الفهرس Only 14 pages are availabe for public view
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Abstract
A generalized model of a complicated overhead crane system of flexible cable and time dependent cable length is considered for the first time. The analysis of such systems is not an easy task since there is a moving boundary as the time-dependent cable length is not prescribed and has to be determined as a part of the solution.
A set of coupled highly non-linear hybrid partial differential and ordinary differential equations of motion are derived by using Hamilton’s principle and the variation approach. An accurate model, where the time dependent spatial domain was considered as dependent variable, resulted in a reasonable and accurate system representation. It should be noted that previous publications in the field considered the spatial variable as an independent variable.
The continuous time dependent flexible cable crane system is discretized by using two methods namely; a modified Galerkin method (MGM) and a variable domain finite element method (MFEM). In the modified Galerkin method, the shape function is time dependent as it is function of the time-dependent cable length. In the variable domain finite element method, the number of elements is fixed while the size of the element changes with time. It can be concluded from results of the thesis that each method has its own merits and drawbacks. It is known the the MFEM is more general as regarding time-dependent domain and the consideration of the payload at the tip of the cable is straight forward. This is not the case for MGM where a different set of mode functions should be assumed to be able to deal with the payload. Also, the MGM depends crtically on the boundary conditions and, as a result, modal functions may not be available in closed form.