Browsing by Subject "FORCED VIBRATION"

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    Non-linear vibration of nanobeams with various boundary condition based on nonlocal elasticity theory
    (ELSEVIER SCI LTD) Bagdatli, SM
    In this study, nonlinear vibrations of Euler-Bernoulli nanobeams with various supports condition is investigated. The non-linear equations of motion including stretching of the neutral axis are derived. Forcing and damping effects are included in the analysis. Exact solutions for the mode shapes and frequencies are obtained for the linear part of the problem. For the non-linear problem approximate solutions using perturbation technique is applied to the equations of motion. The different of support cases are investigated and the cases analyzed in detail. The method of multiple time scale that is a perturbation technique is applied to the equations of motion. Natural frequencies and mode shapes for the linear problem are found for the nanobeam. Nonlinear frequencies are calculated; amplitude and phase modulation figures are presented for different cases. Frequency-response curves are drawn. (C) 2015 Elsevier Ltd. All rights reserved.
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    Nonlinear Vibrations of a Nanobeams Rested on Nonlinear Elastic Foundation Under Primary Resonance Excitation
    (SPRINGER) Bagdatli, SM; Togun, N
    In this paper, a comprehensive analysis of the nonlinear vibrations of nanobeams on nonlinear foundations under primary resonance excitation is presented. By utilizing advanced theories and highlighting the distinctions from previous work, we provide valuable insights into the behavior of these structures and their interaction with the supporting foundation. The results contribute to advancing the understanding and design of micro/nanoscale systems in a wide range of applications. The nanobeam is modeled in this paper as a Euler-Bernoulli beam with size-dependent properties. The material length scale parameter in this non-classical nanobeam model accounts for size effects at the nanoscale. For the nanobeam, two boundary conditions are taken into account: simply supported and clamped-clamped. The system's governing equation of motion is derived using the modified couple stress theory, and the accompanying boundary conditions are obtained by applying Hamilton's principle. This hypothesis enhances the analysis's precision by accounting for size effects. To arrive at an approximative analytical solution, the study employs an analytical method called the multiple-scale method. To manage primary resonance excitation in nonlinear systems, this technique is frequently used. The analysis takes into account a number of parameters, including the nonlinear foundation parameter (KNL), Winkler parameter (KL), Pasternak parameter (KP), and material length scale parameter (l/h). These variables have a significant impact on how the nanobeam behaves on the nonlinear foundation. The study includes numerical results in graphical and tabular formats that show how the linear fundamental frequency, nonlinear frequency ratio, and vibration amplitude are affected by the material length scale parameter and stiffness coefficients of the nonlinear foundation. The research includes a comparison study with prior literature on related issues to verify the accuracy of the results acquired.
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    Investigation of the non-linear vibration behaviour and 3:1 internal resonance of the multi supported nanobeam
    (WALTER DE GRUYTER GMBH) Yapanmis, BE; Bagdatli, SM
    In this present work, linear and non-linear vibration of multi-supported nanobeams, which are a fundamental part of the nano-electromechanical systems, is examined. To the best of the researchers' knowledge, there is no study performed into multi-supported nanobeam in the literature. The governing equations of the system are obtained by dint of the Hamilton principle and solved via the perturbation technique which is divided linear and non-linear parts of the main equations. The natural frequencies and mode shapes are calculated from the linear problem. The non-linear natural frequencies and amplitude-phase modulation graphs are obtained from the non-linear equation. All equations are written in generalized form, and 3, 4 and 5 supported nanobeams are investigated in detail. The nonlocal coefficient, support number and position and end condition types are focused on. The three to one internal resonance cases are also investigated. It is occurred that the clamped-end conditions shift right in the hardening behaviour graphs more than the simply supported condition. Moreover, it is shown that the supported numbers play a significant role in natural frequency.
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    Computational Modeling of Functionally Graded Beams: A Novel Approach
    (SPRINGER HEIDELBERG) Özmen, U; Özhan, BB
    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 haps://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.