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## Modelling of systems of collecting electrodes of electrostatic precipitators by means of the rigid finite element method

### Abstract

The paper presents a model of a rapping system of an electrostatic precipitator. The rapping system consists of a set of collecting electrodes hanging on a suspension bar and braced together in a brushing bar. The suspension and brushing bars are modeled using the rigid finite element method, while the collecting plates are modeled using the hybrid method. The method combines the rigid finite element method with the classical finite element method. As a result, the mass matrix is diagonal. Some results of numerical simulations concerning free vibrations of the collecting plates and the influence of the number of elements, into which the plate is divided, on the vibrations of the rapping system are presented.
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## Application of the rigid finite element method for modelling an offshore pedestal crane

### Abstract

In offshore pedestal cranes one may distinguish three components of considerable length: a pedestal, a boom and a frame present in some designs. It is often necessary in dynamical analyses to take into account their flexibility. A convenient and efficient method for modelling them is the rigid finite element method in a modified form. The rigid finite element method allows us to take into account the flexibility of the beam system in selected directions while introducing a relatively small number of additional degrees of freedom to the system. This paper presents a method for modelling the pedestal, the frame and the boom of an offshore column crane, treating each of these components in a slightly different way. A custom approach is applied to the pedestal, using rigid finite elements of variable length. Results of sample numeric computations are included.
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## Mathematical model of a pipelay spread

### Abstract

The paper presents the mathematical model of a pipelay spread. In the model, elasto-plastic deflections of the pipe, its large deformations and contact problems are considered. The modification of the rigid finite element method (REFM) is used to discretise the pipe. The problem is analyzed in two stages. First, the quasi-static problem is considered. The tip of the pipe is pulled from the reel to the tensioner. Then, dynamic analysis (during ordinary work) of the pipelay spread is carried out. Some results of numerical calculations are presented.
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## Modelling articulated vehicles with a flexible semi-trailer

### Abstract

The paper presents a model of an articulated vehicle with a flexible frame of a semi-trailer. The rigid finite element method in a modified formulation is used for discretisation of the frame. In order to carry out effective numerical simulation, a reduced model with a considerably smaller number of degrees of freedom is proposed. The parameters of the reduced model are chosen in an optimization process by using a genetic algorithm. To this end, it is assumed that the full and reduced model have to be similar in the range of static deflections and frequencies of free vibrations. Numerical simulations are concerned with the influence of the flexibility of the frame on the motion of the articulated vehicle during an overtaking maneuver. Results are presented and discussed.
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## Modification of the rigid finite element method in modeling dynamics of lines and risers

### Abstract

The paper presents an application of the modified rigid finite element method to analysis of the dynamics of slender structures. The equations of motion are formulated for a system discretized by means of the method, and discussion is limited to planar systems and large deformations. Slender elements can be found in offshore engineering as lines, cables and risers. In these cases the hydrostatic influence of water and sea currents has to be taken into account. While analyzing dynamics of risers it may also be necessary to consider the flow of fluid inside the riser. The influence of hydrodynamic coefficients and the velocity of the internal flow of fluid on displacements and forces is presented.
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