We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of t...We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of the complex Jacobian matrix Jf(p) at a boundary point p of Dnfor a holomorphic self-mapping f of Dn. Our results extend the classical Schwarz lemma at the boundary to high dimensions.展开更多
This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitra...This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11101139,11271124 and 11301136)Natural Science Foundation of Zhejiang Province(Grant No.LY14A010017)Natural Science Foundation of Hebei Province(Grant No.A2014205069)
文摘We establish a new type of the classical boundary Schwarz lemma for holomorphic self-mappings of the unit polydisk Dnin Cn. By using the Carath′eodory metric and Kobayashi metric of Dn, we obtain some properties of the complex Jacobian matrix Jf(p) at a boundary point p of Dnfor a holomorphic self-mapping f of Dn. Our results extend the classical Schwarz lemma at the boundary to high dimensions.
基金Project supported by the National Natural Science Foundation of China （Nos. 51209052, 51279038, and 51479041）, the Natural Sci- ence Foundation of Heilongjiang Province （No. QC2011C013）, and the Opening Funds of State Key Laboratory of Ocean Engineering of Shanghai Jiao Tong University （No. 1307）, China
文摘This paper is concerned with the free vibration analysis of open circular cylindrical shells with either the two straight edges or the two curved edges simply supported and the remaining two edges supported by arbitrary classical boundary conditions. Based on the Donnell-Mushtari-Vlasov thin shell theory, an analytical solution of the traveling wave form along the simply supported edges and the modal wave form along the remaining two edges is obtained. With such a unidirectional traveling wave form solution, the method of the reverberation-ray matrix is introduced to derive the equation of natural frequencies of the shell with different classical boundary conditions. The exact solutions for natural frequencies of the open circular cylindrical shell are obtained with the employment of a golden section search algorithm. The calculation results are compared with those obtained by the finite element method and the methods in the available literature. The influence of length, thickness, radius, included angle, and the boundary conditions of the open circular cylindrical shell on the natural frequencies is investigated. The exact calculation results can be used as benchmark values for researchers to check their numerical methods and for engineers to design structures with thin shell components.
