As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has b...As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.展开更多
By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion consta...By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.展开更多
We study the error analysis of the weak Galerkin finite element method in[24,38](WG-FEM)for the Helmholtz problem with large wave number in two and three dimensions.Using a modified duality argument proposed by Zhu an...We study the error analysis of the weak Galerkin finite element method in[24,38](WG-FEM)for the Helmholtz problem with large wave number in two and three dimensions.Using a modified duality argument proposed by Zhu and Wu,we obtain the pre-asymptotic error estimates of the WG-FEM.In particular,the error estimates with explicit dependence on the wave number k are derived.This shows that the pollution error in the broken H1-norm is bounded by O(k(kh)^(2p))under mesh condition k^(7/2)h^(2)≤C0 or(kh)^(2)+k(kh)^(p+1)≤C_(0),which coincides with the phase error of the finite element method obtained by existent dispersion analyses.Here h is the mesh size,p is the order of the approximation space and C_(0) is a constant independent of k and h.Furthermore,numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.展开更多
基金the company PSA Peugeot Citroёn for the financial support
文摘As a promising numerical tool of structural dynamics in mid- and high frequencies, the wave and finite element method（WFEM） is receiving increasingly attention and applications. In this paper, an enhanced WFEM has been developed with a reduced model and a new eigenvalue scheme. The reduced model is applicable for structures with piezoelectric shunts or local dampers;the new eigenvalue scheme can mitigate the ill-conditioning when the wave basis is calculated. The enhanced WFEM is applied to a thin-wall structure with periodically distributed piezoelectric materials（PZT）. Both free wave characteristics and forced response are analyzed and the influences of the suggested enhancements are presented. It is shown that if the control factors are properly chosen, these enhancements can improve the accuracy while accelerating the calculation. Resulting from the complexity of the application, these enhancements are not optional but imperative.
基金Supported by Doctorate Training Fund of National Education Commission of China
文摘By taking infinite periodic beams as examples,the mutual variational principle for analyzing the free wave propagation in periodic structures is established and demonstrated through the use of the propaga- tion constant in the present paper,and the corresponding hierarchical finite element formulation is then de- rived.Thus,it provides the numerical analysis of that problem with a firm theoretical basis of variational prin- ciples,with which one may conveniently illustrate the mathematical and physical mechanisms of the wave prop- agation in periodic structures and the relationship with the natural vibration.The solution is discussed and ex- amples are given.
基金The work was supported in part by the National Natural Science Foundation grants 11471031,91430216,and 11601026NSAF U1530401+1 种基金the U.S.National Science Foundation grant DMS1419040and the China Postdoctoral Science Foundation grant 2016M591053.
文摘We study the error analysis of the weak Galerkin finite element method in[24,38](WG-FEM)for the Helmholtz problem with large wave number in two and three dimensions.Using a modified duality argument proposed by Zhu and Wu,we obtain the pre-asymptotic error estimates of the WG-FEM.In particular,the error estimates with explicit dependence on the wave number k are derived.This shows that the pollution error in the broken H1-norm is bounded by O(k(kh)^(2p))under mesh condition k^(7/2)h^(2)≤C0 or(kh)^(2)+k(kh)^(p+1)≤C_(0),which coincides with the phase error of the finite element method obtained by existent dispersion analyses.Here h is the mesh size,p is the order of the approximation space and C_(0) is a constant independent of k and h.Furthermore,numerical tests are provided to verify the theoretical findings and to illustrate the great capability of the WG-FEM in reducing the pollution effect.
