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

1989 ◽  
Vol 56 (1) ◽  
pp. 149-154 ◽  
Author(s):  
T. M. Cameron ◽  
J. H. Griffin
Keyword(s):  
Steady State ◽  
Frequency Domain ◽  
Dynamic Systems ◽  
Time Domain ◽  
Nonlinear Dynamic ◽  
Nonlinear Dynamic Systems ◽  
System Response ◽  
Steady State Response ◽  
State Response ◽  
The Time Domain

A 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.

Sensitivity Analysis for the Steady-State Response of Damped Linear Elastodynamic Systems Subject to Periodic Loads

1990 ◽  
Author(s):  
Daniel A. Tortorelli
Keyword(s):  
Steady State ◽  
Vibration Amplitude ◽  
Equations Of Motion ◽  
Steady State Response ◽  
Analysis Techniques ◽  
Direct Differentiation ◽  
State Response ◽  
Need To Evaluate ◽  
The Time Domain ◽  
General Response

Abstract Adjoint and direct differentiation methods are used to formulate design sensitivities for the steady-state response of damped linear elastodynamic systems that are subject to periodic loads. Variations of a general response functional are expressed in explicit form with respect to design field perturbations. Modal analysis techniques which uncouple the equations of motion are used to perform the analyses. In this way, it is possible to obtain closed form relations for the sensitivity expressions. This eliminates the need to evaluate the adjoint response and psuedo response (these responses are associated with the adjoint and direct differentiation sensitivity problems) over the time domain. The sensitivities need not be numerically integrated over time, thus they are quickly computed. The methodology is valid for problems with proportional as well as non-proportional damping. In an example problem, sensitivities of steady-state vibration amplitude of a crankshaft subject to engine firing loads are evaluated with respect to the stiffness, inertial, and damping parameters which define the shaft. Both the adjoint and direct differentiation methods are used to compute the sensitivities. Finite difference sensitivity approximations are also calculated to validate the explicit sensitivity results.

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