Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity
This study focuses on the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a moving force under the influence of three types of motions, including accelerating, decelerating and constant velocity types of motion, respectively. The beam’s nonli...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2013 |
| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2013
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| Назва видання: | Нелінійні коливання |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/177129 |
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| Цитувати: | Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity / A. Mamandi, M.H. Kargarnovin, S. Farsi // Нелінійні коливання. — 2013. — Т. 16, № 3. — С. 385-407. — Бібліогр.: 21 назв. — англ. |
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irk-123456789-1771292021-02-11T01:28:35Z Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity Mamandi, A. Kargarnovin, M.H. Farsi, S. This study focuses on the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a moving force under the influence of three types of motions, including accelerating, decelerating and constant velocity types of motion, respectively. The beam’s nonlinear governing coupled partial differential equations (PDEs) of motion for the bending rotation of warped cross-section, longitudinal and transverse displacements are derived using Hamilton’s principle. To obtain the dynamic response of the beam under the action of a moving force, the derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic response is obtained using mode summation technique. Furthermore, the calculated results are verified with those obtained by finite element method (F.E.M.) analysis. In the next step a parametric study on the response of the beam is conducted by changing the magnitude of the traveling concentrated force, its velocity and beam’s boundary conditions and likewise their sensitivity on the beam’s dynamic response are studied, respectively. It is observed that the existence of quadratic-cubic nonlinearity in the governing coupled PDEs of motion renders hardening/softening behavior on the dynamic response of the beam. Moreover, it is noticed that any restriction on the beam mid-plane stretching will introduce nonlinear behavior in the beam’s PDEs of motion. Вивчено нелiнiйну динамiчну реакцiю нахиленої балки Тимошенка з рiзними граничними умовами пiд дiєю рухомої сили, включаючи вплив рухiв трьох типiв, зокрема руху з прискоренням, уповiльненням та сталою швидкiстю. З допомогою принципу Гамiльтона отримано нелiнiйнi зв’язанi рiвняння з частинними похiдними для вигину обертання деформованого перетину, поздовжнього та поперечного зсувiв. Для встановлення динамiчної реакцiї балки пiд дiєю рухомої сили було розв’язано отриманi нелiнiйнi зв’язанi рiвняння з використанням методу Гальоркiна. Далi динамiчну реакцiю балки було одержано з використанням технiки модального пiдсумовування. Встановленi результати було перевiрено за допомогою методу скiнченних елементiв. На наступному кроцi було проведено параметричний аналiз реакцiї балки при змiнi величини рухомої концентрованої сили, її швидкостi та граничних умов, а також чутливостi реакцiї балки на цi параметри. Було помiчено, що наявнiсть квадратичної або кубiчної нелiнiйностi у зв’язаних рiвняннях з частиними похiдними робить динамiчну реакцiю балки бiльш твердою або м’якою, а будь-якi обмеження на розтягування середньої площини вводять нелiнiйнiсть у рiвняння руху балки. 2013 Article Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity / A. Mamandi, M.H. Kargarnovin, S. Farsi // Нелінійні коливання. — 2013. — Т. 16, № 3. — С. 385-407. — Бібліогр.: 21 назв. — англ. 1562-3076 http://dspace.nbuv.gov.ua/handle/123456789/177129 517.9 en Нелінійні коливання Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
This study focuses on the nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions subjected to a moving force under the influence of three types of motions, including accelerating, decelerating and constant velocity types of motion, respectively. The beam’s nonlinear governing coupled partial differential equations (PDEs) of motion for the bending rotation of warped cross-section, longitudinal and transverse displacements are derived using Hamilton’s principle. To obtain the dynamic response of the beam under the action of a moving force, the derived nonlinear coupled PDEs of motion are solved by applying Galerkin’s method. Then the beam’s dynamic response is obtained using mode summation technique. Furthermore, the calculated results are verified with those obtained by finite element method (F.E.M.) analysis. In the next step a parametric study on the response of the beam is conducted by changing the magnitude of the traveling concentrated force, its velocity and beam’s boundary conditions and likewise their sensitivity on the beam’s dynamic response are studied, respectively. It is observed that the existence of quadratic-cubic nonlinearity in the governing coupled PDEs of motion renders hardening/softening behavior on the dynamic response of the beam. Moreover, it is noticed that any restriction on the beam mid-plane stretching will introduce nonlinear behavior in the beam’s PDEs of motion. |
| format |
Article |
| author |
Mamandi, A. Kargarnovin, M.H. Farsi, S. |
| spellingShingle |
Mamandi, A. Kargarnovin, M.H. Farsi, S. Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity Нелінійні коливання |
| author_facet |
Mamandi, A. Kargarnovin, M.H. Farsi, S. |
| author_sort |
Mamandi, A. |
| title |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity |
| title_short |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity |
| title_full |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity |
| title_fullStr |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity |
| title_full_unstemmed |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity |
| title_sort |
nonlinear vibration solution of an inclined timoshenko beam under the action of a moving force with constant/non-constant velocity |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/177129 |
| citation_txt |
Nonlinear vibration solution of an inclined Timoshenko beam under the action of a moving force with constant/non-constant velocity / A. Mamandi, M.H. Kargarnovin, S. Farsi // Нелінійні коливання. — 2013. — Т. 16, № 3. — С. 385-407. — Бібліогр.: 21 назв. — англ. |
| series |
Нелінійні коливання |
| work_keys_str_mv |
AT mamandia nonlinearvibrationsolutionofaninclinedtimoshenkobeamundertheactionofamovingforcewithconstantnonconstantvelocity AT kargarnovinmh nonlinearvibrationsolutionofaninclinedtimoshenkobeamundertheactionofamovingforcewithconstantnonconstantvelocity AT farsis nonlinearvibrationsolutionofaninclinedtimoshenkobeamundertheactionofamovingforcewithconstantnonconstantvelocity |
| first_indexed |
2023-10-18T22:42:51Z |
| last_indexed |
2023-10-18T22:42:51Z |
| _version_ |
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