Prediction method of natural frequency of liquid-filled cylindrical shell

Abstract

The object of the present invention is to provide a method for predicting the natural frequency of a liquid-filled cylindrical shell, comprising the following steps: establishing the free vibration equation of the cylindrical shell by using the Kennard thin shell theory; by solving the Helmholtz wave equation under the cylindrical coordinate system, the fluid acts as a radial load On the cylindrical shell, the dynamic model of the liquid-filled cylindrical shell is established; the improved state vector is selected; the relationship between the element displacement, rotation angle, force, etc. of the traditional state vector and the mid-plane displacement is obtained from the Kennard thin shell theory, so as to establish the improved state vector and the traditional state vector. Transition matrix between state vectors. The natural frequencies of the liquid-filled cylindrical shell are predicted by introducing boundary conditions at both ends of the liquid-filled cylindrical shell. The invention reduces the derivation workload of the first-order derivative equation and the transfer matrix and the possibility of derivation errors, has wide application range, simple implementation process, and is very beneficial to programming calculation; the prediction accuracy is high, and the whole solution process does not lead to variable degrees of freedom. increase to ensure a higher forecasting efficiency.

Description

technical field [0001] The invention relates to a natural frequency prediction method. Background technique [0002] Liquid-filled cylindrical shell structures are common in building and ship piping systems, and there are many methods for predicting their natural frequencies. The transfer matrix method has become a common method to solve the dynamic problems of chain structures because of its advantages of less variable degrees of freedom and simple and quick solution. There are many applications when the problem occurs. [0003] If the structural control differential equation is written in the form of a first-order differential equation system, the transfer matrix can be used to establish a simple relationship between the state vectors of the starting point and the end point, and the natural frequency of the liquid-filled cylindrical shell can be predicted by using the boundary conditions. Therefore, the calculation accuracy of the transfer matrix method mainly depends on...

AI Technical Summary

Problems solved by technology

However, with the application of the transfer matrix method in the multi-degree-of-freedom system, the derivation of the first-order equation of the state vector becomes more and more difficult

The traditional state vector is generally composed of displacement, velocity, force, moment, etc., but the state vector cannot be directly obtained from the vibration equation, which makes the derivation process of the state vector first-order differential equation very complicated, not only increases the workload, but also often makes mistakes

[0004] Luo Wen (Luo Wen, Computational Research on Fluid-Structure Interaction of Conveying Pipelines. Master Thesis of Harbin Engineering University. 2014.) applied the transfer matrix method to solve the dimensionless natural frequency of the liquid-filled cylindrical shell, but its state vector first-order differential equation The derivation process is more complicated, and its transfer matrix is ​​a circumferential transfer matrix, which is different from the general transfer matrix along the length direction of the chain structure

[0005] Wan Haochuan et al. (Wan Haochuan, Li Yinong, Zheng Ling, Improved Structural Vibration Transfer Matrix Method, Vibration and Shock, 2013,32(1):173–177.) proposed a method using the improved transfer matrix method to calculate the Compared with the traditional solution method, the derivation and solution process of the solution proposed by them is simplified, but the influence of the internal liquid filling on the improved transfer matrix and natural frequency of the cylindrical shell is not considered.

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