Browsing by Author "Özhan B.B."
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Item General solution algorithm for three-to-one internal resonances of a cubic nonlinear vibration model(2009) Özhan B.B.; Pakdemirli M.A generalized nonlinear vibration model of continuous systems is considered. The model includes arbitrary linear and cubic differential and/or integral operators. Linear operators represent the linear parts and cubic operators represent the nonlinear parts of the model. The generalized equation of motion is analyzed by using the method of multiple scales (a perturbation method). Three-to-one internal resonances between natural frequencies are obtained. The amplitude and phase modulation equations are presented. Approximate solution is derived. Steady state solutions and their stability are discussed. Solution algorithm is applied to nonlinear vibration model of an axially moving Euler Bernoulli beam. Constant velocity case of axially moving beam is analyzed. Natural frequencies of beam are given for different velocity values. Steady state solutions and their stability are determined numerically. Frequency response relations are obtained. Energy transfer of one mode to another via a three-to-one internal resonance is observed. Jump phenomena of the system are shown graphically by choosing different vibration and beam parameter values.Item Effect of viscoelasticity on the natural frequencies of axially moving continua(2013) Özhan B.B.; Pakdemirli M.Linear models of axially moving viscoelastic beams and viscoelastic pipes conveying fluid are considered. The natural frequencies of the models are calculated. For both models, viscoelasticity terms are assumed to be of order one. Natural frequencies corresponding to various beam and pipe parameters are presented. Effects of viscoelasticity on the natural frequencies are discussed. © 2013 B. Burak Özhan and Mehmet Pakdemirli.Item Buckling configurations and dynamic response of buckled euler-bernoulli beams with non-classical supports(Brazilian Association of Computational Mechanics, 2014) Sinir B.G.; Özhan B.B.; Reddy J.N.Exact solutions of buckling configurations and vibration response of post-buckled configurations of beams with non-classical boundary conditions (e.g., elastically supported) are presented using the Euler-Bernoulli theory. The geometric nonlinearity arising from mid-plane stretching (i.e., the von Kármán nonlinear strain) is considered in the formulation. The nonlinear equations are reduced to a single linear equation in terms of the transverse deflection by eliminating the axial displacement and incorporating the nonlinearity and the applied load into a constant. The resulting critical buckling loads and their associated mode shapes are obtained by solving the linearized buckling problem analytically. The buckling configurations are determined in terms of the applied axial load and the transverse deflection. The first buckled shape is the only stable equilibrium position for all boundary conditions considered. Then the pseudo-dynamic response of buckled beams is also determined analytically. Natural frequency versus buckling load and natural frequency versus amplitudes of buckling configurations are plotted for various non-classical boundary conditions. © 2014, Brazilian Association of Computational Mechanics. All rights reserved.Item Vibration and stability analysis of axially moving beams with variable speed and axial force(World Scientific Publishing Co. Pte Ltd, 2014) Özhan B.B.The well-known vibration model of axially moving beam is considered. Both axial moving speed and axial force are assumed to vary harmonically. The Method of Multiple Time Scales (a perturbation method) is used. The natural vibrations of beam are considered for different values of beam parameters. Resonances are obtained for seven different conditions. Solvability conditions for each resonance case are found analytically. Effects of transport velocity, axial force, rigidity and damping are discussed. Stability analysis are obtained for principal parametric resonances. Stable and unstable regions are obtained regarding velocity and force effects separately and together. © 2014 World Scientific Publishing Company.Item Preface of the "minisymposium on Applied Symmetries and Perturbation Methods"(American Institute of Physics Inc., 2016) Pakdemirli M.; Özhan B.B.; Dolapci H.