Finite element analysis of coupled vibration for hoisting cable with time-varying length

The coupled axial-torsional responses of the hoisting cable with time-varying length are investigated in order to predict the longitudinal vibration more accurately. The equations of motion are formulated by Hamilton’s principle and the finite element method (FEM), in which a variable-length cable element is introduced. In order to validate this theoretical model, an ADAMS simulation model is established in the framework of the multi-body system dynamic. The result shows that the numerical solution is in reasonably good agreement with the ADAMS simulation. The frequencies of the cables with the coupling considered and neglected are analyzed by varying the excitation frequency, which indicates that the coupling effect reduces the natural frequency of the cable and the maximum amplitude shifts from the resonance region to the deceleration stage as the coupling coefficient increases

Coupled vibration of hoisting cable in cable-guided hoisting system with different swivels

In most cases, the hoisting cable in the cable-guided hoisting system is connected to the hoisting bucket with the swivel. The coupled longitudinal-torsional responses of the hoisting cable with time-varying length are investigated. The hoisting cable and two guiding cables are discretized by employing the assumed modes method, while the equations of motion are derived using Lagrange equations of the first kind, where a coefficient λ varying from 0 to 1 is introduced to represent the free spinning, proportional and self-locking swivels. The longitudinal and torsional displacements with different swivels are obtained. The results indicate the torsional displacement in the free spinning swivel is much larger than that in the proportional and there is one resonance in the former, while the longitudinal resonance in the free spinning swivel occurs earlier than that in the other two, which implies the system frequencies decrease. In addition, the presented model could also be used to describe the coupled vibration in the rigid rail-guided hoisting system but needs more modes

Partition of a Binary Matrix into k

A biclustering problem consists of objects and an attribute vector for each object. Biclustering aims at finding a bicluster—a subset of objects that exhibit similar behavior across a subset of attributes, or vice versa. Biclustering in matrices with binary entries (“0”/“1”) can be simplified into the problem of finding submatrices with entries of “1.” In this paper, we consider a variant of the biclustering problem: the k-submatrix partition of binary matrices problem. The input of the problem contains an n×m matrix with entries (“0”/“1”) and a constant positive integer k. The k-submatrix partition of binary matrices problem is to find exactly k submatrices with entries of “1” such that these k submatrices are pairwise row and column exclusive and each row (column) in the matrix occurs in exactly one of the k submatrices. We discuss the complexity of the k-submatrix partition of binary matrices problem and show that the problem is NP-hard for any k≥3 by reduction from a biclustering problem in bipartite graphs