Analysis of the effect of axial force on natural frequency of arbitrarily elastically constrained beam

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Journal of Vibration and Shock ›› 2023, Vol. 42 ›› Issue (11) : 34-41.

BAO Siyuan, WU Jiali, SHEN Feng

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Abstract

The transverse vibration characteristics of Bernoulli-Euler beam subjected to axial loads is given. Firstly, the analytical expression of deflection is obtained to satisfy the differential equation for free vibration of beam subjected to axial force, and the natural frequency equations of beam’s transverse vibration under general elastic boundary conditions are presented. The natural frequencies can be solved and the corresponding mode for each order can be obtained. Secondly, The brief forms of the frequency equation for beams subjected to axial forces under five kinds of classical boundary conditions are obtained, and the numerical computation is carried out for four kinds of boundary conditions. The obtained results are found to be coincided with those by using the dynamic stiffness method and Wittrick-Williams algorithm. Then for five kinds of boundary conditions including elastic constraint at the beam end, the analytical frequency equation are obtained and some numerical results of natural frequency for beams under axial force are presented. The analytical form of the frequency equation is accurate in theory, which can be used to check the accuracy of other numerical methods, and has good reference in vibration optimization and modal analysis. The influence of axial forces on structural vibration response is analyzed, and the results show that the dimensionless frequency of beams under axial tension is obviously larger than that under axial compression. The dimensionless frequency of beams under axial tension increases with the increase of axial tension. The beam’s dimensionless frequency decreases with the increase of axial compression, in which the value of the axial compression should be less than the critical Euler force. For beams subjected to axial force with several kinds of boundary conditions, practical approximate equations is proposed with the errors less than 1%.

Key words

Bernoulli-Euler beam / axial load / free vibration / natural frequency

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BAO Siyuan, WU Jiali, SHEN Feng. Analysis of the effect of axial force on natural frequency of arbitrarily elastically constrained beam[J]. Journal of Vibration and Shock, 2023, 42(11): 34-41

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