{"title":"功能梯度梁的力学：分析、计算和实验分析","authors":"Uğur Özmen, Bozkurt Burak Özhan","doi":"10.1007/s10999-025-09750-y","DOIUrl":null,"url":null,"abstract":"<div><p>Bending and vibration (modal) analyses of a functionally graded beam are proposed. Analytical, computational, and experimental results are obtained and compared. The functionally graded beam is modeled according to Euler- Bernoulli beam theory. The power-law rule is assumed to show the functional gradation of the beam. Displacement fields and energy expressions are given. Hamilton’s principle is used to derive the equation of motion. Firstly, free vibration analysis of the functionally graded Euler–Bernoulli beam is investigated. Natural frequencies and mode shape expressions are analytically obtained for four support conditions. Secondly, a novel computational model is constructed using the finite element method based Ansys Workbench software. The new approach allows the simulation of exact continuous variation of material gradation. Finally, the experimental process is presented. The functionally graded beam is manufactured with 3-D printing technology using the additive manufacturing method. PETG/CF and PLA polymer materials are utilized to manufacture the test samples. Bending and vibration tests are done. The experimental results are compared with analytical and computational results. The effects of the power law index on the bending displacements and natural frequencies of the functionally graded beam are shown. The analytical and computational results are close to those of the experimental ones. Consistency of analytical computational and experimental results is proposed. The results show that the error percentages are very low compared to existing works.</p></div>","PeriodicalId":593,"journal":{"name":"International Journal of Mechanics and Materials in Design","volume":"21 3","pages":"577 - 590"},"PeriodicalIF":3.6000,"publicationDate":"2025-04-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s10999-025-09750-y.pdf","citationCount":"0","resultStr":"{\"title\":\"Mechanics of functionally graded beams: analytical, computational, and experimental analyses\",\"authors\":\"Uğur Özmen, Bozkurt Burak Özhan\",\"doi\":\"10.1007/s10999-025-09750-y\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Bending and vibration (modal) analyses of a functionally graded beam are proposed. Analytical, computational, and experimental results are obtained and compared. The functionally graded beam is modeled according to Euler- Bernoulli beam theory. The power-law rule is assumed to show the functional gradation of the beam. Displacement fields and energy expressions are given. Hamilton’s principle is used to derive the equation of motion. Firstly, free vibration analysis of the functionally graded Euler–Bernoulli beam is investigated. Natural frequencies and mode shape expressions are analytically obtained for four support conditions. Secondly, a novel computational model is constructed using the finite element method based Ansys Workbench software. The new approach allows the simulation of exact continuous variation of material gradation. Finally, the experimental process is presented. The functionally graded beam is manufactured with 3-D printing technology using the additive manufacturing method. PETG/CF and PLA polymer materials are utilized to manufacture the test samples. Bending and vibration tests are done. The experimental results are compared with analytical and computational results. The effects of the power law index on the bending displacements and natural frequencies of the functionally graded beam are shown. The analytical and computational results are close to those of the experimental ones. Consistency of analytical computational and experimental results is proposed. The results show that the error percentages are very low compared to existing works.</p></div>\",\"PeriodicalId\":593,\"journal\":{\"name\":\"International Journal of Mechanics and Materials in Design\",\"volume\":\"21 3\",\"pages\":\"577 - 590\"},\"PeriodicalIF\":3.6000,\"publicationDate\":\"2025-04-09\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s10999-025-09750-y.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Journal of Mechanics and Materials in Design\",\"FirstCategoryId\":\"88\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s10999-025-09750-y\",\"RegionNum\":3,\"RegionCategory\":\"材料科学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"ENGINEERING, MECHANICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Journal of Mechanics and Materials in Design","FirstCategoryId":"88","ListUrlMain":"https://link.springer.com/article/10.1007/s10999-025-09750-y","RegionNum":3,"RegionCategory":"材料科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}
Mechanics of functionally graded beams: analytical, computational, and experimental analyses
Bending and vibration (modal) analyses of a functionally graded beam are proposed. Analytical, computational, and experimental results are obtained and compared. The functionally graded beam is modeled according to Euler- Bernoulli beam theory. The power-law rule is assumed to show the functional gradation of the beam. Displacement fields and energy expressions are given. Hamilton’s principle is used to derive the equation of motion. Firstly, free vibration analysis of the functionally graded Euler–Bernoulli beam is investigated. Natural frequencies and mode shape expressions are analytically obtained for four support conditions. Secondly, a novel computational model is constructed using the finite element method based Ansys Workbench software. The new approach allows the simulation of exact continuous variation of material gradation. Finally, the experimental process is presented. The functionally graded beam is manufactured with 3-D printing technology using the additive manufacturing method. PETG/CF and PLA polymer materials are utilized to manufacture the test samples. Bending and vibration tests are done. The experimental results are compared with analytical and computational results. The effects of the power law index on the bending displacements and natural frequencies of the functionally graded beam are shown. The analytical and computational results are close to those of the experimental ones. Consistency of analytical computational and experimental results is proposed. The results show that the error percentages are very low compared to existing works.
期刊介绍：
It is the objective of this journal to provide an effective medium for the dissemination of recent advances and original works in mechanics and materials'' engineering and their impact on the design process in an integrated, highly focused and coherent format. The goal is to enable mechanical, aeronautical, civil, automotive, biomedical, chemical and nuclear engineers, researchers and scientists to keep abreast of recent developments and exchange ideas on a number of topics relating to the use of mechanics and materials in design.
Analytical synopsis of contents:
The following non-exhaustive list is considered to be within the scope of the International Journal of Mechanics and Materials in Design:
Intelligent Design:
Nano-engineering and Nano-science in Design;
Smart Materials and Adaptive Structures in Design;
Mechanism(s) Design;
Design against Failure;
Design for Manufacturing;
Design of Ultralight Structures;
Design for a Clean Environment;
Impact and Crashworthiness;
Microelectronic Packaging Systems.
Advanced Materials in Design:
Newly Engineered Materials;
Smart Materials and Adaptive Structures;
Micromechanical Modelling of Composites;
Damage Characterisation of Advanced/Traditional Materials;
Alternative Use of Traditional Materials in Design;
Functionally Graded Materials;
Failure Analysis: Fatigue and Fracture;
Multiscale Modelling Concepts and Methodology;
Interfaces, interfacial properties and characterisation.
Design Analysis and Optimisation:
Shape and Topology Optimisation;
Structural Optimisation;
Optimisation Algorithms in Design;
Nonlinear Mechanics in Design;
Novel Numerical Tools in Design;
Geometric Modelling and CAD Tools in Design;
FEM, BEM and Hybrid Methods;
Integrated Computer Aided Design;
Computational Failure Analysis;
Coupled Thermo-Electro-Mechanical Designs.
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