Several popular time-frequency techniques,including the Wigner-Ville distribution,smoothed pseudo-Wigner-Ville distribution,wavelet transform,synchrosqueezing transform,Hilbert-Huang transform,and Gabor-Wigner transfo...Several popular time-frequency techniques,including the Wigner-Ville distribution,smoothed pseudo-Wigner-Ville distribution,wavelet transform,synchrosqueezing transform,Hilbert-Huang transform,and Gabor-Wigner transform,are investigated to determine how well they can identify damage to structures.In this work,a synchroextracting transform(SET)based on the short-time Fourier transform is proposed for estimating post-earthquake structural damage.The performance of SET for artificially generated signals and actual earthquake signals is examined with existing methods.Amongst other tested techniques,SET improves frequency resolution to a great extent by lowering the influence of smearing along the time-frequency plane.Hence,interpretation and readability with the proposed method are improved,and small changes in the time-varying frequency characteristics of the damaged buildings are easily detected through the SET method.展开更多
This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are ...This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.展开更多
In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the ...In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.展开更多
This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coeff...This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.展开更多
Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for ...Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.展开更多
When disturbed, the interaction between power grid and wind farm may cause serious sub/super-synchronous oscillation (SSO), affecting the security and stability of the system. It is therefore important to detect the t...When disturbed, the interaction between power grid and wind farm may cause serious sub/super-synchronous oscillation (SSO), affecting the security and stability of the system. It is therefore important to detect the time-varying amplitude and frequency of SSO to provide information for its control. The matching synchroextracting wavelet transform (MSEWT) is a new method proposed in this paper to serve this purpose. Based on the original synchrosqueezing wavelet transform, MSEWT uses a synchronous extraction operator to calculate the time-frequency coefficients and a chirp-rate estimation to modify the instantaneous frequency estimation. Thus, MSEWT can improve the concentration degree and reconstruction accuracy of the signal's time-frequency representation without iterative calculation, and can achieve superior noise robustness. After the time-frequency analysis and modal decomposition of the SSO by MSEWT, the amplitudes and frequencies of each oscillation component can be obtained by Hilbert transform (HT). The simulation studies demonstrate that the proposed scheme can accurately identify the modal parameters of SSO even in the case of noise interference, providing a reliable reference for stable operation of power system time-frequency.展开更多
文摘Several popular time-frequency techniques,including the Wigner-Ville distribution,smoothed pseudo-Wigner-Ville distribution,wavelet transform,synchrosqueezing transform,Hilbert-Huang transform,and Gabor-Wigner transform,are investigated to determine how well they can identify damage to structures.In this work,a synchroextracting transform(SET)based on the short-time Fourier transform is proposed for estimating post-earthquake structural damage.The performance of SET for artificially generated signals and actual earthquake signals is examined with existing methods.Amongst other tested techniques,SET improves frequency resolution to a great extent by lowering the influence of smearing along the time-frequency plane.Hence,interpretation and readability with the proposed method are improved,and small changes in the time-varying frequency characteristics of the damaged buildings are easily detected through the SET method.
文摘This paper is devoted to the study of the linearization problem of system of three second-order ordinary differential equations and . The necessary conditions for linearization by general point transformation and are found. The sufficient conditions for linearization by restricted class of point transformation and are obtained. Moreover, the procedure for obtaining the linearizing transformation is provided in explicit forms. Examples demonstrating the procedure of using the linearization theorems are presented.
文摘In this paper, we are concerned with the numerical solution of second-order partial differential equations. We analyse the use of the Sine Transform precondilioners for the solution of linear systems arising from the discretization of p.d.e. via the preconditioned conjugate gradient method. For the second-order partial differential equations with Dirichlel boundary conditions, we prove that the condition number of the preconditioned system is O(1) while the condition number of the original system is O(m 2) Here m is the number of interior gridpoints in each direction. Such condition number produces a linear convergence rale.
文摘This paper presents an analytical solution to the unsteady flow of the second-order non-Newtonian fluids by the use of intergral transformation method. Based on the numerical results, the effect of non-Newtonian coefficient Hc and other parameters on the flow are analysed. It is shown that the annular flow has a shorter characteristic time than the general pipe flow while the correspondent velocity, average velocity have a ... nailer value for a given Hc. Else, when radii ratio keeps unchanged, the shear stress of inner wall of annular flow will change with the inner radius -compared with the general pipe flow and is always smaller than that of the outer wall.
基金Project supported by the National Natural Science Foundation of China (No. 12272323)。
文摘Second-order axially moving systems are common models in the field of dynamics, such as axially moving strings, cables, and belts. In the traditional research work, it is difficult to obtain closed-form solutions for the forced vibration when the damping effect and the coupling effect of multiple second-order models are considered.In this paper, Green's function method based on the Laplace transform is used to obtain closed-form solutions for the forced vibration of second-order axially moving systems. By taking the axially moving damping string system and multi-string system connected by springs as examples, the detailed solution methods and the analytical Green's functions of these second-order systems are given. The mode functions and frequency equations are also obtained by the obtained Green's functions. The reliability and convenience of the results are verified by several examples. This paper provides a systematic analytical method for the dynamic analysis of second-order axially moving systems, and the obtained Green's functions are applicable to different second-order systems rather than just string systems. In addition, the work of this paper also has positive significance for the study on the forced vibration of high-order systems.
基金supported by National Natural Science Foundation of China(No.52077081)Guangdong Basic and Applied Basic Research Foundation(No.2022A1515011608).
文摘When disturbed, the interaction between power grid and wind farm may cause serious sub/super-synchronous oscillation (SSO), affecting the security and stability of the system. It is therefore important to detect the time-varying amplitude and frequency of SSO to provide information for its control. The matching synchroextracting wavelet transform (MSEWT) is a new method proposed in this paper to serve this purpose. Based on the original synchrosqueezing wavelet transform, MSEWT uses a synchronous extraction operator to calculate the time-frequency coefficients and a chirp-rate estimation to modify the instantaneous frequency estimation. Thus, MSEWT can improve the concentration degree and reconstruction accuracy of the signal's time-frequency representation without iterative calculation, and can achieve superior noise robustness. After the time-frequency analysis and modal decomposition of the SSO by MSEWT, the amplitudes and frequencies of each oscillation component can be obtained by Hilbert transform (HT). The simulation studies demonstrate that the proposed scheme can accurately identify the modal parameters of SSO even in the case of noise interference, providing a reliable reference for stable operation of power system time-frequency.
