Jinlong Zhang, Liaojun Zhang, R. Ge, Li Yang, J. Xia
{"title":"Study on Natural Frequencies of Transverse Free Vibration of Functionally Graded Axis Beams by the Differential Quadrature Method","authors":"Jinlong Zhang, Liaojun Zhang, R. Ge, Li Yang, J. Xia","doi":"10.3813/aaa.919388","DOIUrl":null,"url":null,"abstract":"Functionally gradient materials with special mechanical characteristics are more and more widely used in engineering. The functionally graded beam is one of the commonly used components to bear forces in the structure. Accurate analysis of the dynamic characteristics of the axially\n functionally graded (AFG) beam plays a vital role in the design and safe operation of the whole structure. Based on the Euler-Bernoulli beam theory (EBT), the characteristic equation of transverse free vibration for the AFG Euler-Bernoulli beam with variable cross-section is obtained in the\n present work, and the governing equations of the beam are transformed into ordinary differential equations with variable coefficients. Using differential quadrature method (DQM), the solution formulas of characteristic equations under different boundary conditions are derived, and the natural\n frequencies of the AFG beam are calculated, while the node partition of a non-uniform geometric progression is discussed.","PeriodicalId":35085,"journal":{"name":"Acta Acustica united with Acustica","volume":"44 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2019-11-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Acustica united with Acustica","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3813/aaa.919388","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"Arts and Humanities","Score":null,"Total":0}
引用次数: 0
Abstract
Functionally gradient materials with special mechanical characteristics are more and more widely used in engineering. The functionally graded beam is one of the commonly used components to bear forces in the structure. Accurate analysis of the dynamic characteristics of the axially
functionally graded (AFG) beam plays a vital role in the design and safe operation of the whole structure. Based on the Euler-Bernoulli beam theory (EBT), the characteristic equation of transverse free vibration for the AFG Euler-Bernoulli beam with variable cross-section is obtained in the
present work, and the governing equations of the beam are transformed into ordinary differential equations with variable coefficients. Using differential quadrature method (DQM), the solution formulas of characteristic equations under different boundary conditions are derived, and the natural
frequencies of the AFG beam are calculated, while the node partition of a non-uniform geometric progression is discussed.
期刊介绍：
Cessation. Acta Acustica united with Acustica (Acta Acust united Ac), was published together with the European Acoustics Association (EAA). It was an international, peer-reviewed journal on acoustics. It published original articles on all subjects in the field of acoustics, such as
• General Linear Acoustics, • Nonlinear Acoustics, Macrosonics, • Aeroacoustics, • Atmospheric Sound, • Underwater Sound, • Ultrasonics, • Physical Acoustics, • Structural Acoustics, • Noise Control, • Active Control, • Environmental Noise, • Building Acoustics, • Room Acoustics, • Acoustic Materials and Metamaterials, • Audio Signal Processing and Transducers, • Computational and Numerical Acoustics, • Hearing, Audiology and Psychoacoustics, • Speech,
• Musical Acoustics, • Virtual Acoustics, • Auditory Quality of Systems, • Animal Bioacoustics, • History of Acoustics.
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