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Purpose This paper aims to present an approach for calibrating the numerical models of dynamical systems that have spatially localized nonlinear components. The approach implements the extended constitutive relation error (ECRE) method using multi-harmonic coefficients and is conceived to separate the errors in the representation of the global, linear and local, nonlinear components of the dynamical system through a two-step process. Design/methodology/approach The first step focuses on the system’s predominantly linear dynamic response under a low magnitude periodic excitation. In this step, the discrepancy between measured and predicted multi-harmonic coefficients is calculated in terms of residual energy. This residual energy is in turn used to spatially locate errors in the model, through which one can identify the erroneous model inputs which govern the linear behavior that need to be calibrated. The second step involves measuring the system’s nonlinear dynamic response under a high magnitude periodic excitation. In this step, the response measurements under both low and high magnitude excitation are used to iteratively calibrate the identified linear and nonlinear input parameters. Findings When model error is present in both linear and nonlinear components, the proposed iterative combined multi-harmonic balance method (MHB)-ECRE calibration approach has shown superiority to the conventional MHB-ECRE method, while providing more reliable calibration results of the nonlinear parameter with less dependency on a priori knowledge of the associated linear system. Originality/value This two-step process is advantageous as it reduces the confounding effects of the uncertain model parameters associated with the linear and locally nonlinear components of the system.
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Smart Automatic Modal Hammer: Predictor–Corrector Approach for Accurate Excitation of Dynamical Systems
Purpose This research introduces an innovative solution that revolutionizes the study of linear and nonlinear dynamical systems—a smart automatic modal hammer. With its affordability and intelligent capabilities, this automatic modal hammer becomes an invaluable tool for research and industry, enabling repeatable strikes with precise force control. This system's significance becomes particularly evident when studying nonlinear systems, which heavily rely on the excitation level for their dynamics. By offering a cost-effective design this proposed system proves to be robust in accelerating research on nonlinear dynamics, providing researchers with an efficient and accessible means to delve deeper into these complex systems. Methods The proposed design integrates a commercial modal hammer, commonly used in modal testing, and a stepper motor. This stepper motor is enhanced with an encoder and servo driver, all expertly controlled by a Raspberry Pi. Results What sets this system apart is its clever utilization of regression models to acquire knowledge of the intrinsic relationship between the applied force and hammer velocity precisely during the impact. This acquired knowledge is the foundation for controlling the motor's behavior, ensuring consistent and accurate excitation of the structure with the desired force. Conclusion The capabilities of the proposed automatic modal hammer are demonstrated using a linear two-story tower and a model airplane wing with a nonlinear vibration absorber.
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- Award ID(s):
- 2237715
- PAR ID:
- 10531725
- Publisher / Repository:
- Journal of Vibration Engineering & Technologies
- Date Published:
- Journal Name:
- Journal of Vibration Engineering & Technologies
- ISSN:
- 2523-3920
- Subject(s) / Keyword(s):
- Automatic modal hammer Modal analysis Nonlinear dynamics
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s42417-024-01461-6
