Advances in Engineering Advances in Engineering features breaking research judged by Advances in Engineering advisory team to be of key importance in the Engineering field. Papers are selected from over 10,000 published each week from most peer reviewed journals.
Significance
Most structural systems are subjected typically to stochastic excitations exhibiting strong variations both in the frequency and the time domains. In this regard, it is important to develop efficient and robust joint time-frequency analysis techniques for determining accurately the time-varying frequency content of the system response. In the past few decades, various standard concepts from random vibration theory have been generalized based on wavelets for practical applications. These wavelet-based techniques have been successfully used to address a wide range of problems, including evolutionary power spectrum (EPS) estimation, damage detection, system response analysis and system identification.
Among the known wavelet families, the generalized harmonic wavelets (GHWs) have emerged as an efficacious basis for expanding system excitation and response processes. This yields a system of algebraic equations to be solved for determining the associated wavelet coefficients and for evaluating the response process EPS. GHWs possess additional coefficients for decoupling and enhancing the resolution of the wavelet analysis in the frequency domain, making it an indispensable tool for structural dynamics applications.
Most recently, a new GHW-based input-output relationship has been developed to determine the response EPS of linear systems. This novel relationship not only avoided the common local stationarity assumption inherent in most early developments, but also improved the accuracy of the system response EPS estimate. This was achieved by obtaining in closed form the wavelet interaction coefficients at different scales and translation levels, and by employing periodized GHWs to address the non-orthogonality of the GHW basis on a finite time interval. Due to these benefits, this approach has been extended to different nonlinear systems.
Herein, PhD candidate George Pasparakis, Dr. Vasileios Fragkoulis and Professor Michael Beer from Leibniz Universität Hannover in collaboration with Professor Ioannis Kougioumtzoglou from Columbia University and Professor Fan Kong from Wuhan University of Technology further extended this novel technique to account for multi-degree-of-freedom (MDOF) linear structural systems with singular parameter matrices. An excitation-response relationship for such systems was derived based on periodized generalized harmonic wavelets for determining system response statistics in the joint time–frequency domain. To determine the response wavelet coefficients, a linear system of algebraic equations was derived and solved by employing the Moore–Penrose matrix inverse concept. Their work is published in the journal, Mechanical Systems and Signal Processing.
The authors demonstrated the effectiveness of the derived excitation-response relationships in determining the system response statistics in the joint time-frequency domain in a direct and straightforward manner. The proposed technique could be interpreted as a generalization of previous efforts found in the literature to account for the presence of singular parameter matrices in the governing equations of motion. Further, this technique overcomes the strong local stationarity assumption that limited the accuracy degree and application scope of the previously developed techniques.
In summary, the research team developed a new periodized GHWs-based technique for determining the joint time-frequency response of linear systems with singular parameter matrices. The derivation of the input-output relationships in the wavelet domain proved effective for accurately determining the EPS matrix of the system response. The reliability of this technique was validated by comparing the analytical results with pertinent Monte Carlo simulation data. This was accomplished by considering diverse numerical examples, such as energy harvesters whose dynamics are governed by coupled electromechanical equations. In a joint statement to Advances in Engineering, the authors explained their findings provide valuable insights for improving the performance of structural systems.
Reference
Pasparakis, G., Kougioumtzoglou, I. A., Fragkoulis, V. C., Kong, F., & Beer, M. (2022). Excitation–response relationships for linear structural systems with singular parameter matrices: A periodized harmonic wavelet perspective. Mechanical Systems and Signal Processing, 169, 108701.
