{ "article_id": 1042, "public_id": "c1483776-ea68-4354-bee4-f720a5be68ec", "internal_identifier": null, "source_identifier": "42:47", "status": "published", "type": "research_article", "title": "BASİT MESNETLİ KİRİŞİN DİFERANSİYEL TRANSFORM METODUYLA SERBEST TİTREŞİM ANALİZİ", "title_secondary": null, "abstract": "Taşıyıcı elemanların zorlanmış titreşimlerin analizinde, serbest titreşim analizi önemli bir yer tutmaktadır. Kirişlerin yapısal davranışının incelenmesinde sadece eğilme tesirlerinin dikkate alındığı teoriye Euler kiriş teorisi denilmektedir. Mühendislik analizlerinde Euler kiriş teorisi yaygın olarak kullanılmaktadır. Sürekli kütleli dinamik hesap modeli kurulan Euler kiriş teorisine uyan kirişin serbest titreşimine ait homojen kısmi diferansiyel denklemin dördüncü mertebeden olduğu bilinmektedir. Bu denklemin analitik çözümü neticesinde açısal frekanslarının hesaplanabilmesi için başlangıç ve sınır koşulları kullanılarak elde edilen frekans denkleminin köklerinin bulunması yeterlidir. Bu tür diferansiyel denklemlerin uygulaması geçmişte elektrik devrelerinin analizinde kullanılan diferansiyel transform metodu (DTM) ile çözümü mümkündür. İteratif bir çözümü olan yöntemde kullanılan terim sayısı arttıkça sayıl çözüm sonuçları , analitik çözüm sonuçlarıyla örtüşmektedir. Çalışmada her iki ucu basit olarak mesnetlendirilmiş Euler kirşinin ilk üç moduna ait açısal frekanslarının DTM ile çözüm adımları sunulmuş, bu yöntem ve analitik çözüm yöntemi kullanılarak elde edilen açısal frekans değerlerinin kıyaslaması sayısal örneklerle sunulmuştur.", "language": "tr", "english_title": "FREE VIBRATION ANALYSIS OF A SIMPLY SUPPORTED BEAM USING THE DIFFERENTIAL TRANSFORM METHOD", "english_abstract": "In the analysis of forced vibrations of load-bearing elements, free vibration analysis plays a significant role. The theory that considers only bending forces in the investigation of the structural behavior of beams is called Euler beam theory. Euler beam theory is widely used in engineering analyses. It is known that the homogeneous partial differential equation for the free vibration of a beam obeying Euler beam theory, which establishes a continuous mass dynamic analysis model, is of the fourth order. To calculate the angular frequencies as a result of the analytical solution of this equation, it is sufficient to find the roots of the frequency equation obtained using the initial and boundary conditions. The application of such differential equations is possible with the differential transform method (DTM), which was previously used in the analysis of electrical circuits. In this method, which has an iterative solution, as the number of terms used increases, the numerical solution results coincide with the analytical solution results. This study presents the solution steps for the angular frequencies of the first three modes of an Euler beam simply supported at both ends using DTM (Directional Mathematical Transformation), and a comparison of the angular frequency values ​​obtained using this method and the analytical solution method is presented with numerical examples.", "doi": null, "doi_url": null, "resource_url": "https://www.set-science.com/a/c1483776-ea68-4354-bee4-f720a5be68ec", "pdf_url": "https://www.set-science.com/a/c1483776-ea68-4354-bee4-f720a5be68ec/pdf", "og_image": "https://www.set-science.com/assets/img/og-card-v2.png", "authors": [ { "public_id": "0f15ad52-8d3a-4616-ad16-4654b3bf5475", "given": "Seval ", "family": "Çatal  ", "full": "Seval  Çatal  ", "literal": null, "orcid": null, "orcid_url": null, "email": "seval.catal@deu.edu.tr", "corresponding": true, "sequence": "first", "affiliations": [ { "name": "Dokuz Eylül Üniversitesi  ", "department": null, "country": null, "country_code": null, "ror": null, "ror_url": null } ] } ], "keywords": [ "Diferansiyel transform metodu", "serbest titreşim", "açısal frekans", "mod", "Euler Kiriş Teorisi" ], "translations": [ { "language": "en", "title": "FREE VIBRATION ANALYSIS OF A SIMPLY SUPPORTED BEAM USING THE DIFFERENTIAL TRANSFORM METHOD", "abstract": "In the analysis of forced vibrations of load-bearing elements, free vibration analysis plays a significant role. The theory that considers only bending forces in the investigation of the structural behavior of beams is called Euler beam theory. Euler beam theory is widely used in engineering analyses. It is known that the homogeneous partial differential equation for the free vibration of a beam obeying Euler beam theory, which establishes a continuous mass dynamic analysis model, is of the fourth order. To calculate the angular frequencies as a result of the analytical solution of this equation, it is sufficient to find the roots of the frequency equation obtained using the initial and boundary