Baijie Qiao

A Novel Method for Force Identification Based on the Discrete Cosine Transform

Force identification is a classical inverse problem in which the measured data and the mathematical models of mechanical structures are used to determine the applied force. However, the identified force may seriously diverge from the true solution due to the unknown noise contaminating the measured data and the inverse of the ill-posed transfer matrix characterizing the mechanical structure. In this paper, a novel method based on the discrete cosine transform (DCT) in the time domain is proposed for force identification, which overcomes the deficiency of the ill-posedness of the transfer matrix. The unknown force is expanded by a set of cosine basis functions and then the original governing equation is reformulated to find the coefficient of each cosine basis function. Furthermore, a modified generalized cross-validation (GCV) criterion for determining the regularization parameter is developed for the truncated singular value decomposition (TSVD), Chebyshev polynomial and DCT solutions. Numerical simulation reveals that compared with the L-curve criterion, the modified GCV criterion is quite robust in the presence of noise. Finally, a clamped-free shell structure that is excited by an impact hammer is selected as an example to validate the performance of the proposed method. Experimental results demonstrate that compared with the TSVD-based and Chebyshev-based methods, the DCT-based method combined with the modified GCV criterion can reconstruct the force time history and identify the peak of impact force with high accuracy. Additionally, the identification of force location using the DCT-based method is also discussed.

Hermitian plane wavelet finite element method: Wave propagation and load identification

Abstract The two-dimensional Hermitian interpolation wavelet is constructed by using the tensor product of the modified Hermitian wavelets expanded at each coordinate. Then the two-dimensional Hermitian interpolation wavelet is substituted into finite element formulations to address the wave propagation and load identification problems. Hermitian wavelet finite element can be used to describe the wave propagation and to reveal the rule of the wave propagation in plane. The wave propagation response is used to solve the load identification inverse problem. Results show that the identified load value is similar to the applied load when the location of the response node is close to the applied load position. The proposed method can accurately identify the location, waveform and amplitude of the applied load.

Hermitian Mindlin Plate Wavelet Finite Element Method for Load Identification

A new Hermitian Mindlin plate wavelet element is proposed. The two-dimensional Hermitian cubic spline interpolation wavelet is substituted into finite element functions to construct frequency response function (FRF). It uses a system’s FRF and response spectrums to calculate load spectrums and then derives loads in the time domain via the inverse fast Fourier transform. By simulating different excitation cases, Hermitian cubic spline wavelets on the interval (HCSWI) finite elements are used to reverse load identification in the Mindlin plate. The singular value decomposition (SVD) method is adopted to solve the ill-posed inverse problem. Compared with ANSYS results, HCSWI Mindlin plate element can accurately identify the applied load. Numerical results show that the algorithm of HCSWI Mindlin plate element is effective. The accuracy of HCSWI can be verified by comparing the FRF of HCSWI and ANSYS elements with the experiment data. The experiment proves that the load identification of HCSWI Mindlin plate is effective and precise by using the FRF and response spectrums to calculate the loads.

Multi-objective active vibration optimization of dynamic frequency responses for shell structures

Vibration is the main factor influencing the stable operation of mechanical equipment. Malfunction in large mechanical equipment is always attributed to excessive vibration. Active control plays a key role in vibration optimization and secures the safe operation of mechanical equipment. However, the current active control methods mainly focus on optimization of local vibration characteristics. Few studies deal with multi-point and multi-objective active control of the equipment. Therefore, based on the neural network algorithm, a multi-objective active vibration control method (MACM) is constructed to achieve the multi-objective active control of frequency responses for shell structures and guarantee the steady operation of mechanical equipment.