Dynamics forecasting method of random branch structure

Abstract

The invention provides a dynamics forecasting method of a random branch structure. The dynamics forecasting method comprises the following steps of: (1) selecting a main transmission path, i.e. for a system which comprises the random branch structure, firstly, selecting one chain-type main transmission path from one boundary end to the other boundary end; (2) establishing each branch point model, i.e. by the influence of adsorbing each sub branch, establishing the model between state vectors of both front and rear ends of each branch point on the main transmission path; (3) establishing an integral model, i.e. establishing the integral model between state vectors of both initial and tail ends by an arrangement sequence of transfer elements and point elements of each field on the main transmission path; and (4) forecasting a structural dynamics problem, i.e. introducing a boundary condition and an external acting force which serve as definite conditions and applying a transfer matrix method to forecast the dynamics problem of a chain system. The dynamics forecasting method has wide application range, has simple and convenient implementing process, is very beneficial to programming calculating and has high forecasting accuracy; the integral solving process cannot cause the increase of a variable freedom degree value; and the forecasting efficiency is ensured high.

Description

technical field [0001] The invention relates to a method for predicting arbitrary branch structures, in particular to a method for predicting the dynamics of one-dimensional elastic structures such as beams and pipes containing arbitrary branches. Background technique [0002] Arbitrary branch structures are ubiquitous in buildings and ship piping systems, and there are many methods for dynamic prediction of arbitrary branch structures. The transfer matrix method has become the solution chain method because of its advantages of less variable degrees of freedom and easy and quick solution. It is a common method for structural dynamics problems, and it is widely used in solving problems such as structural dynamics of beams or pipes, sound propagation in pipes, and fluid-solid coupling in piping systems. However, this method is still difficult to apply to complex structures. One of the reasons is that traditional methods are difficult to solve dynamic problems of systems with m...

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Problems solved by technology

However, for the branch structure, since the transfer relationship of the state vectors of any two sub-branch ends at the branch point depends on other sub-branches and cannot be directly determined, it cannot be directly solved

[0004] Ni Zhenhua (Ni Zhenhua, Vibration Mechanics, Xi'an: Xi'an Jiaotong University Press, 1989) proposed an absorption transfer matrix method when applying the transfer matrix method to solve the dynamic problems of the disc torsional vibration system with branches, that is, to select a part of the chain The formula structure is used as the main transmission system, and other branches are used as subsystems. As long as the influence of the subsystems on the main system is "absorbed", the transfer relationship of the state vectors on both sides of the branch point on the main system can be deduced, but Ni Fa did not establish a multi-branch structure. The general form of the transfer matrix between the torsional vibration state vectors on both sides of the branch point still needs to be derived and solved separately for any branch structure

[0005] Yu Baisheng et al. (Yu Baisheng, Zheng Ganggang, Du Huajun, Calculation method of transfer matrix of bifurcated structural system, Vibration and Shock, 2002,22(1):93–95.) proposed a transfer matrix method to calculate bifurcation The method of structural dynamic characteristics, the solution proposed by them has less variable degrees of freedom than the traditional solution, but the derivation and solution process is too cumbersome and inconvenient to promote

[0006] The traditional solution is to combine multi-terminal state vectors together to form a new state vector with many dimensions, and then derive and establish the transfer relationship between the new state vectors, which not only causes the number of degrees of freedom to double with the increase in the number of branches , and there is no uniform solution method for different branch structures, all need to be solved by formula derivation, and the derivation process is often very cumbersome. These reasons lead to a relatively large limitation in the application of the transfer matrix method

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