TY - JOUR

T1 - An iteration-free approach to excitation harmonization

AU - Hippold, Patrick

AU - Kleyman, Gleb

AU - Woiwode, Lukas

AU - Wei, Tong

AU - Müller, Florian

AU - Schwingshackl, Christoph

AU - Scheel, Maren

AU - Tatzko, Sebastian

AU - Krack, Malte

N1 - Publisher Copyright: © 2025 The Authors

PY - 2025/4/26

Y1 - 2025/4/26

N2 - Sinusoidal excitation is particularly popular for testing structures in the nonlinear regime. Due to the nonlinear behavior and the inevitable feedback of the structure on the exciter, higher harmonics in the applied excitation are generated. This is undesired, because the acquired response may deviate substantially from that of the structure under purely sinusoidal excitation, in particular if one of the higher harmonics engages into resonance. We present a new approach to suppress those higher excitation harmonics and thus the unwanted exciter-structure interaction: Higher harmonics are added to the voltage input to the shaker whose Fourier coefficients are adjusted via feedback control until the excitation is purely sinusoidal. The stability of this method is analyzed for a simplified model; the resulting closed-form expressions are useful, among others, to select an appropriate exciter configuration, including the drive point. A practical, model-free procedure for the control design is suggested. The proposed method is validated in virtual and physical experiments of internally resonant structures, in the two common configurations of force excitation via a stinger and base excitation. Excellent performance is achieved when simply using the same control gains for all harmonics, throughout the tested range of amplitudes and frequencies, even in the strongly nonlinear regime. Compared to the iterative state of the art, it is found that the proposed method is simpler to implement, enables faster testing and it is easy to achieve a lower harmonic distortion.

AB - Sinusoidal excitation is particularly popular for testing structures in the nonlinear regime. Due to the nonlinear behavior and the inevitable feedback of the structure on the exciter, higher harmonics in the applied excitation are generated. This is undesired, because the acquired response may deviate substantially from that of the structure under purely sinusoidal excitation, in particular if one of the higher harmonics engages into resonance. We present a new approach to suppress those higher excitation harmonics and thus the unwanted exciter-structure interaction: Higher harmonics are added to the voltage input to the shaker whose Fourier coefficients are adjusted via feedback control until the excitation is purely sinusoidal. The stability of this method is analyzed for a simplified model; the resulting closed-form expressions are useful, among others, to select an appropriate exciter configuration, including the drive point. A practical, model-free procedure for the control design is suggested. The proposed method is validated in virtual and physical experiments of internally resonant structures, in the two common configurations of force excitation via a stinger and base excitation. Excellent performance is achieved when simply using the same control gains for all harmonics, throughout the tested range of amplitudes and frequencies, even in the strongly nonlinear regime. Compared to the iterative state of the art, it is found that the proposed method is simpler to implement, enables faster testing and it is easy to achieve a lower harmonic distortion.

KW - Frequency response

KW - Harmonic distortion

KW - Modal interaction

KW - Shaker-structure interaction

KW - Stepped sine testing

UR - http://www.scopus.com/inward/record.url?scp=105003556635&partnerID=8YFLogxK

U2 - 10.1016/j.ymssp.2025.112732

DO - 10.1016/j.ymssp.2025.112732

M3 - Article

AN - SCOPUS:105003556635

VL - 233

JO - Mechanical Systems and Signal Processing

JF - Mechanical Systems and Signal Processing

SN - 0888-3270

M1 - 112732

ER -