An Alternating Frequency/Time Domain Method for Calculating the Steady-State Response of Nonlinear Dynamic Systems

Abstract

International audienceA method is proposed for analyzing the steady-state response of nonlinear dynamic systems. The method iterates to obtain the discrete Fourier transform of the system response, returning to the time domain at each iteration to take advantage of the ease in evaluating nonlinearities there-rather than analytically describing the nonlinear terms in the frequency domain. The updated estimates of the nonlinear terms are transformed back into the frequency domain in order to continue iterating on the frequency spectrum of the steady-state response. The method is demonstrated by solving a problem with friction damping in which the excitation has multiple discrete frequencies

Optimization of nonlinear structural resonance using the incremental harmonic balance method

“…where G is defined in equation (12). Then the average value of the axial strain in one beam element is constant as…”

“…Chen et al combined the IHB and finite element methods to analyze nonlinear vibrations of plane structures [8] whereas Lewandowski presented a general formulation for computing steady-state vibrations of geometrically nonlinear structures by using a harmonic balance and finite element method [9,10,11]. The classical IHB method is suitable for structural vibration with polynomial nonlinearity, whereas for structural vibration with a more complex nonlinearity, the alternating frequency/time (AFT) domain method proposed by Cameron [12] is widely used. The AFT method takes advantage of the convenience of evaluating nonlinear terms in the time domain.…”

Nonlinear Forced Response of a Stator Vane With Multiple Friction Contacts Using a Coupled Static/Dynamic Approach

“…For this reason the normal relative static displacement v 0 (interference) is the necessary value to calculate the normal load of the contact model. [15,16] also known as Hybrid Frequency Time (HFT) method [17] should be used in order to pass from the frequency domain to the time domain to calculate the hysteresis loop and then again to go back to the frequency domain by the Fourier series: The calculation procedure follows the following steps:…”

Qualitative analysis of forced response of blisks with friction ring dampers

“…To overcome this problem when more harmonics are considered, the use of an Alternating Frequency Time method (e.g. Cameron and Griffin, 1989) can be a solution. This method will be detailed in the next section.…”