The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resona...The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.展开更多
Rheological experiments under steady and oscillatory shear were conducted for fumed silica suspen- sions in polyethylene glycol. Under steady shear the shear-thinning and thickening response were exhibited and the flo...Rheological experiments under steady and oscillatory shear were conducted for fumed silica suspen- sions in polyethylene glycol. Under steady shear the shear-thinning and thickening response were exhibited and the flow exponent N was determined. With the increase of concentration the flow exponent N showed a rapid increase, and it increased dramatically when the discontinuous shear-thickening took place. Oscillatory shear experiments were conducted at constant frequency and constant amplitude strain, respectively. The shear-thinning and the discontinuous shear-thickening behavior were observed under different constant frequencies from 10 to 80 rad/s. The correlation between complex modulus (G*) and sweep frequency (ω) was illuminated at γ =750%. It was found that the correlation between G* and ω could be fitted by equation: G*∝ωn. The indexes in shear-thinning region and shear-thickening were determined. The indexes were similar to some extent at shear-thinning region and increased dramati- cally to a much higher value when the shear-thickening occurred,especially at higher weight fractions. The behaviors can be qualitatively explained as follows: the shear-thinning owes to decrease of viscos- ity, which results from disruption of the aggregates; the cluster theory attributes the shear-thickening to the formation of metastable, flow induced clusters, which block the system.展开更多
In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The...In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The main advantage of the proposed analysis is that even though the transfer function model of a PWM push-pull DC-DC converter is perturbed, the complete analysis has been done on a linear transfer function model of a PWM push-pull DC-DC converter. The proposed analysis is verified using MATLAB simulation. This analysis will be very much useful to power electronics engineers, since the technique is very simple and computationally efficient and easily applicable in precise applications such as aerospace applications.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 12072118)the Natural Science Funds for Distinguished Young Scholar of the Fujian Province, China (Grant No. 2021J06024)the Project for Youth Innovation Fund of Xiamen, China (Grant No. 3502Z20206005)。
文摘The majority of nonlinear stochastic systems can be expressed as the quasi-Hamiltonian systems in science and engineering. Moreover, the corresponding Hamiltonian system offers two concepts of integrability and resonance that can fully describe the global relationship among the degrees-of-freedom(DOFs) of the system. In this work, an effective and promising approximate semi-analytical method is proposed for the steady-state response of multi-dimensional quasi-Hamiltonian systems. To be specific, the trial solution of the reduced Fokker–Plank–Kolmogorov(FPK) equation is obtained by using radial basis function(RBF) neural networks. Then, the residual generated by substituting the trial solution into the reduced FPK equation is considered, and a loss function is constructed by combining random sampling technique. The unknown weight coefficients are optimized by minimizing the loss function through the Lagrange multiplier method. Moreover, an efficient sampling strategy is employed to promote the implementation of algorithms. Finally, two numerical examples are studied in detail, and all the semi-analytical solutions are compared with Monte Carlo simulations(MCS) results. The results indicate that the complex nonlinear dynamic features of the system response can be captured through the proposed scheme accurately.
基金Supported by the National Natural Science Foundation of China (Grant No. 50774096, 50604017)
文摘Rheological experiments under steady and oscillatory shear were conducted for fumed silica suspen- sions in polyethylene glycol. Under steady shear the shear-thinning and thickening response were exhibited and the flow exponent N was determined. With the increase of concentration the flow exponent N showed a rapid increase, and it increased dramatically when the discontinuous shear-thickening took place. Oscillatory shear experiments were conducted at constant frequency and constant amplitude strain, respectively. The shear-thinning and the discontinuous shear-thickening behavior were observed under different constant frequencies from 10 to 80 rad/s. The correlation between complex modulus (G*) and sweep frequency (ω) was illuminated at γ =750%. It was found that the correlation between G* and ω could be fitted by equation: G*∝ωn. The indexes in shear-thinning region and shear-thickening were determined. The indexes were similar to some extent at shear-thinning region and increased dramati- cally to a much higher value when the shear-thickening occurred,especially at higher weight fractions. The behaviors can be qualitatively explained as follows: the shear-thinning owes to decrease of viscos- ity, which results from disruption of the aggregates; the cluster theory attributes the shear-thickening to the formation of metastable, flow induced clusters, which block the system.
文摘In this paper, an analytical technique is presented for time domain analysis （transient and steady-state response） of perturbed PWM push-pull DC-DC converter using interesting corollary on Kharitonov＇s theorem. The main advantage of the proposed analysis is that even though the transfer function model of a PWM push-pull DC-DC converter is perturbed, the complete analysis has been done on a linear transfer function model of a PWM push-pull DC-DC converter. The proposed analysis is verified using MATLAB simulation. This analysis will be very much useful to power electronics engineers, since the technique is very simple and computationally efficient and easily applicable in precise applications such as aerospace applications.
