The Hamiltonian dynamics is adopted to solve the eigenvalue problem for transverse vibrations of axially moving strings. With the explicit Hamiltonian function the canonical equation of the free vibration is derived. ...The Hamiltonian dynamics is adopted to solve the eigenvalue problem for transverse vibrations of axially moving strings. With the explicit Hamiltonian function the canonical equation of the free vibration is derived. Non-singular modal functions are obtained through a linear, symplectic eigenvalue analysis, and the symplectic-type orthogonality conditions of modes are derived. Stability of the transverse motion is examined by means of analyzing the eigenvalues and their bifurcation, especially for strings transporting with the critical speed. It is pointed out that the motion of the string does not possess divergence instability at the critical speed due to the weak interaction between eigenvalue pairs. The expansion theorem is applied with the non-singular modal functions to solve the displacement response to free and forced vibrations. It is demonstrated that the modal functions can be used as the base functions for solving linear and nonlinear vibration problems.展开更多
The boundary element method for the modal analysis of freevibration for 3-D anisotropic structures using particular solutionshas been developed. The complete polynomials of order two are used toconstruct the particula...The boundary element method for the modal analysis of freevibration for 3-D anisotropic structures using particular solutionshas been developed. The complete polynomials of order two are used toconstruct the particular solutions for general anisotropic materials.The numerical results for 3-D free vibra- tion analysis of anisotropic cantilever beam by the method presented is in goodagreement with the results us- ing the Ritz technique. Foranisotropic materials, the numerical results calculated form theproposed method are in good agreement with the results from MSC.NASTRAN.展开更多
基金supported by the National Natural Science Foundation of China(10472021,10421002 and 10032030)the NSFC-RFBR Collaboration Project(1031120166/10411120494)the Scientific Research Foundation for the Retumed 0verseas Chinese Scholars,State Education Ministry.
文摘The Hamiltonian dynamics is adopted to solve the eigenvalue problem for transverse vibrations of axially moving strings. With the explicit Hamiltonian function the canonical equation of the free vibration is derived. Non-singular modal functions are obtained through a linear, symplectic eigenvalue analysis, and the symplectic-type orthogonality conditions of modes are derived. Stability of the transverse motion is examined by means of analyzing the eigenvalues and their bifurcation, especially for strings transporting with the critical speed. It is pointed out that the motion of the string does not possess divergence instability at the critical speed due to the weak interaction between eigenvalue pairs. The expansion theorem is applied with the non-singular modal functions to solve the displacement response to free and forced vibrations. It is demonstrated that the modal functions can be used as the base functions for solving linear and nonlinear vibration problems.
基金the National Natural Science Foundation of China (No.19872011)
文摘The boundary element method for the modal analysis of freevibration for 3-D anisotropic structures using particular solutionshas been developed. The complete polynomials of order two are used toconstruct the particular solutions for general anisotropic materials.The numerical results for 3-D free vibra- tion analysis of anisotropic cantilever beam by the method presented is in goodagreement with the results us- ing the Ritz technique. Foranisotropic materials, the numerical results calculated form theproposed method are in good agreement with the results from MSC.NASTRAN.
