A receptance based method for the calculation of nonlinear normal modes of large ordered structures with distributed localized nonlinearities

Date

2022-12-01

Author

Samandari, Hamed
Ciğeroğlu, Ender

Metadata

Show full item record

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

Item Usage Stats

166
views

0
downloads

In recent years, the concept of nonlinear normal modes (NNMs) has gained interest for interpreting a broad range of nonlinear dynamic phenomena. Present study introduces a simple and efficient computational framework to compute NNMs of large order nonlinear structures overcoming difficulties associated with commonly used time-integration and discretization methods. In this paper, a Receptance Based Nonlinear Normal Mode Calculation Method (RBNM) is developed to determine the NNMs of large ordered realistic finite element models in frequency domain. Describing Function Method (DFM), which makes it possible to write the nonlinear internal forcing vector as a nonlinear displacement dependent stiffness matrix multiplied by displacement vector, is used to model the internal nonlinear forcing vector in frequency domain. A unique matrix manipulation based on dynamic stiffness and receptance concepts is used, as a result of which the number of governing nonlinear equations becomes independent from the total number of degrees of freedom of the model and it only depends on the number of degrees of freedom associated with the nonlinear elements. This brings a significant computational advantage over the classical reduced order modeling techniques. A simple 2-degree of freedom (DOF) system, the results of which are available in the literature, is used to verify the proposed method in determining NNMs. A 20-DOF lumped parameter system model and later a complex finite element model of a large structure are used to demonstrate the applicability of RBNM in determining NNMs of larger systems with several different types of nonlinear elements distributed among the degrees of freedom.

Subject Keywords

Nonlinear normal modes, Receptance Based Nonlinear Normal Mode, Calculation Method, Multi harmonic NNM, NNMs of large ordered systems, Nonlinear vibrations, WALLED CARBON NANOTUBES, HARMONIC-BALANCE METHOD, NUMERICAL COMPUTATION, DYNAMICS, VIBRATIONS, RESPONSES

URI

https://hdl.handle.net/11511/100513

Journal

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS

DOI

https://doi.org/10.1016/j.ijnonlinmec.2022.104240

Collections

Department of Mechanical Engineering, Article

Suggestions

OpenMETU
Core

A Novel Computational Method to Calculate Nonlinear Normal Modes of Complex Structures Samandarı, Hamed; Ciğeroğlu, Ender (2019-01-31) In this study, a simple and efficient computational approach to obtain nonlinear normal modes (NNMs) of nonlinear structures is presented. Describing function method (DFM) is used to capture the nonlinear internal forces under periodic motion. DFM has the advantage of expressing the nonlinear internal force as a nonlinear stiffness matrix multiplied by a displacement vector, where the off-diagonal terms of the nonlinear stiffness matrix can provide a comprehensive knowledge about the coupling between the mo...
A Modal Superposition Method for the Analysis of Nonlinear Systems Ferhatoglu, Erhan; Ciğeroğlu, Ender; Özgüven, Hasan Nevzat (2016-01-28) In the determination of response of nonlinear structures, computational burden is always a major problem even if frequency domain methods are used. One of the methods used to decrease the computational effort is the modal superposition method for nonlinear systems where the modes of the linear system are used in the calculation. However, depending on the type of the nonlinearity, in order to obtain an accurate response, the number of modes retained in the response calculations needs to be increased, which i...
A New modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes Ferhatoğlu, Erhan; Özgüven, Hasan Nevzat; Ciğeroğlu, Ender; Department of Mechanical Engineering (2017) In this thesis, a new modal superposition method based on a hybrid mode shape concept is developed for the determination of steady state vibration response of nonlinear structures. The method is developed specifically for systems having nonlinearities where the stiffness of the system may take different limiting values. Stiffness variation of these nonlinear systems enables one to define different linear systems corresponding to each value of the limiting equivalent stiffness. Moreover, the response of the ...
A weak-form spectral Chebyshev technique for nonlinear vibrations of rotating functionally graded beams Lotfan, Saeed; Dedekoy, Demir; Bediz, Bekir; Ciğeroğlu, Ender (2023-02-01) This study presents the spectral Chebyshev technique (SCT) for nonlinear vibrations of rotating beams based on a weak formulation. In addition to providing a fast-converging and precise solution for linear vibrations of structures with complex geometry, material, and physics, this method is further advanced to be able to analyze the nonlinear vibration behavior of continuous systems. Rotational motion and material gradation further complicate this nonlinear behavior. Accordingly, the beam is considered to b...
A new real-time suboptimum filtering and prediction scheme for general nonlinear discrete dynamic systems with Gaussian or non-Gaussian noise Demirbaş, Kerim (Informa UK Limited, 2011-01-01) A new suboptimum state filtering and prediction scheme is proposed for nonlinear discrete dynamic systems with Gaussian or non-Gaussian disturbance and observation noises. This scheme is an online estimation scheme for real-time applications. Furthermore, this scheme is very suitable for state estimation under either constraints imposed on estimates or missing observations. State and observation models can be any nonlinear functions of the states, disturbance and observation noises as long as noise samples ...

Citation Formats

H. Samandari and E. Ciğeroğlu, “A receptance based method for the calculation of nonlinear normal modes of large ordered structures with distributed localized nonlinearities,” INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol. 147, pp. 0–0, 2022, Accessed: 00, 2022. [Online]. Available: https://hdl.handle.net/11511/100513.