In this paper,we consider the model updating problem of the undamped vibroacoustic system with no spill-over(MUP-UVA),which is to update the original system to a new system such that some“unstable”eigenvalues are re...In this paper,we consider the model updating problem of the undamped vibroacoustic system with no spill-over(MUP-UVA),which is to update the original system to a new system such that some“unstable”eigenvalues are replaced by some newly measured ones.Based on the spectral decomposition of the undamped vibroacoustic system,a necessary and sufficient condition is derived such that the updated system can preserve no spill-over,and a set of parametric solutions of MUP-UVA is characterized.Furthermore,a gradient optimization algorithm for the minimum norm solution of MUP-UVA is proposed and the performance of the algorithm is illustrated by several numerical experiments.展开更多
In this paper, a boundary feedback system of a class of non-uniform undamped Timoshenko beam with both ends free is considered. A linearized three-level difference scheme for the Timoshenko beam equations is derived b...In this paper, a boundary feedback system of a class of non-uniform undamped Timoshenko beam with both ends free is considered. A linearized three-level difference scheme for the Timoshenko beam equations is derived by the method of reduction of order on uniform meshes. The unique solvability, unconditional stability and convergence of the difference scheme are proved by the discrete energy method. The convergence order in maximum norm is of order two in both space and time. The validity of this theoretical analysis is verified experimentally.展开更多
The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is deri...The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.展开更多
In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for ...In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.展开更多
A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback.By the method,the required...A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback.By the method,the required displacement and acceleration output feedback gain matrices are determined,and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found.The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions.The numerical example shows that the proposed method is reliable and attractive.展开更多
In the synthesis of the control algorithm for complex systems, we are often faced with imprecise or unknown mathematical models of the dynamical systems, or even with problems in finding a mathematical model of the sy...In the synthesis of the control algorithm for complex systems, we are often faced with imprecise or unknown mathematical models of the dynamical systems, or even with problems in finding a mathematical model of the system in the open loop. To tackle these difficulties, an approach of data-driven model identification and control algorithm design based on the maximum stability degree criterion is proposed in this paper. The data-driven model identification procedure supposes the finding of the mathematical model of the system based on the undamped transient response of the closed-loop system. The system is approximated with the inertial model, where the coefficients are calculated based on the values of the critical transfer coefficient, oscillation amplitude and period of the underdamped response of the closed-loop system. The data driven control design supposes that the tuning parameters of the controller are calculated based on the parameters obtained from the previous step of system identification and there are presented the expressions for the calculation of the tuning parameters. The obtained results of data-driven model identification and algorithm for synthesis the controller were verified by computer simulation.展开更多
Ultracold atoms with cavity-mediated long-range interactions offer a promising platform for exploring emergent quantum phenomena.Building on recent experimental progress,we propose a novel scheme to create supersolid ...Ultracold atoms with cavity-mediated long-range interactions offer a promising platform for exploring emergent quantum phenomena.Building on recent experimental progress,we propose a novel scheme to create supersolid square and plane wave phases in spin-1/2 condensates.We demonstrate that the self-ordered supersolid phase supports an undamped gapless Goldstone mode across a broad parameter regime.This proposal is comprehensively described by the two-component Tavis–Cummings model with hosting a U(1)symmetry.By exploiting the superradiant photon-exchange process,our approach also constructs the cavity-mediated spin-momentummixing interactions between highly correlated spin and momentum modes,which may open avenues for exploring spin-momentum squeezing and spatially distributed multipartite entanglement.展开更多
基金supported by the Research Foundation of Education Department of Hunan Province(Grant No.23A0266)Hunan Provincial Natural Science Foundation(Grand No.2025JJ50034)Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering(Grant No.2017TP1017).
文摘In this paper,we consider the model updating problem of the undamped vibroacoustic system with no spill-over(MUP-UVA),which is to update the original system to a new system such that some“unstable”eigenvalues are replaced by some newly measured ones.Based on the spectral decomposition of the undamped vibroacoustic system,a necessary and sufficient condition is derived such that the updated system can preserve no spill-over,and a set of parametric solutions of MUP-UVA is characterized.Furthermore,a gradient optimization algorithm for the minimum norm solution of MUP-UVA is proposed and the performance of the algorithm is illustrated by several numerical experiments.
基金Supported by Shandong Provincial Natural Science Foundation (No.ZR2009AL012)
文摘In this paper, a boundary feedback system of a class of non-uniform undamped Timoshenko beam with both ends free is considered. A linearized three-level difference scheme for the Timoshenko beam equations is derived by the method of reduction of order on uniform meshes. The unique solvability, unconditional stability and convergence of the difference scheme are proved by the discrete energy method. The convergence order in maximum norm is of order two in both space and time. The validity of this theoretical analysis is verified experimentally.
