Shape function and performance analysis of Fourier horn
To design a horn with excellent amplitude factor and shape factor,a Fourier horn model with different orders of Fourier series as vibration displacement function is researched.The shape functions of the horn with different orders of Fourier series are derived,and the corresponding shape factors and displacement nodes are calculated.The resonant frequency,displacement amplitude and displacement node of the horn are calculated by the finite element method,and the performance of the horn is compared with that of the traditional horns.The results show that when the area factor is large(more than 3.34),the stepped horn has the largest amplitude factor,followed by the second order Fourier horn,catenary linear horn,exponent horn,and the smallest is conical horn.The shape factor of conical horn is the largest,followed by exponent horn,catenary linear horn,second order Fourier horn,and the smallest is stepped horn.Under the same resonant frequency and area factor,the amplitude factor of the second order Fourier horn is much larger than that of the exponent horn,catenary linear horn and conical horn,and the shape factor of the second order Fourier horn is much larger than that of the stepped horn.Compared with the traditional horns,the second order Fourier horn has better comprehensive performance when considering both the amplitude factor and the shape factor.
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