TY  - JOUR
T1  - The effects of elastic supports on nonlinear vibrations of a slightly curved beam
TT  - ELASTİK MESNETLERİN HAFİFÇE EĞRİ BİR KİRİŞİN NONLİNEER TİTREŞİMLERİNE ETKİLERİ
AU  - Sarıgül, Murat
PY  - 2018
DA  - August
Y2  - 2018
DO  - 10.17482/uumfd.315108
JF  - Uludağ Üniversitesi Mühendislik Fakültesi Dergisi
JO  - UUJFE
PB  - Bursa Uludağ University
WT  - DergiPark
SN  - 2148-4155
SP  - 255
EP  - 274
VL  - 23
IS  - 2
LA  - en
AB  - In this study, nonlinear vibrations of a slightlycurved beam having arbitrary rising function are handled. The beam isrestricted in longitudinal direction using elastic supports on both ends.Sag-to-span ratio of the beam, which is assumed to have sinusoidal curvaturefunction at the beginning, is taken as 1/10. Beam being of Euler-Bernoulli typerests on Winkler elastic foundation and carries an arbitrarily placedconcentrated mass. Equations of motion are obtained by using HamiltonPrinciple. Cubic and quadratic nonlinear terms have been aroused at themathematical model because of the foundation and the beam's elongation. TheMethod of Multiple Scales (MMS), a perturbation technique, is used to solve theequations of motion analytically. The primary resonance case is taken intoaccount during steady-state vibrations. The natural frequencies are obtainedexactly for different control parameters such as supports' types, locations ofthe masses and linear coefficient of foundation. Frequency-amplitude and frequency-responsegraphs are drawn by using amplitude-phase modulation equations.
KW  - Nonlinear vibrations
KW  - Slightly curved beam
KW  - Elastic supports
KW  - Elastic foundation.
N2  - Bu çalışmada, keyfi başlangıçfonksiyonuna sahip hafifçe eğri bir kirişin lineer olmayan titreşimleri elealınmaktadır. Her iki ucundan elastik mesnetler kullanılarak kiriş, boyunayönünde kısıtlanmıştır. Başlangıçta sinüsoidal eğrilik fonksiyonuna sahip olduğuvarsayılan kiriş için, ulaşılan eğrilik yüksekliğinin izdüşüme oranı 1/10alınmaktadır. Euler-Bernoulli tipinde olan kiriş Winkler elastik zemini üzerineoturmakta ve üzerinde keyfi olarak yerleştirilmiş kütleler taşımaktadır.Hamilton prensibi kullanılarak hareket denklemleri elde edilmiştir. Zeminden vekiriş uzamasından dolayı matematiksel modelde kübik ve quadratik lineer olmayanterimler ortaya çıkmaktadır. Hareket denklemlerini analitik olarak çözümlemekiçin bir Pertürbasyon tekniği olan Çok Ölçekli Metod(MMS) kullanılmaktadır.Geçici-durum titreşimleri süresince baskın rezonans durumu dikkatealınmaktadır. Mesnetlerin tipleri, kütlelerin konumları ve zeminin lineerbileşeni gibi farklı mukayese parametreleri için doğal frekanslar elde edilmektedir.Genlik-faz modülasyon denklemleri kullanılarak frekans-genlik ve frekans-cevapgrafikleri çizilmiştir.
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UR  - https://doi.org/10.17482/uumfd.315108
L1  - https://dergipark.org.tr/en/download/article-file/555587
ER  -