{"title":"由非线性季莫申科梁结构元素组成的建筑材料内的非线性波传播分析","authors":"Abdallah Wazne , Hilal Reda , Jean-François Ganghoffer , Hassan Lakiss","doi":"10.1016/j.wavemoti.2024.103344","DOIUrl":null,"url":null,"abstract":"<div><p>In the present work, a full nonlinear Timoshenko beam employing nonlinear shape functions is developed. The extended Hamilton principle is employed for deriving the differential equations of motion and the associated boundary conditions. The general form of the boundary conditions is then utilized to determine the static solution of the beam motion. Using this solution for the deformation and rotation of the beam, the nonlinear shape functions of the beam are identified, which leads to the linear and nonlinear mass and stiffness matrices of the Timoshenko beam element. The nonlinear dispersion diagram incorporating the non-linear corrections is obtained using the Linstedt–Poincaré perturbation method. An analysis of the effect of internal transverse shear and bending on the nonlinear dispersion characteristics of wave propagation in two-dimensional periodic network materials made of nonlinear Timoshenko beams is done. The formulated theory shows that the percentage of correction factor of the nonlinear kinematics versus the linear dynamical behavior is inversely proportional to the frequency amplitude. The shear and extension modes are shown to have the higher effect in the non-linear correction term in comparison to the flexural mode.</p></div>","PeriodicalId":49367,"journal":{"name":"Wave Motion","volume":"130 ","pages":"Article 103344"},"PeriodicalIF":2.1000,"publicationDate":"2024-05-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Analysis of nonlinear wave propagation within architected materials consisting of nonlinear Timoshenko beam structural elements\",\"authors\":\"Abdallah Wazne , Hilal Reda , Jean-François Ganghoffer , Hassan Lakiss\",\"doi\":\"10.1016/j.wavemoti.2024.103344\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>In the present work, a full nonlinear Timoshenko beam employing nonlinear shape functions is developed. The extended Hamilton principle is employed for deriving the differential equations of motion and the associated boundary conditions. The general form of the boundary conditions is then utilized to determine the static solution of the beam motion. Using this solution for the deformation and rotation of the beam, the nonlinear shape functions of the beam are identified, which leads to the linear and nonlinear mass and stiffness matrices of the Timoshenko beam element. The nonlinear dispersion diagram incorporating the non-linear corrections is obtained using the Linstedt–Poincaré perturbation method. An analysis of the effect of internal transverse shear and bending on the nonlinear dispersion characteristics of wave propagation in two-dimensional periodic network materials made of nonlinear Timoshenko beams is done. The formulated theory shows that the percentage of correction factor of the nonlinear kinematics versus the linear dynamical behavior is inversely proportional to the frequency amplitude. The shear and extension modes are shown to have the higher effect in the non-linear correction term in comparison to the flexural mode.</p></div>\",\"PeriodicalId\":49367,\"journal\":{\"name\":\"Wave Motion\",\"volume\":\"130 \",\"pages\":\"Article 103344\"},\"PeriodicalIF\":2.1000,\"publicationDate\":\"2024-05-08\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wave Motion\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S016521252400074X\",\"RegionNum\":3,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ACOUSTICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wave Motion","FirstCategoryId":"101","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S016521252400074X","RegionNum":3,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ACOUSTICS","Score":null,"Total":0}
Analysis of nonlinear wave propagation within architected materials consisting of nonlinear Timoshenko beam structural elements
In the present work, a full nonlinear Timoshenko beam employing nonlinear shape functions is developed. The extended Hamilton principle is employed for deriving the differential equations of motion and the associated boundary conditions. The general form of the boundary conditions is then utilized to determine the static solution of the beam motion. Using this solution for the deformation and rotation of the beam, the nonlinear shape functions of the beam are identified, which leads to the linear and nonlinear mass and stiffness matrices of the Timoshenko beam element. The nonlinear dispersion diagram incorporating the non-linear corrections is obtained using the Linstedt–Poincaré perturbation method. An analysis of the effect of internal transverse shear and bending on the nonlinear dispersion characteristics of wave propagation in two-dimensional periodic network materials made of nonlinear Timoshenko beams is done. The formulated theory shows that the percentage of correction factor of the nonlinear kinematics versus the linear dynamical behavior is inversely proportional to the frequency amplitude. The shear and extension modes are shown to have the higher effect in the non-linear correction term in comparison to the flexural mode.
期刊介绍:
Wave Motion is devoted to the cross fertilization of ideas, and to stimulating interaction between workers in various research areas in which wave propagation phenomena play a dominant role. The description and analysis of wave propagation phenomena provides a unifying thread connecting diverse areas of engineering and the physical sciences such as acoustics, optics, geophysics, seismology, electromagnetic theory, solid and fluid mechanics.
The journal publishes papers on analytical, numerical and experimental methods. Papers that address fundamentally new topics in wave phenomena or develop wave propagation methods for solving direct and inverse problems are of interest to the journal.