Eigenvalue and stability analysis for transverse vibrations of axially moving strings based on Hamiltonian dynamics |
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Authors: | Email author" target="_blank">Yuefang?WangEmail author Lihua?Huang Xuetao?Liu |
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Institution: | (1) Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China;(2) School of Civil Engineering, Dalian University of Technology, Dalian, 116024, China |
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Abstract: | 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.
The project supported by the National Natural Science Foundation of China (10472021, 10421002 and 10032030), the NSFC-RFBR
Collaboration Project (1031120166/10411120494) and the Scientific Research Foundation for the Returned Overseas Chinese Scholars,
State Education Ministry
The English text was polished by Keren Wang |
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Keywords: | Axially moving strings Symplectic Modal analysis Stability Divergence |
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