文摘The chaotic phenomena of subharmonic resonant waves in undamped and damped strings are investigated in this paper. The model consistS of a constant-tension, stretched string whose partial differential equation is derived by taking into account its exact configuration. Simplification via a Taylor series expansion of the curvature term and then employing the Galerkin method, an ordinary differential equation for the nonlinear dyamics is obtained. For the undamped case, we can formulate the Hamiltonian energy form of the conservative string, under the influence of an external periodic excitation. This permits the subharmonic resonant condition for this system to be derived. We truncate the resulting infinite number of subharmonic resonant waves to just two waves by renormalizing the Hamiltonian energy function near the subharmonic resonant orbit of the system. Adopting the renormalization group technique for the nit6raction of the two subharmonic resonant waves, an approximate chaotic condition associated with the subharmonic resonance of this system is determined. For the case fo the damped string, the minimum condition for the bifurcation of the subharmonic resonant wave is computed using the incremental energy balance method. For model verification, we carried out numerical simulations and they show good agreement with our analytical results.
基金Taif University Researchers Supporting Project number(TURSP-2020/275),Taif University,Taif,Saudi Arabia.
文摘In this paper,a new approach is devoted to find novel analytical and approximate solutions to the damped quadratic nonlinear Helmholtz equation(HE)in terms of the Weiersrtrass elliptic function.The exact solution for undamped HE(integrable case)and approximate/semi-analytical solution to the damped HE(non-integrable case)are given for any arbitrary initial conditions.As a special case,the necessary and sufficient condition for the integrability of the damped HE using an elementary approach is reported.In general,a new ansatz is suggested to find a semi-analytical solution to the non-integrable case in the form of Weierstrass elliptic function.In addition,the relation between the Weierstrass and Jacobian elliptic functions solutions to the integrable case will be derived in details.Also,we will make a comparison between the semi-analytical solution and the approximate numerical solutions via using Runge-Kutta fourth-order method,finite difference method,and homotopy perturbation method for the first-two approximations.Furthermore,the maximum distance errors between the approximate/semi-analytical solution and the approximate numerical solutions will be estimated.As real applications,the obtained solutions will be devoted to describe the characteristics behavior of the oscillations in RLC series circuits and in various plasma models such as electronegative complex plasma model.
文摘A novel numerical method is presented to update mass and stiffness matrices simultaneously with measured vibration data by means of the combined acceleration and displacement output feedback.By the method,the required displacement and acceleration output feedback gain matrices are determined,and thus the optimal approximation mass matrix and stiffness matrix which satisfy the required orthogonality relation and eigenvalue equation are found.The proposed method is computationally efficient and the updated mass and stiffness matrices are also symmetric and have the compact expressions.The numerical example shows that the proposed method is reliable and attractive.
文摘In the synthesis of the control algorithm for complex systems, we are often faced with imprecise or unknown mathematical models of the dynamical systems, or even with problems in finding a mathematical model of the system in the open loop. To tackle these difficulties, an approach of data-driven model identification and control algorithm design based on the maximum stability degree criterion is proposed in this paper. The data-driven model identification procedure supposes the finding of the mathematical model of the system based on the undamped transient response of the closed-loop system. The system is approximated with the inertial model, where the coefficients are calculated based on the values of the critical transfer coefficient, oscillation amplitude and period of the underdamped response of the closed-loop system. The data driven control design supposes that the tuning parameters of the controller are calculated based on the parameters obtained from the previous step of system identification and there are presented the expressions for the calculation of the tuning parameters. The obtained results of data-driven model identification and algorithm for synthesis the controller were verified by computer simulation.
基金National Natural Science Foundation of China(12274473,12135018)National Key Research and Development Program of China(2021YFA0718304)+1 种基金Strategic Priority Research Program of CAS(XDB28000000)Fundamental Research Funds for the Central Universities(24qnpy120)。
文摘Ultracold atoms with cavity-mediated long-range interactions offer a promising platform for exploring emergent quantum phenomena.Building on recent experimental progress,we propose a novel scheme to create supersolid square and plane wave phases in spin-1/2 condensates.We demonstrate that the self-ordered supersolid phase supports an undamped gapless Goldstone mode across a broad parameter regime.This proposal is comprehensively described by the two-component Tavis–Cummings model with hosting a U(1)symmetry.By exploiting the superradiant photon-exchange process,our approach also constructs the cavity-mediated spin-momentummixing interactions between highly correlated spin and momentum modes,which may open avenues for exploring spin-momentum squeezing and spatially distributed multipartite entanglement.
