Split iteration method for solving kinetic equation of flexible beam system

Abstract

The invention relates to a split iteration method for solving a kinetic equation of a flexible beam system, and belongs to the field of multi-flexible body system dynamics. The method has an inner-layer iteration process and an outer-layer iteration process. The method comprises the following steps: 1, in an outer layer iteration process, dividing generalized coordinates of a system into two parts, namely master coordinates and slave coordinates; 2, in the inner layer iteration, expanding the slave coordinate iteration into the Taylor series of the master coordinate and the Lagrange multiplier; 3, substituting the obtained Taylor series into a system equation, and solving a main coordinate and a Lagrange multiplier; 4, solving a slave coordinate; and 5, judging whether an obtained result meets a precision requirement or not, if so, ending iteration, if not, correcting the obtained generalized coordinates, updating a system equation by using the corrected generalized coordinates, setting the corrected main coordinates and the Lagrange multiplier as Taylor series expansion points of the next round of inner layer iteration, skipping to the next round of outer layer iteration, until a numerical solution meeting the precision requirement is obtained.

Description

technical field [0001] The invention belongs to the field of multi-flexible body system dynamics, in particular to a method for solving dynamic equations of multi-section mutually coupled flexible beams. Background technique [0002] Mutually coupled multi-section flexible beam systems are widely used in engineering fields. For example, the working booms of cranes and aerial work platforms are all flexible arm structures that are nested or articulated with each other. In order to improve the safety and stability of lifting equipment, especially high-altitude manned operation equipment, it is necessary to carry out dynamic modeling and simulation solution for the multi-section flexible beam system coupled with each other. [0003] At present, the commercial finite element software on the market cannot effectively simulate and solve the telescopic motion and compound motion of the flexible beam system that is nested with each other. In the corresponding engineering applicatio...

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Problems solved by technology

For the pitching motion and slewing motion of the jib, the Floating Frame of Reference (FFR) method is generally used for modeling analysis. The elements of the mass matrix of the system obtained by this method are functions of generalized coordinates, which makes it difficult to solve

Some scholars also use the D-H method (Denavit-Hartenberg Method) combined with commercial finite element software for correlation analysis. The cost is that the coupling between the rigid motion and elastic deformation of the boom is ignored, which reduces the solution accuracy.

Using the ANCF (Absolute Nodal Coordinate Formulation) method to model the interconnected flexible beam system can obtain the constant mass matrix of the beam, but this method has the disadvantages of a large number of generalized coordinates and a large amount of calculation when solving

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