[No abstract available]Item A Taylor-Splitting Collocation approach and applications to linear and nonlinear engineering models(Elsevier Ltd, 2022) Çayan S.; Özhan B.B.; Sezer M.A novel matrix method based on the Taylor series called Taylor-Splitting Collocation Method is presented to solve linear and nonlinear ordinary differential equations. Unlike the previous approaches, the fundamental matrix equation is reformulated using interval splitting. The residual error estimation algorithm is presented. Convergence analysis is given in a general form. Four different mechanical models are analyzed: 1. Forced oscillations of a linear spring-mass model 2. Forced oscillations of a nonlinear spring-mass model 3. Free oscillations of a cubic nonlinear spring-dashpot-mass model 4. Forced oscillations of a damped nonlinear pendulum model Displacement-time and velocity-time dependencies are plotted for each model. Phase portraits of nonlinear models are presented. Appropriate absolute or residual error analyses are obtained for the proposed application models. The results of the new solution approach are compared with exact, numerical, and approximate solutions from previous works. Consistent results are found. © 2022 Elsevier LtdItem Collocation approaches to the mathematical model of an Euler–Bernoulli beam vibrations(Elsevier B.V., 2022) Çayan S.; Özhan B.B.; Sezer M.Taylor-Matrix and Hermite-Matrix Collocation methods are presented to obtain the modal vibration behavior of an Euler Bernoulli Euler–Bernoulli beam. The methods provide approximate solutions in the truncated Taylor series and the truncated Hermite series by using Chebyshev-Lobatto Chebyshev–Lobatto collocation points and operational matrices. The approaches are applied to the well-known transverse vibration model of a simply-supported Euler–Bernoulli type beam. The beam is assumed under the effect of external harmonic force with spatially varying amplitude. Firstly, the model problem is transformed into a system of linear algebraic equations. Then the approximate solution is computed by solving the obtained algebraic system. The proposed methods are compared with the exact solutions. Mode shapes of the first three fundamental frequencies are obtained for each approach. The convergence behaviors of transverse displacements and absolute errors are calculated for each mode. The numerical results are shown and compared. Based on the given figures and tables, one can state that the methods are remarkable, dependable, and accurate for approaching the mentioned model problems. © 2022 International Association for Mathematics and Computers in Simulation (IMACS)Item Computational Modeling of Functionally Graded Beams: A Novel Approach(Springer, 2022) Özmen U.; Özhan B.B.Aim: A novel computational approach is propounded to model the material gradation of a functionally graded Euler–Bernoulli beam using Ansys Workbench, the finite element method-based software. Novelty: Contrary to layer-by-layer modeling approaches to express functional material gradation for different structures in the literature, the new approach states a continuous variation of the material gradation obeying gradation laws (e.g., power-law). Method: The new approach is applied to the computational free vibration analyses of functionally graded beams. Three types of functionally graded beams are investigated: (1) One-directional beam with a uniform cross section. (2) One-directional beam with a non-uniform cross section. (3) Bi-directional beam with a uniform cross section. Power-law and exponential-law types mathematical expressions are used in modeling the material gradation of functionally graded beams. Results: The finite element results of free vibration analyses for each beam are obtained. The results are compared with the analytical results from the literature [Lee and Lee, Int J Mech Sci 122:1–17; Sinir et al., Compos Part B Eng 148:123–131; Karamanli, Anadolu Univ J Sci Technol A Appl Sci Eng https://doi.org/10.18038/aubtda.361095; Simsek, Compos Struct 133:968–978] to present the accuracy of the novel approach. Several support conditions are investigated. The effects of the gradient indices (power-law and exponential-law indices) on the natural frequencies of the beams are discussed. © 2022, Krishtel eMaging Solutions Private Limited.Item An adaptive approach for solving fourth-order partial differential equations: algorithm and applications to engineering models(Springer Nature, 2022) Çayan S.; Özhan B.B.; Sezer M.A novel numerical technique based on orthogonal Laguerre polynomials called the Laguerre matrix collocation method is proposed. The motivation of the study is to reduce the computational cost in mathematical models by adapting Laguerre polynomials directly without transforming them into the truncated Taylor polynomial basis. The new approach is suitable for solving fourth-order partial differential equations arising in physics and engineering. The algorithm and error analyses are presented in general form and applied to two physical models from solid mechanics. First, the technique is used to solve the governing equation for a plate deflection under a harmonically distributed static load. Second, the algorithm is applied to the bending model of a shear deformable plate under the harmonically distributed static load. The boundary conditions of the models are specified, and the bending responses of the models are obtained. The numerical results are compared with the exact results from the literature. The comparisons show that the new approach is suitable for numerical solutions of fourth-order partial differential equations which arise in physics and engineering. © 2022, The Author(s) under exclusive licence to Sociedade Brasileira de Matemática Aplicada e Computacional.