FORCED HARMONIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES USING DESCRIBING FUNCTIONS

Date

1993-07-01

Author

TANRIKULU, O
KURAN, B
Özgüven, Hasan Nevzat
IMREGUN, M

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

278
views

0
downloads

The dynamic response of multiple-degree-of-freedom nonlinear structures is usually determined by numerical integration of the equations of motion, an approach which is computationally very expensive for steady-state response analysis of large structures. In this paper, an alternative semianalytical quasilinear method based on the describing function formulation is proposed for the harmonic response analysis of structures with symmetrical nonlinearities. The equations of motion are converted to a set of nonlinear algebraic equations and the solution is obtained iteratively. The linear and nonlinear parts of the structure are dealt with separately, the former being represented by the constant linear receptance matrix [alpha], and the latter by the generalized quasilinear matrix [DELTA] which is updated at each iteration. A special technique that reduces the computation time significantly when the nonlinearities are localized is used with success to analyze large structures. The proposed method is fully compatible with standard modal analysis procedures. Several examples dealing with cubic stiffness, piecewise linear stiffness, and coulomb friction type of nonlinearities are presented in the case of a ten-degree-of-freedom structure.

Subject Keywords

Time-integration methods, Non-linear structures, Dynamics, Clearance

URI

https://hdl.handle.net/11511/34372

Journal

AIAA JOURNAL

DOI

https://doi.org/10.2514/3.11769

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

Numerical Solution of Multi-scale Electromagnetic Boundary Value Problems by Utilizing Transformation-Based Metamaterials Ozgun, Ozlem; Kuzuoğlu, Mustafa (2011-06-23) We present numerical solution techniques for efficiently handling multi-scale electromagnetic boundary value problems having fine geometrical details or features, by utilizing spatial coordinate transformations. The principle idea is to modify the computational domain of the finite methods (such as the finite element or finite difference methods) by suitably placing anisotropic metamaterial structures whose material parameters are obtained by coordinate transformations, and hence, to devise easier and effic...
Least squares differential quadrature time integration scheme in the dual reciprocity boundary element method solution of convection-diffusion problems Bozkaya, Canan (2005-03-18) The least squares differential quadrature method (DQM) is used for solving the ordinary differential equations in time, obtained from the application of the dual reciprocity boundary element method (DRBEM) for the spatial partial derivatives in convection-diffusion type problems. The DRBEM enables us to use the fundamental solution of the Laplace equation which is easy to implement computationally. The time derivative and the convection terms are considered as the nonhomogeneity in the equation which are ap...
Nonlinear flutter calculations using finite elements in a direct Eulerian-Lagrangian formulation Seber, Guclu; Bendiksen, Oddvar O. (American Institute of Aeronautics and Astronautics (AIAA), 2008-06-01) A fully nonlinear aeroelastic formulation of the direct Eulerian-Lagrangian computational scheme is presented in which both structural and aerodynamic nonlinearities are treated without approximations. The method is direct in the sense that the calculations are done at the finite element level, both in the fluid and structural domains, and the fluid-structure system is time-marched as a single dynamic system using a multistage Runge-Kutta scheme. The exact nonlinear boundary condition at the fluid-structure...
Assessment of alternative simulation techniques in nonlinear time history analyses of multi-story frame buildings: A case study Karim Zadeh Naghshineh, Shaghayegh; Askan Gündoğan, Ayşegül; Yakut, Ahmet (2017-07-01) In regions with sparse ground motion data, simulations provide alternative acceleration time series for evaluation of the dynamic response of a structure. Different ground motion simulation methods provide varying levels of goodness of fit between observed and synthetic data. Before using the seismologically acceptable synthetic records for engineering purposes, it is critical to investigate the efficiency of synthetics in predicting observed seismic responses of structures. For this purpose, in this study ...
Near-field performance analysis of locally-conformal perfectly matched absorbers via Monte Carlo simulations Ozgun, Ozlem; Kuzuoğlu, Mustafa (2007-12-10) In the numerical solution of some boundary value problems by the finite element method (FEM), the unbounded domain must be truncated by an artificial absorbing boundary or layer to have a bounded computational domain. The perfectly matched layer (PML) approach is based on the truncation of the computational domain by a reflectionless artificial layer which absorbs outgoing waves regardless of their frequency and angle of incidence. In this paper, we present the near-field numerical performance analysis of o...

Citation Formats

O. TANRIKULU, B. KURAN, H. N. Özgüven, and M. IMREGUN, “FORCED HARMONIC RESPONSE ANALYSIS OF NONLINEAR STRUCTURES USING DESCRIBING FUNCTIONS,” AIAA JOURNAL, pp. 1313–1320, 1993, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/34372.