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euler bernoulli theory
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تکرار جستجوی کلیدواژه euler bernoulli theory در مقالات مجلات علمی
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In this research, the free vibrations of beams made of saturated proelastic materials under different boundary conditions have been investigated. The equation governing the transverse movement of the beam is derived based on the Euler-Bernoulli theory of beams and using the relations governing the stress-strain of proelastic materials using Hamilton's principle. Different models of porosity distribution along the longitudinal length of the beam have been considered. The governing equation in different boundary conditions of double-ended, double-ended, and single-ended single-ended boundary conditions is determined by the differential quadratic method for three different types of uniform, linear, and quadratic porosity distribution along the length of the hollow beam. The natural frequencies of free vibration of the longitudinal porous beam have been obtained. The effect of porous material parameters on the change of natural frequencies in different boundary conditions has been concluded. The results obtained have been compared and validated with the results presented by other researchers.
Keywords: Free Vibration, Proelastic Beam, Euler-Bernoulli Theory, Natural Frequency -
A complete investigation on the free vibration of bilayer graphene nanoribbons (BLGNRs) mod-eled as sandwich beams taking into account tensile-compressive and shear effects of van der Waals (vdWs) interactions between adjacent graphene nanoribbons (GNRs) as well as between GNRs and polymer matrix is performed in this research. In this modeling, nanoribbon layers play role of sandwich beam layers and are modeled based upon Euler-Bernoulli theory. To consider effects of vdWs interactions between adjacent GNRs as well as between GNRs and polymer matrix, their equivalent tensile-compressive and shear moduli are considered and utilized in derivation of governing equations instead of employing conventional Winkler and Pasternak effects for elastic medium. The governing equations of motion are derived by considering the assumptions and employing sandwich beam theory, and natural frequencies are obtained by implementing harmonic differential quadrature method (HDQM). A detailed study is performed to examine the influences of the tensile-compressive and shear effects of vdWs interactions between adjacent GNRs as well as between GNRs and polymer matrix on the free vibration of BLGNRs.Keywords: Elastic medium, Sandwich theory, Tensile-compressive effects, Shear effects, Euler-Bernoulli theory
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Bending responses are the important characteristics of structures. In this paper, the bending solution of the thin and thick beams which are elastically restrained against rotation and translation are presented using various theories. Hence, accurate and direct modeling technique is offered for modeling of the thin and thick beams. The effect of the values of the span-to-depth ratio and type of the beam supports are assessed to state accurate comparison of various theories. Finally, the numerical examples are shown in order to present the evaluation of the efficiency and simplicity of the various theories. The results of the theories are compared with the results of the finite element method (ABAQUS). Based on the results, using the Timoshenko beam theory, the obtained values are in good agreement with the Finite Element modeling for the values of the span-to-depth ratio (L/h) less than 3. On the other hands, due to ignoring the shear deformation effect, the Euler–Bernoulli theory underestimates the deflection of the moderately deep beams (L/h=5).Keywords: Euler-Bernoulli Theory, Timoshenko Theory, Flexural deformation, Span-to-depth ratio
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امروزه استفاده از سازه های کامپوزیتی به علت نسبت استحکام به وزن بالا و خصوصیات مناسب ارتعاشاتی در بسیاری از صنایع مخصوصا سازه های دریایی بیش از پیش مورد توجه قرار گرفته است. یکی از پایه ای ترین اجزای تشکیل دهنده بسیاری ساز ها می-تواند به صورت یک تیر در نظر گرفته شود که نقش مهمی در طراحی سازه ای دارد لذا بررسی تیر کامپوزیتی لایه ای از لحاظ ارتعاشاتی یکی از مسائل پایه ای در تولیدات صنعتی می باشد. متفاوت بودن خصوصیات مکانیکی در جهات مختلف به طراح امکان ایجاد طرحه های مختلف و مناسب برای بارگذاری و شرایط مرزی خاص می دهدتا از اثرات مخرب تشدید در سازه ها که منجر به خرابی می شود، ممانعت به عمل آید. در مطالعه حال حاضر با استفاده از روش های تحلیلی مانند تئوری تیموشنکو و اولر برنولی با کمک از تئوری کلاسیک ورق ها فرکانس طبیعی ارتعاشات در صفحه x-y وx-z برای یک نمونه تیر تقویت شده با الیاف شیشه بدست می آید سپس با مدلسازی به روش اجزامحدود در نرم افزار انسیس ارزیابی از صحت نتایج این روش انجام می شود. مشاهده می شود که نتایج به یکدیگر نزدیک می باشد. بعد از آن تاثیر پارامترهایی مانند زاویه الیاف و ابعاد تیر در سه بعد روی میزان فرکانس ارتعاشات در هر دو صفحه مورد بررسی و مقایسه قرار می گیرد. در انتها با لایه چینی های مختلف چیدمانی متناظر با بیشترین فرکانس بدست آورده می شود.کلید واژگان: تیر کامپوزیت چند لایه، فرکانس طبیعی، چیدمانی لایه ها، تئوری تیموشنکو و اولر برنولیMarine Technology, Volume:5 Issue: 1, 2018, PP 90 -100The Composites are used in industrial structural systems for decreasing weight and increasing specific stiffness and improvement of vibration characteristics. Beam analysis plays an important role in mechanical structural design, so that Finding free vibration characteristics of laminated composite beams (LCBs) is one of the bases for designing and modeling of industrial products. Anisotropy of these composites allows the designer to tailor the material in order to achieve the desired performance requirements to prevent of resonant that lead failure in structures. In this study the out of plane and in-plane vibration of Epoxy-glass laminated composite beam are investigated by Timoshenko and Euler Bernouli analytical theory. It should be noted that classical lamination theory is used to determine requirement bending stiffness. Then a finite element modeling are implemented in ANSYS and the validation of results are conducted. it is seen that the results are very close to each other. After that the effective parameter on natural frequency in x-y and x-z vibration plane such fiber angle and dimension of beam in three directions are discussed. Finally the special stacking sequence consistent with maximum natural frequency is obtained between several optional stackingKeywords: Composite laminated beam, Natural frequency, Stacking sequence, Timoshenko, Euler Bernoulli Theory
نکته
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