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1.	Chen, Yousheng, 1985-, et al. (author) Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods 2014 In: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 9783319045221 - 9783319045221 ; 2, s. 35-44 Conference paper (peer-reviewed)abstract Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.

Chen, Yousheng, 1985-, et al. (author)
Frequency Response Calculations of a Nonlinear Structure a Comparison of Numerical Methods
2014
In: Nonlinear Dynamics, Volume 2. - Cham : Springer. - 9783319045221 - 9783319045221 ; 2, s. 35-44
Conference paper (peer-reviewed)abstract
- Mechanical systems having presence of nonlinearities are often represented by nonlinear ordinary differential 5 equations. For most of such equations, exact analytic solutions are not found; thus numerical techniques have to be used. 6 In many applications, among which model calibration can be one, steady-state frequency response functions are the desired 7 quantities to calculate. 8 The objective of this paper is to compare the performance of computations of nonlinear frequency response functions 9 (FRFs) calculated directly within the frequency domain, using the Multi-Harmonic Balance method, with the time-domain 10 methods Runge–Kutta, Newmark and Pseudo Force in State Space (PFSS). The PFSS method is a recently developed state- 11 space based force feedback method that is shown to give efficient solutions. 12 The accuracy and efficiency of the methods are studied and compared using a model of a cantilever beam connected to a 13 non-linear spring at its free end.

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