A macroscopic frost heave model with more clear parameters was established. Based on a porosity rate frost heave model and segregation potential theory, a porosity rate function was deduced and introduced into the str...A macroscopic frost heave model with more clear parameters was established. Based on a porosity rate frost heave model and segregation potential theory, a porosity rate function was deduced and introduced into the stress-strain relationship. Numerical simulation was conducted and verified by frost heave tests. Results show that the porosity rate within the frozen fringe is proportional to the square of temperature gradient and current porosity, and is also proportional to the exponential function of applied pressure. The relative errors between the calculated and measured results of frost depth and frost heave are within 3% and 15% respectively, demonstrating that the temperature gradient, applied pressure and current porosity are the main influencing factors, while temperature is just the constraint of frozen fringe. The improved model have meaningful and accessible parameters, which can be used in engineering with good accuracy.展开更多
The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays expo...The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.展开更多
This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that...This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.展开更多
In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and ...In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.展开更多
The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-E...The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.展开更多
基金Supported by National Natural Science Foundation of China (No. 40571032)Open Research Fund Program of State Key Laboratory for Geomechanics and Deep Underground Engineering (SKLGDUE 08001X)
文摘A macroscopic frost heave model with more clear parameters was established. Based on a porosity rate frost heave model and segregation potential theory, a porosity rate function was deduced and introduced into the stress-strain relationship. Numerical simulation was conducted and verified by frost heave tests. Results show that the porosity rate within the frozen fringe is proportional to the square of temperature gradient and current porosity, and is also proportional to the exponential function of applied pressure. The relative errors between the calculated and measured results of frost depth and frost heave are within 3% and 15% respectively, demonstrating that the temperature gradient, applied pressure and current porosity are the main influencing factors, while temperature is just the constraint of frozen fringe. The improved model have meaningful and accessible parameters, which can be used in engineering with good accuracy.
基金Project supported by the National Natural Science Foundation of China(No.60174008).
文摘The wave equation with variable coefficients with a nonlinear dissipative boundary feedbackis studied. By the Riemannian geometry method and the multiplier technique, it is shown thatthe closed loop system decays exponentially or asymptotically, and hence the relation betweenthe decay rate of the system energy and the nonlinearity behavior of the feedback function isestablished.
基金Project supported by the National Natural Science Foundation of China (No.60334040, No.60225003).
文摘This paper considers the exponential decay of the solution to a damped semilinear wave equation with variable coefficients in the principal part by Riemannian multiplier method. A differential geometric condition that ensures the exponential decay is obtained.
文摘In this paper,we consider a multi-state device redundant systems with common-cause failures and one standby unit. We proved C0-semigroup generated by the system operator is quasi-compact by analyzing its spectrum and estimating essential growth bound semi-group generated by this system, 0 is an isolated eigenvalue with algebra multiply one. Moreover, we prove it is also irreducible. So we obtain the time-dependent solution exponentially converges to the steady-state solution.
文摘The probabilistic solutions to some nonlinear stochastic dynamic (NSD) systems with various polynomial types of nonlinearities in displacements are analyzed with the subspace-exponential polynomial closure (subspace-EPC) method. The space of the state variables of the large-scale nonlinear stochastic dynamic system excited by Gaussian white noises is separated into two subspaces. Both sides of the Fokker-Planck-Kolmogorov (FPK) equation corresponding to the NSD system are then integrated over one of the subspaces. The FPK equation for the joint probability density function of the state variables in the other subspace is formulated. Therefore, the FPK equations in low dimensions are obtained from the original FPK equation in high dimensions and the FPK equations in low dimensions are solvable with the exponential polynomial closure method. Examples about multi-degree-offreedom NSD systems with various polynomial types of nonlinearities in displacements are given to show the effectiveness of the subspace-EPC method in these cases.
