A Mass Assignment Method for Calculating the Natural Frequency of Frame Structures Using the Lumped Mass Method

Abstract

The invention discloses a mass distribution method for calculating the inherent frequency of a frame structure based on a centralized mass method. The method comprises the following steps: firstly, measuring the horizontal displacement of each layer of cross beam of a three-layer frame structure under the action of a static load, deriving a flexibility matrix according to a flexibility theory, further solving the inherent frequency value of the frame structure under a common mass distribution method, and analyzing the relative error between the inherent frequency value and each frequency of afree vibration test result; On the basis of a traditional distribution method, quantitatively changing the equivalent mass of each layer, and studying the influence of the change of the equivalent mass of each layer on theoretical calculation of inherent frequency precision; Accurately calculating the optimal distribution proportion of the quality of each layer under a certain error constraint byutilizing a cyclic nesting theory; And finally, changing the initial mass of each cross beam, and carrying out test verification on the mass distribution ratio on a three-layer frame vibration test device. The method has the advantages of small calculated amount, simplicity, intuitiveness, high calculation precision and the like, and the accuracy of calculating the inherent frequency of the framestructure through the centralized mass method is improved.

Description

technical field [0001] The invention belongs to the calculation of the natural frequency and mode shape of a frame structure in the field of vibrations, and in particular relates to a mass distribution method for calculating the natural frequency of a frame structure by using a lumped mass method. Background technique [0002] Frame structures are ubiquitous in production and life, such as factory buildings, high-rise buildings, etc. The number of layers and quality of various frame structures are different, and the analysis and research on their natural frequency and mode shape is conducive to avoiding resonance caused by external excitation in production This phenomenon has great practical significance to the production efficiency and the service life of the device. [0003] At present, the research on the natural frequency and mode shape of the frame structure mostly focuses on three aspects: calculation method, optimal design and device fabrication. The existing theoret...

AI Technical Summary

Problems solved by technology

When using the concentrated mass method to calculate the natural frequency of the frame structure, the mass of the side plate between the beams of each layer is ignored, and the side plate is simply equivalent to a spring with a certain stiffness. There are few studies on how the mass of each layer should be distributed. Moreover, the calculation error of the traditional mass allocation method is relatively large, and there is little research on the influence of mass allocation on the accuracy of the theoretical calculation of the natural frequency of the frame structure.

Images