Browsing by Subject "Beams and girders"

Now showing 1 - 15 of 15
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    Nonlinear vibrations of a beam-spring-mass system
    (1994) Pakdemirli M.; Nayfeh A.H.
    The nonlinear response of a simply supported beam with an attached spring-mass system to a primary resonance is investigated, taking into account the effects of beam midplane stretching and damping. The spring-mass system has also a cubic nonlinearity. The response is found by using two different perturbation approaches. In the first approach, the method of multiple scales is applied directly to the nonlinear partial differential equations and boundary conditions. In the second approach, the Lagrangian is averaged over the fast time scale, and then the equations governing the modulation of the amplitude and phase are obtained as the Euler-Lagrange equations of the averaged Lagrangian. It is shown that the frequency-response and force-response curves depend on the midplane stretching and the parameters of the spring-mass system. The relative importance of these effects depends on the parameters and location of the spring-mass system. © 1994 ASME.
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    Non-liner vibrations of a beam-mass system under different boundary conditions
    (Academic Press, 1997) Özkaya E.; Pakdemirli M.; Öz H.R.
    An Euler-Bernoulli beam and a concentrated mass on this beam are considered as a beam-mass system. The beam is supported by immovable end conditions, thus leading to stretching during the vibrations. This stretching produces cubic non-linearities in the equations. Forcing and damping terms are added into the equations. The dimensionless equations are solved for five different set of boundary conditions. Approximate solutions of the equations are obtained by using the method of multiple scales, a perturbation technique. The first terms of the perturbation series lead to the linear problem. Natural frequencies and mode shapes for the linear problem are calculated exactly for different end conditions. Second order non-linear terms of the perturbation series appear as corrections to the linear problem. Amplitude and phase modulation equations are obtained. Non-linear free and forced vibrations are investigated in detail. The effects of the position and magnitude of the mass, as well as effects of different end conditions on the vibrations, are determined. © 1997 Academic Press Limited.
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    Vibrations of a beam-mass systems using artificial neural networks
    (Elsevier Ltd, 1998) Karlik B.; Özkaya E.; Aydin S.; Pakdemirli M.
    The nonlinear vibrations of an Euler-Bernoulli beam with a concentrated mass attached to it are investigated. Five different sets of boundary conditions are considered. The transcendental equations yielding the exact values of natural frequencies are presented. Using the Newton-Raphson method, natural frequencies are calculated for different boundary conditions, mass ratios and mass locations. The corresponding nonlinear correction coefficients are also calculated for the fundamental mode. The calculated natural frequencies and nonlinear corrections are used in training a multi-layer, feed-forward, backpropagation artificial neural network (ANN) algorithm. The algorithm produces results within 0.5 and 1.5% error limits for linear and nonlinear cases, respectively. By employing the ANN algorithm, computational time is drastically reduced compared with the conventional numerical techniques. © 1998 Published by Elsevier Science Ltd. All rights reserved.
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    Approximate boundary layer solution of a moving beam problem
    (Assoc Sci Res, 1998) Pakdemirli M.; Ozkaya E.
    The transverse vibrations of a simply supported beam moving with constant velocity is considered. The case of transition from string to beam effects is treated. In this model, the fourth order spatial derivative multiplies a small parameter and hence leads to a boundary layer problem. The problem is solved approximately using the method of multiple scales.
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    Calculation of the natural frequencies of a beam-mass system using finite element method
    (Assoc Sci Res, 2000) Oz H.R.
    In this study, the natural frequencies of an Euler-Bernoulli type beam with a mass are calculated. The beam is supported with different end conditions. The mass is located on different locations. The linear natural frequencies are calculated by using finite element method for the first five modes. Results are compared with those of exact and other approximate methods.
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    Vibrations of an axially accelerating beam with small flexural stiffness
    (Academic Press Ltd, 2000) Özkaya E.; Pakdemirli M.
