In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetri...In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.展开更多
In this paper, the eigenvalue problem with multiple uncertain parameters is analyzed by the sparse grid stochastic collocation method. This method provides an interpolation approach to approximate eigenvalues and eige...In this paper, the eigenvalue problem with multiple uncertain parameters is analyzed by the sparse grid stochastic collocation method. This method provides an interpolation approach to approximate eigenvalues and eigenvectors＇ functional dependencies on uncertain parame- ters. This method repetitively evaluates the deterministic solutions at the pre-selected nodal set to construct a high- dimensional interpolation formula of the result. Taking advantage of the smoothness of the solution in the uncer- tain space, the sparse grid collocation method can achieve a high order accuracy with a small nodal set. Compared with other sampling based methods, this method converges fast with the increase of the number of points. Some numerical examples with different dimensions are presented to demon- strate the accuracy and efficiency of the sparse grid stochastic collocation method.展开更多
基金supported by the EPSRC (UK)the National Science Fund for Distinguished Young Scholars (11125209)the National Natural Science Foundation of China (10902068 and 51121063)
文摘In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom （MDOF） structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force trans- missibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.
基金supported by the National Nature Science Foundation of China for Distinguished Young Scholars(Grant11125209)the National Nature Science Foundation of China(Grants11322215,51121063)the Scientifi Research Foundation for the Returned Overseas Chinese Scholars
文摘In this paper, the eigenvalue problem with multiple uncertain parameters is analyzed by the sparse grid stochastic collocation method. This method provides an interpolation approach to approximate eigenvalues and eigenvectors＇ functional dependencies on uncertain parame- ters. This method repetitively evaluates the deterministic solutions at the pre-selected nodal set to construct a high- dimensional interpolation formula of the result. Taking advantage of the smoothness of the solution in the uncer- tain space, the sparse grid collocation method can achieve a high order accuracy with a small nodal set. Compared with other sampling based methods, this method converges fast with the increase of the number of points. Some numerical examples with different dimensions are presented to demon- strate the accuracy and efficiency of the sparse grid stochastic collocation method.
