TY - GEN

T1 - Direct detection of nonlinear modal interactions and model updating using measured time series

AU - Moore, Keegan

AU - Kurt, Mehmet

AU - Eriten, Melih

AU - McFarland, D. Michael

AU - Bergman, Lawrence A.

AU - Vakakis, Alexander F

PY - 2019/1/1

Y1 - 2019/1/1

N2 - We describe a new method for identifying mechanical systems with strongly nonlinear attachments using measured transient response data. The procedure is motivated by the desire to quantify the degree of nonlinearity of a system, with the ultimate goal of updating a finite-element or other mathematical model to capture the nonlinear effects accurately. Our method relies on the proper orthogonal decomposition to extract proper orthogonal mode shapes (POMs), which are inherently energy dependent, directly from the measured transient response. Using known linear properties, the system’s frequencies are estimated using the Rayleigh quotient and an estimated frequency-energy plot (FEP) is created by them as functions of the system’s mechanical energy. The estimated FEP reveals distinct linear and nonlinear regimes which h are characterized by constant frequency (horizontal lines) and large frequency changes, respectively. The nonlinear regimes also contain spikes that connect different modes and indicate strongly nonlinear modal interactions. The nonlinearity is identified by plotting the estimated frequencies as functions of characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. We demonstrate the method on the response of a cantilevered, model airplane wing with a nonlinear energy sink attached at its free end.

AB - We describe a new method for identifying mechanical systems with strongly nonlinear attachments using measured transient response data. The procedure is motivated by the desire to quantify the degree of nonlinearity of a system, with the ultimate goal of updating a finite-element or other mathematical model to capture the nonlinear effects accurately. Our method relies on the proper orthogonal decomposition to extract proper orthogonal mode shapes (POMs), which are inherently energy dependent, directly from the measured transient response. Using known linear properties, the system’s frequencies are estimated using the Rayleigh quotient and an estimated frequency-energy plot (FEP) is created by them as functions of the system’s mechanical energy. The estimated FEP reveals distinct linear and nonlinear regimes which h are characterized by constant frequency (horizontal lines) and large frequency changes, respectively. The nonlinear regimes also contain spikes that connect different modes and indicate strongly nonlinear modal interactions. The nonlinearity is identified by plotting the estimated frequencies as functions of characteristic displacement and fitting a frequency equation based on the model of the nonlinearity. We demonstrate the method on the response of a cantilevered, model airplane wing with a nonlinear energy sink attached at its free end.

KW - Frequency-energy plot

KW - Nonlinear energy sink

KW - Nonlinear normal modes

KW - Nonlinear system identification

KW - Proper orthogonal decomposition

UR - http://www.scopus.com/inward/record.url?scp=85061144109&partnerID=8YFLogxK

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U2 - 10.1007/978-3-319-74280-9_3

DO - 10.1007/978-3-319-74280-9_3

M3 - Conference contribution

AN - SCOPUS:85061144109

SN - 9783319742793

T3 - Conference Proceedings of the Society for Experimental Mechanics Series

SP - 23

EP - 25

BT - Nonlinear Dynamics - Proceedings of the 36th IMAC, A Conference and Exposition on Structural Dynamics 2018

A2 - Kerschen, Gaetan

PB - Springer New York LLC

T2 - 36th IMAC, A Conference and Exposition on Structural Dynamics, 2018

Y2 - 12 February 2018 through 15 February 2018

ER -