    Transverse vibrations of an axially moving beam are considered. The axial velocity is harmonically varying about a mean velocity. The equation of motion is expressed in terms of dimensionless quantities. The beam effects are assumed to be small. Since, in this case, the fourth order spatial derivative multiplies a small parameter, the mathematical model becomes a boundary layer type of problem. Approximate solutions are searched using the method of multiple scales and the method of matched asymptotic expansions. Results of both methods are contrasted with the outer solution.
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    On the nonlinear transverse vibrations and stability of an axially accelerating beam
    (Assoc Sci Res, 2000) Oz H.R.
    Nonlinear vibrations and stability analysis of an axially moving Euler-Bernoulli type beam are investigated. The beam is on fixed supports and moving with a harmonically varying velocity about a constant mean value. The method of multiple scales is used in the analysis. Nonlinear frequencies depending on vibration amplitudes are obtained. Stability and bifurcations of steady-state solutions are analyzed for frequencies close to two times any natural frequency. It is shown that the amplitudes are bounded in time for frequencies close to zero. The effect of fixed supports is discussed.
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    Linear transverse vibrations of a simply supported beam carrying concentrated masses
    (Association for Scientific Research, 2001) Özkaya E.
    Linear transverse vibrations of an Euler-Bernoulli beam are considered. The beam carries masses and is simply supported at both ends. The equations of motion are obtained and solved. Linear frequency equations are obtained. Natural frequencies are calculated for different number of masses, mass ratios, and mass locations.
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    Vibrations of a stretched beam with non-ideal boundary conditions
    (Association for Scientific Research, 2001) Pakdemirli M.; Boyaci H.
    A simply supported Euler-Bernoulli beam with immovable end conditions is considered. The concept of non-ideal boundary conditions is applied to the beam problem. In accordance, the boundaries are assumed to allow small deflections. Approximate analytical solution of the problem is found using the method of multiple scales, a perturbation technique.
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    Group - Theoretic approach to axially accelerating beam problem
    (2002) Özkaya E.; Pakdemirli M.
    Transverse vibrations of a beam moving with time dependent axial velocity have been investigated. Analytical solutions of the problem are found using the systematic approach of Lie group theory. Group classification with respect to the arbitrary velocity function has been performed using a newly developed technique of equivalence transformations. From the symmetries of the partial differential equation, the way of deriving exact solutions for the case of arbitrary velocity is shown. Special cases of interest such as constant velocity, harmonically varying velocity and exponentially decaying velocity are investigated in detail. Finally, for a simply supported beam, approximate solutions are presented for the exponentially decaying and harmonically varying cases.
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    Three-to-one internal resonances in a general cubic non-linear continuous system
    (Academic Press, 2003) Pakdemirli M.; Özkaya E.
    A general continuous system with an arbitrary cubic non-linearity is considered. The non-linearity is expressed in terms of an arbitrary cubic operator. Three-to-one internal resonance case is considered. A general approximate solution is presented for the system. Amplitude and phase modulation equations are derived. Steady state solutions and their stability are discussed in the general sense. The sufficiency condition for such resonances to occur is derived. Finally the algorithm is applied to a beam resting on a non-linear elastic foundation.
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    Three-to-one internal resonance in multiple stepped beam systems
    (Springer Netherlands, 2009) Tekin A.; Özkaya E.; Bağdatlı S.M.
    In this study, the vibrations of multiple stepped beams with cubic nonlinearities are considered. A three-to-one internal resonance case is investigated for the system. A general approximate solution to the problem is found using the method of multiple scales (a perturbation technique). The modulation equations of the amplitudes and the phases are derived for two modes. These equations are utilized to determine steady state solutions and their stabilities. It is assumed that the external forcing frequency is close to the lower frequency. For the numeric part of the study, the three-to-one ratio in natural frequencies is investigated. These values are observed to be between the first and second natural frequencies in the cases of the clamped-clamped and clamped-pinned supports, and between the second and third natural frequencies in the case of the pinned-pinned support. Finally, a numeric algorithm is used to solve the three-to-one internal resonance. The first mode is externally excited for the clamped-clamped and clamped-pinned supports, and the second mode is externally excited for the pinned-pinned support. Then, the amplitudes of the first and second modes are investigated when the first mode is externally excited. The amplitudes of the second and third modes are investigated when the second mode is externally excited. The force-response, damping-response, and frequency-response curves are plotted for the internal resonance modes of vibrations. The stability analysis is carried out for these plots. © 2009 Shanghai University and Springer Berlin Heidelberg.
