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Analytical solutions for generalized duffing equation

Aghdam, M. M ; Sharif University of Technology | 2016

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  1. Type of Document: Article
  2. DOI: 10.1007/978-3-319-27055-5_8
  3. Publisher: Springer International Publishing , 2016
  4. Abstract:
  5. Structures like beams, plates, shells, and sectors have a key role in different fields of science and engineering. Reliable design of structures requires detailed understanding of their behavior in different service conditions including statics, dynamics, and vibration. For instance, dynamics and vibration characteristics of structures such as natural frequencies, mode shapes, and damping ratios are among interesting properties. Furthermore, in most severe conditions, linear theories are not enough to accurately capture real structural behavior. Thus, investigation of nonlinear and/or large amplitude vibration of structures which is normally governed by system of nonlinear differential equations is necessary. In this chapter, large amplitude vibration of engineering structures such as beams, plate, and sectors is investigated. In all cases, the vibrational behavior of the structure is governed by the well-known Duffing equation. In addition to classical cubic nonlinearity in Duffing equation, inclusion of quadratic nonlinearity in the governing equation is also necessary for some special cases. Therefore, the generalized form of Duffing equation with both odd and even nonlinearities should be considered. In this chapter, an approximate analytical solution for generalized Duffing equation with both odd and even higher order nonlinearities is presented. Validity of the presented solution is examined through some numerical examples
  6. Keywords:
  7. Duffing equation ; He’s variational method ; Nonlinear differential equation ; Perturbation theory
  8. Source: Nonlinear Approaches in Engineering Applications: Advanced Analysis of Vehicle Related Technologies ; 2016 , Pages 263-278 ; 9783319270555 (ISBN)
  9. URL: http://link.springer.com/chapter/10.1007%2F978-3-319-27055-5_8