic Analysis of Anisotropic Rotating Sandwich Circular Ring With a Functionally Graded Transition Region","authors":"PENG Xulong, XIE Xiaopeng, HUANG Haiping, WEI Wenchao, TANG Xuesong","doi":"10.21656/1000-0887.440003","DOIUrl":"https://doi.org/10.21656/1000-0887.440003","url":null,"abstract":"The elastic analysis of anisotropic rotating sandwich ring with a functionally graded transition region was carried out. Like the shell sandwich structure in nature, the ring is composed of 3 well-bonded regions, of which the inner and outer regions are made of homogeneous anisotropic materials, and the intermediate transition region is made of a material with arbitrary-gradient properties along the radial direction. Based on the boundary conditions and the continuity conditions at the interface, the 2nd Fredholm integral equation for the radial stress was obtained with the integral equation method, then the stress and displacement fields of the sandwich ring structure were obtained through numerical solution. The distributions of the stress and displacement fields in the sandwich ring structure were given. Different gradient changes encountered in engineering practice can be solved only through substitution of the corresponding function model. The effectiveness and accuracy of the integral equation method were verified through comparison of the numerical solutions with the exact ones for a special power function gradient variation form. The more general Voigt function model was adopted for the intermediate transition region, and the influences of the anisotropy degree, the gradient parameter, and the thickness on the stress and displacement fields were analyzed. The proposed Fredholm integral equation method provides a powerful tool for the optimal design of anisotropic functionally graded materials and sandwich ring structures. The numerical results make a theoretical guidance for the safety design of anisotropic functionally graded sandwich ring structures.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135838754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.440055
WANG Jingzhe, CHEN Baocai, ZHU Shaowei, CHEN Liming
Since negative stiffness metamaterials are reusable as energy-absorbing materials, it is necessary to investigate the energy-absorbing performances and reusability of negative stiffness metamaterials. The designed negative stiffness metamaterial was prepared with the 3D printing technology, and the energy absorption performance of the metamaterial in the multi-stable mode and the mono-stable mode was investigated by repeated loading experiments. The effect of the residual stress on the energy absorption performance of the metamaterial was studied with the natural aging method. The results show that, the specific energy absorption of the designed metamaterial first decreases and then stabilizes with the increase of the number of loading times in the case of repeated loading. In both the multi-stable mode and the mono-stable mode, the natural aging method can effectively release the residual stresses in the metamaterial, thus improving its repeated energy absorption performance.
{"title":"Study on Energy Absorption Performances of Conical Negative Stiffness Metamaterials","authors":"WANG Jingzhe, CHEN Baocai, ZHU Shaowei, CHEN Liming","doi":"10.21656/1000-0887.440055","DOIUrl":"https://doi.org/10.21656/1000-0887.440055","url":null,"abstract":"Since negative stiffness metamaterials are reusable as energy-absorbing materials, it is necessary to investigate the energy-absorbing performances and reusability of negative stiffness metamaterials. The designed negative stiffness metamaterial was prepared with the 3D printing technology, and the energy absorption performance of the metamaterial in the multi-stable mode and the mono-stable mode was investigated by repeated loading experiments. The effect of the residual stress on the energy absorption performance of the metamaterial was studied with the natural aging method. The results show that, the specific energy absorption of the designed metamaterial first decreases and then stabilizes with the increase of the number of loading times in the case of repeated loading. In both the multi-stable mode and the mono-stable mode, the natural aging method can effectively release the residual stresses in the metamaterial, thus improving its repeated energy absorption performance.","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"276 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135505384","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430077
Zhang Kai, Wang Keyong, Qiao Dongping
{"title":"Research on the Fictitious Source Points of the Hybrid Fundamental Solution-Based Finite Element Method for Heat Conduction Problems","authors":"Zhang Kai, Wang Keyong, Qiao Dongping","doi":"10.21656/1000-0887.430077","DOIUrl":"https://doi.org/10.21656/1000-0887.430077","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67810880","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430149
Huang Rong, Deng Yangfang, Wen Zhifeng
{"title":"The SAV Scheme Based on the Barycentric Interpolation Collocation Method for the Allen-Cahn Equation","authors":"Huang Rong, Deng Yangfang, Wen Zhifeng","doi":"10.21656/1000-0887.430149","DOIUrl":"https://doi.org/10.21656/1000-0887.430149","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"17 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67811554","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430298
Zhao Xiang, Meng Shiyao
{"title":"Forced vibration analysis of Euler-Bernoulli double-beam system by means of Green's functions","authors":"Zhao Xiang, Meng Shiyao","doi":"10.21656/1000-0887.430298","DOIUrl":"https://doi.org/10.21656/1000-0887.430298","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430292
Wang Qijun, Zhang Dechun, Li Peng, Wang Jun
{"title":"Numerical Approach Using Panel Method for Added Mass Coefficients of a Group of Rigid Sections and Its Application for Fuel Assemblies","authors":"Wang Qijun, Zhang Dechun, Li Peng, Wang Jun","doi":"10.21656/1000-0887.430292","DOIUrl":"https://doi.org/10.21656/1000-0887.430292","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814196","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430299
Zhao Shixiang, Zeng Xiangguo, Wang Yuntian, Yan Yigang
{"title":"First Principles Study on the Influence Mechanism of Impurity Gas O2 on the Adsorption Properties of ZrCo Alloy","authors":"Zhao Shixiang, Zeng Xiangguo, Wang Yuntian, Yan Yigang","doi":"10.21656/1000-0887.430299","DOIUrl":"https://doi.org/10.21656/1000-0887.430299","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814232","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.21656/1000-0887.430318
Xu Xiaoyang, Zhao Yuting
{"title":"Numerical Simulation of Transient Non-Isothermal Viscoelastic Couette Flows Based on the SPH Method","authors":"Xu Xiaoyang, Zhao Yuting","doi":"10.21656/1000-0887.430318","DOIUrl":"https://doi.org/10.21656/1000-0887.430318","url":null,"abstract":"","PeriodicalId":8341,"journal":{"name":"Applied Mathematics and Mechanics","volume":"1 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"67814472","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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