Title: Analytical estimation of the first natural frequency and analysis of a planar regular truss oscillation spectrum // Magazine of Civil Engineering. – 2022. – С. 11114
Creators: Kirsanov M. N.; Safronov V. S.
Imprint: 2022
Collection: Общая коллекция
Subjects: Строительство; Строительная механика; construction farms; flat regular farms; fluctuations of construction farms; oscillation frequency; vibration of construction farms; kinematic variability; строительные фермы; плоские регулярные фермы; колебания строительных ферм; частота колебаний; вибрации строительных ферм; кинематическая изменчивость
UDC: 624.04
LBC: 38.112
Document type: Article, report
File type: PDF
Language: English
DOI: 10.34910/MCE.111.14
Rights: Свободный доступ из сети Интернет (чтение, печать, копирование)
Record key: RU\SPSTU\edoc\68951

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A statically determinate truss of a beam type with a triple lattice with short descending and long ascending braces is considered. The mass of a truss is modeled by concentrated loads at its nodes. For the first natural frequency, the Dunkerley’s method derives a formula for the dependence of its lower boundary on the number of panels. The calculation of the efforts in the truss required to obtain the stiffness value according to the Maxwell-Mohr formula is performed in the Maple computer mathematics system by cutting out the nodes. It is shown that for a certain number of panels the proposed scheme of the truss has the property of kinematic variability. For admissible numbers of panels, by induction, the sequence of solutions for trusses with different numbers of panels is generalized to an arbitrary case. The coefficients of the required dependence are obtained as solutions of linear homogeneous recurrent equations. To obtain and solve recurrent equations, the operators of the Maple system are used. The found solution is compared with the minimum frequency of the spectrum obtained numerically. It is shown that the accuracy of the analytical assessment monotonically increases with the increase in the number of panels. Multiple frequencies and the independence of several higher frequencies from the number of panels were found in the frequency spectrum.

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Table of Contents

  • Analytical estimation of the first natural frequency and analysis of a planar regular truss oscillation spectrum
    • 1. Introduction
    • 2. Methods
      • 2.1. Calculation of forces. Kinematic analysis
      • 2.2. First frequency. The analytical solution according to the Dunkerley’s method
    • 3. Results and Discussion
      • 3.1. Numerical calculation of the spectrum of natural frequencies
      • 3.2. Natural frequency spectrum
    • 4. Conclusion
    • 5. Acknowledgments

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