conditions. The application of such differential equations is possible with the differential transform method (DTM), which was previously used in the analysis of electrical circuits. In this method, which has an iterative solution, as the number of terms used increases, the numerical solution results coincide with the analytical solution results. This study presents the solution steps for the angular frequencies of the first three modes of an Euler beam simply supported at both ends using DTM (Directional Mathematical Transformation), and a comparison of the angular frequency values ​​obtained using this method and the analytical solution method is presented with numerical examples.", "keywords": [ "Differential transform method", "free vibration", "angular frequency", "mode", "Euler Beam Theory" ] } ], "subjects": [], "subject_names": [], "published_date": "2019-06-01", "published_year": "2019", "received_date": null, "accepted_date": null, "volume": "4", "issue": null, "page_first": "241", "page_last": "245", "article_number": null, "conference": { "short_name": "ISAS2019-ENS", "full_title": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "name": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "acronym": "ISAS2019-ENS", "location": "Ankara, Türkiye", "start_date": "2019-04-19", "end_date": null, "public_id": "ed3b36e9-38cf-4aeb-a135-833c969cc89f" }, "proceedings": { "title": "3rd International Symposium on Innovative Approaches in Scientific Studies (Engineering and Natural Sciences)", "series_title": "Setsci conference indexing system", "publisher": "SET Technology", "isbn": null, "eisbn": null, "issn": "2618-6446", "eissn": null, "doi": null, "doi_prefix": null, "slug": "setsci-volume-4-2019-legacy-42", "public_id": "24d215ef-a545-4351-9725-6e9bdb167b3c", "url": "https://www.set-science.com/p/setsci-volume-4-2019-legacy-42" }, "license": { "name": "CC BY 4.0", "url": "https://creativecommons.org/licenses/by/4.0/", "code": "CC-BY-4.0", "open_access": true }, "copyright": { "holder": "SET Technology", "year": "2019" }, "funding_statement": null, "funders": [], "references": [ { "order": 1, "raw": "A.Chopra, “Dynamics of Structures”,Prentice Hall, Second Edition, USA,2004.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 2, "raw": "R.W.Clough, J. Penzien, “Dynamics of Structures”, McGraw-Hill,Inc., Second Edition, Singapore, 1993.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 3, "raw": "Z. Celep,N. Kumbasar “Yapı Dinamiği”, Beta Dağıtım, İstanbul, 2001.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 4, "raw": "H.H. Çatal, “Free vibration of partially supported piles with the effetcs of bending moment, axial and shear forces”, Engineering Structures, 24, pp. 1615-1622, 2002.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 5, "raw": "H.H. Çatal,”Free vibration of semi-rigid connected and partially embedded piles with the effects of bending moment, axial and shear force”, Enginnering Structures, 28,pp.1911-1918,2006.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 6, "raw": "Y.Yeşilce, H.H. Çatal, “Solution of free vibration equations of semirigid connected Reddy-Bickford beams resting on elastic soil using differential transform method”, Arch. Appl. Mechanic, 81, pp. 199-213, 2011.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 7, "raw": "Y. Yeşilce, S. Çatal, “Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method”, Structural Engineering Mechanics, 31 (4), pp. 453-475, 2009. ,", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 8, "raw": "J.K. Zhou, “Differential Transformation and Its Applications for Electrical Circuits”,Whuan China:Huazhong University Press, 1986.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 9, "raw": "B. Bozyiğit, Y.Yeşilce, S. Çatal, “Free vibration of axial-loaded beams resting on viscoelastic foundation using Adomian decomposition method and differential transform method”, Engineering Science and Technology an International Journal, 21(6), pp. 1181-1193, 2018.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 10, "raw": "Ö.Özdemir, M.O. Kaya, “Flap wise bending vibration analysis of rotating tapared cantilever Bernoulli-Euler beam by differential transform method”, J. Sound Vibration, 289, pp. 413-420, 2006.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null }, { "order": 11, "raw": "S. Çatal, “Analysis of free vibration of beam on elastic soil using differential transform method”, Structural Engineering and Mevchanics, 24(1), pp.51-62,2006.", "doi": null, "title": null, "authors": null, "source": null, "year": null, "volume": null, "pages": null } ], "statements": { "acknowledgements": null, "conflict_of_interest": null, "data_availability": null, "ai_disclosure": null }, "credit": [], "history": { "published": "2019-06-01" } }