A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes

Date

2018-07-01

Author

Ferhatoglu, Erhan
Ciğeroğlu, Ender
Özgüven, Hasan Nevzat

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In this paper, 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 nonlinear system is bounded by the confinement of these linear systems. In this study, a modal superposition method utilizing novel hybrid mode shapes which are defined as linear combinations of the modal vectors of the limiting linear systems is proposed to determine periodic response of nonlinear systems. In this method the response of the nonlinear system is written in terms of hybrid modes instead of the modes of the underlying linear system. This provides decrease of the number of modes that should be retained for an accurate solution, which in turn reduces the number of nonlinear equations to be solved. In this way, computational time for response calculation is directly curtailed. In the solution, the equations of motion are converted to a set of nonlinear algebraic equations by using describing function approach, and the numerical solution is obtained by using Newton's method with arc length continuation. The method developed is applied on two different systems: a lumped parameter model and a finite element model. Several case studies are performed and the accuracy and computational efficiency of the proposed modal superposition method with hybrid mode shapes are compared with those of the classical modal superposition method which utilizes the mode shapes of the underlying linear system.

Subject Keywords

Control and Systems Engineering, Signal Processing, Mechanical Engineering, Civil and Structural Engineering, Aerospace Engineering, Computer Science Applications

URI

https://hdl.handle.net/11511/37670

Journal

MECHANICAL SYSTEMS AND SIGNAL PROCESSING

DOI

https://doi.org/10.1016/j.ymssp.2018.01.036

Collections

Department of Mechanical Engineering, Article

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Citation Formats

E. Ferhatoglu, E. Ciğeroğlu, and H. N. Özgüven, “A new modal superposition method for nonlinear vibration analysis of structures using hybrid mode shapes,” MECHANICAL SYSTEMS AND SIGNAL PROCESSING, pp. 317–342, 2018, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/37670.