Fundamental frequency analysis method for medium-low frequency concentrated mass cantilever reed instrument

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (5) : 272-277.

HUI Anmin1, YAN Ming1, FENG Linhan2,JIANG Lijie1, LIU Haochao1

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Abstract

Reed instrument is a measuring device for medium-low frequency impact response spectra.It can be simplified as a cantilever beam with concentrated mass at its free end during its design.There is a transcendental function in its vibration mode shape equation.For a reed instrument with uniform cross-section, this equation can be solved with the bisection method, but the numerical computation is time-consuming.This method is not suitable for fundamental frequency design of reed instruments with complex cross-section.Here, firstly, the deflection formula for a cantilever beam subjected to a concentrated force at its free end was used to derive the equivalent stiffness of a single-DOF spring-mass system equivalent to the beam.The relevant natural frequency formula of this single-DOF spring-mass system was proposed to solve the fundamental frequency problem for a uniform cross-section cantilever beam with a concentrated mass.Comparing the beam’s fundamental frequency calculated using the proposed method with that using the vibration mode shape equation, it was found that within the medium-low frequency range of less than 10 Hz, the fundamental frequency accuracy of the cantilever beam with uniform cross-section can be well kept; within the medium frequency range of larger than 10 Hz, error rapidly increases with increase in frequency; Mohr integral method was used to deduce the maximum deflection at free end of a uniform strength concentrated mass cantilever beam, and give the design formula of its fundamental frequency.Comparing its fundamental frequency data calculated with the proposed method to test data, it was found that the error has the same trend as that of the cantilever beam with uniform cross-section; Rayleigh energy method is used to modify mass parameters in the design formula, and the error between the modified data and test ones is about 5%.Through theoretical calculation and test verification, it was shown that the proposed design method for a reed instrument’s fundamental frequency is simple and feasible, and the computation results are believable.

Key words

reed instrument / uniform strength concentrated mass cantilever beam / fundamental frequency / Mohr integral

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HUI Anmin1, YAN Ming1, FENG Linhan2,JIANG Lijie1, LIU Haochao1. Fundamental frequency analysis method for medium-low frequency concentrated mass cantilever reed instrument[J]. Journal of Vibration and Shock, 2020, 39(5): 272-277

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