Nonlinear resonances of axially functionally graded beams rotating with varying speed including Coriolis effects

2021-11-01
Lotfan, Saeed
Anamagh, Mirmeysam Rafiei
Bediz, Bekir
Ciğeroğlu, Ender
The purpose of the current study was to develop an accurate model to investigate the nonlinear resonances in an axially functionally graded beam rotating with time-dependent speed. To this end, two important features including stiffening and Coriolis effects are modeled based on nonlinear strain relations. Equations governing the axial, chordwise, and flapwise deformations about the determined steady-state equilibrium position are obtained, and the rotating speed variation is considered as a periodic disturbance about this equilibrium condition. Multi-mode discretization of the equations is performed via the spectral Chebyshev approach and the method of multiple scales for gyroscopic systems is employed to study the nonlinear behavior. After determining the required polynomial number based on convergence analysis, results obtained are verified by comparing to those found in literature and numerical simulations. Moreover, the model is validated based on simulations carried out by commercial finite element software. Properties of the functionally graded material and the values of average rotating speed leading to 2:1 internal resonance in the system are found. Time and steady-state responses of the system under primary and parametric resonances caused by the time-dependent rotating speed are investigated when the system is tuned to 2:1 internal resonance. A comprehensive study on the time response, frequency response, and stability behavior shows that the rotating axially functionally graded beam exhibits a complicated nonlinear behavior under the effect of the rotating speed fluctuation frequency, damping coefficient, and properties of the functionally graded material.
NONLINEAR DYNAMICS

Suggestions

Nonlinear 3D Modeling and Vibration Analysis of Horizontal Drum Type Washing Machines
Baykal, Cem; Ciğeroğlu, Ender; Yazıcıoğlu, Yiğit (2020-01-01)
In this study, a nonlinear 3-D mathematical model for horizontal drum type washing machines is developed considering rotating unbalance type excitation. Nonlinear differential equations of motion are converted into a set of nonlinear algebraic equations by using Harmonic Balance Method (HBM). The resulting nonlinear algebraic equations are solved by using Newton’s method with arc-length continuation. Several case studies are performed in order to observe the effects of orientation angles of springs and damp...
Nonlinear system identification and nonlinear experimental modal analysis by using response controlled stepped sine testing
Karaağaçlı, Taylan; Özgüven, Hasan Nevzat; Department of Mechanical Engineering (2020-12-24)
In this work, two novel nonlinear system identification methods are proposed in both the modal and spatial domains, respectively, based on response-controlled stepped-sine testing (RCT) where the displacement amplitude of the excitation point is kept constant throughout the frequency sweep. The proposed nonlinear modal identification method, which is also a nonlinear experimental modal analysis technique, applies to systems with several nonlinearities at different (and even unknown) locations (e.g. joint no...
Free vibration characteristics of a 3d mixed formulation beam element with force-based consistent mass matrix
Soydas, Ozan; Sarıtaş, Afşin (2017-09-01)
In this analytical study, free vibration analyses of a 3d mixed formulation beam element are performed by adopting force-based consistent mass matrix that incorporates shear and rotary inertia effects. The force-based approach takes into account the actual distribution of mass of an element in the derivation of the mass matrix. Moreover, the force-based approach enables accurate determination of free vibration frequencies of members with varying geometry and material distribution without any need for specif...
Nonlinear Vibrations of a Beam with a Breathing Edge Crack Using Multiple Trial Functions
Batihan, Ali C.; Ciğeroğlu, Ender (2016-01-28)
In this paper, a beam like structure with a single edge crack is modeled and analyzed in order to study the nonlinear effects of breathing crack on transverse vibrations of a beam. In literature, edge cracks are generally modeled as open cracks, in which the beam is separated into two pieces at the crack location and these pieces are connected to each other with a rotational spring to represent the effect of crack. The open edge crack model is a widely used assumption; however, it does not consider the nonl...
Nonlinear Structural Coupling: Experimental Application
Kalaycioglu, Taner; Özgüven, Hasan Nevzat (2014-02-06)
In this work, the nonlinear structural modification/coupling technique proposed recently by the authors is applied to a test system in order to study the applicability of the method to real structures. The technique is based on calculating the frequency response functions of a modified system from those of the original system and the dynamic stiffness matrix of the nonlinear modifying part. The modification can also be in the form of coupling a nonlinear system to the original system. The test system used i...
Citation Formats
S. Lotfan, M. R. Anamagh, B. Bediz, and E. Ciğeroğlu, “Nonlinear resonances of axially functionally graded beams rotating with varying speed including Coriolis effects,” NONLINEAR DYNAMICS, pp. 0–0, 2021, Accessed: 00, 2021. [Online]. Available: https://hdl.handle.net/11511/94863.