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    An approach for estimating the capacity of RC beams strengthened in shear with FRP reinforcements using artificial neural networks
    (2012) Tanarslan H.M.; Secer M.; Kumanlioglu A.
    An artificial neural network model is developed to predict the shear capacity of reinforced concrete (RC) beams, retrofitted in shear by means of externally bonded wrapped and U-jacketed fiber-reinforced polymer (FRP) in this study. However, unlike the existing design codes the model considers the effect of strengthening configurations dissimilarity. In addition model also considers the effect of shear span-to-depth ratio (a/d) ratio at the ultimate state. It is also aimed to develop an efficient and practical artificial neural network (ANN) model. Therefore, mechanical properties of strengthening material and mechanical and dimensional properties of beams are selected as inputs. ANN model is trained, validated and tested using the literature of 84 RC beams. Then neural network results are compared with those 'theoretical' predictions calculated directly from International Federation for Structural Concrete (fib14), the American guideline (ACI 440.2R), the Australian guideline (CIDAR), the Italian National Research Council (CNR-DT 200) and Canadian guideline (CHBDC) for verification. Performed analysis showed that the neural network model is more accurate than the guideline equations with respect to the experimental results and can be applied satisfactorily within the range of parameters covered in this study. © 2011 Elsevier Ltd. All rights reserved.
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    Low velocity impact behavior of concrete beam strengthened with CFRP strip
    (Techno Press, 2012) Kantar E.; Anil O.
    Nowadays CFRP (Carbon Fiber Reinforced Polymer) became widely used materials for the strengthening and retrofitting of structures. Many experimental and analytical studies are encountered at literature about strengthening beams by using this kind of materials against static loads and cyclic loads such as earthquake or wind loading for investigating their behavior. But authors did not found any study about strengthening of RC beams by using CFRP against low velocity impact and investigating their behavior. For these reasons an experimental study is conducted on totally ten strengthened RC beams. Impact loading is applied on to specimens by using an impact loading system that is designed by authors. Investigated parameters were concrete compression strength and drop height. Two different sets of specimens with different concrete compression strength tested under the impact loading that are applied by dropping constant weight hammer from five different heights. The acceleration arises from the impact loading is measured against time. The change of velocity, displacement and energy are calculated for all specimens. The failure modes of the specimens with normal and high concrete compression strength are observed under the loading of constant weight impact hammer that are dropped from different heights. Impact behaviors of beams are positively affected from the strengthening with CFRP. Measured accelerations, the number of drops up to failure and dissipated energy are increased. Finite element analysis that are made by using ABAQUS software is used for the simulation of experiments, and model gave compatible results with experiments.
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    Nonlinear free and forced vibration analyses of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section
    (Elsevier Ltd, 2018) Sınır S.; Çevik M.; Sınır B.G.
    Nonlinear free and forced vibrations of axially functionally graded Euler-Bernoulli beams with non-uniform cross-section are investigated. The beam has immovable, namely clamped-clamped and pinned-pinned boundary conditions, which leads to midplane stretching in the course of vibrations. Nonlinearities occur in the system due to this stretching. Damping and forcing terms are included after nondimensionalization. The equations are solved approximately using perturbation method and mode shapes by differential quadrature method. In the linear order natural frequencies and mode shapes are computed. In the nonlinear order, some corrections arise to the linear problem; the effect of these nonlinear correction terms on natural frequency is examined and frequency –response curves are drawn to show the unstable regions. In order to confirm the validity, our results are compared with others available in literature. © 2018