{
    "article_id": 1043,
    "public_id": "1b5191da-c712-4281-a8e2-50d25307978d",
    "internal_identifier": null,
    "source_identifier": "42:48",
    "status": "published",
    "type": "research_article",
    "title": "ANKASTRE MESNETLİ TIMOSHENKO KİRİŞİNİN DİFERANSİYEL TRANSFORMASYON YÖNTEMİYLE SERBEST TİTREŞİM ANALİZİ",
    "title_secondary": null,
    "abstract": "Eğilme tesirleriyle birlikte kesme tesirlerinin de dikkate alındığı teori, literatürde Timoshenko kiriş teorisi olarak bilinmektedir. Bu teoriye uygun davranan kirişlerin serbest titreşim analizi mühendisliğin ilgi çeken konuların birisi olmuştur. Timoshenko kiriş teorisine uyan çubukların serbest titreşimine ait kısmi diferansiyel denklemi dördüncü mertebeden olup bu denklemin analitik çözümü mevcuttur. Bir ucu ankastre olarak mesnetlendirilmiş, diğer ucu serbest kirişin serbest titreşimine ait kısmi diferansiyel denklemi, kirişin başlangıç ve sınır koşulları kullanılarak elde edilebilir. İteratif bir çözüm yöntemi olan Diferansiyel Transformasyon metodu (DTM) kullanılarak Timoshenko kirişinin serbest titreşimine ait açısal frekansları hesaplanabilmektedir. Kirişin başlangıç, sınır koşulları ve DTM uygulanarak ilk üç moda ait serbest titreşim açısal frekans değerleri ile diferansiyel denklemin analitik olarak çözülmesiyle elde edilen açısal frekans değerlerikıyaslanmış, DTM’da kullanılan terim sayısı arttıkça elde edilen sayısal sonuçları analitik çözüm yöntemi kullanılarak elde edilen sayısal sonuçlara yakınsadığı belirlenmiştir.",
    "language": "tr",
    "english_title": "FREE VIBRATION ANALYSIS OF A CANTILEVER-SUPPORTED TIMOSHENKO BEAM USING THE DIFFERENTIAL TRANSFORMATION METHOD",
    "english_abstract": "The theory that considers both bending and shear forces is known in the literature as Timoshenko beam theory. The free vibration analysis of beams behaving according to this theory has become a topic of interest in engineering. The partial differential equation for the free vibration of bars obeying Timoshenko beam theory is of the fourth order, and an analytical solution exists for this equation. The partial differential equation for the free vibration of a beam supported at one end with a cantilever and the other end free can be obtained using the initial and boundary conditions of the beam. Using the Differential Transformation method (DTM), an iterative solution method, the angular frequencies of the free vibration of the Timoshenko beam can be calculated. The angular frequency values ​​of the beam's initial and boundary conditions, as well as the angular frequency values ​​obtained from the first three modes of free vibration using DTM, were compared with the angular frequency values ​​obtained by analytically solving the differential equation. It was determined that as the number of terms used in DTM increased, the numerical results obtained converged with the numerical results obtained using the analytical solution method.",
    "doi": null,
    "doi_url": null,
    "resource_url": "https://www.set-science.com/a/1b5191da-c712-4281-a8e2-50d25307978d",
    "pdf_url": "https://www.set-science.com/a/1b5191da-c712-4281-a8e2-50d25307978d/pdf",
    "og_image": "https://www.set-science.com/assets/img/og-card-v2.png",
    "authors": [
        {
            "public_id": "f643a3b6-0048-46c7-ba3f-3f2c67e6916a",
            "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": [],
    "translations": [
        {
            "language": "en",
            "title": "FREE VIBRATION ANALYSIS OF A CANTILEVER-SUPPORTED TIMOSHENKO BEAM USING THE DIFFERENTIAL TRANSFORMATION METHOD",
            "abstract": "The theory that considers both bending and shear forces is known in the literature as Timoshenko beam theory. The free vibration analysis of beams behaving according to this theory has become a topic of interest in engineering. The partial differential equation for the free vibration of bars obeying Timoshenko beam theory is of the fourth order, and an analytical solution exists for this equation. The partial differential equation for the free vibration of a beam supported at one end with a cantilever and the other end free can be obtained using the initial and boundary conditions of the beam. Using the Differential Transformation method (DTM), an iterative solution method, the angular frequencies of the free vibration of the Timoshenko beam can be calculated. The angular frequency values ​​of the beam's initial and boundary conditions, as well as the angular frequency values ​​obtained from the first three modes of free vibration using DTM, were compared with the angular frequency values ​​obtained by analytically solving the differential equation. It was determined that as the number of terms used in DTM increased, the numerical results obtained converged with the numerical results obtained using the analytical solution method.",
            "keywords": [
                "Timoshenko Kiriş Teorisi, Diferansiyel Transformasyon Metodu, Açısal Frekans, Ankastre Mesnetli Kiriş, Serbest Titreşim"
            ]
        }
    ],
    "subjects": [],
    "subject_names": [],
    "published_date": "2019-06-01",
    "published_year": "2019",
    "received_date": null,
    "accepted_date": null,
    "volume": "4",
    "issue": null,
    "page_first": "246",
    "page_last": "251",
    "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,
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            "order": 4,
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            "order": 6,
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    ],
    "statements": {
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        "conflict_of_interest": null,
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    "credit": [],
    "history": {
        "published": "2019-06-01"
    }
}