Research On The Near-field Sound Pressure Of The Piston Radiator Based On The Angular Spectrum Method

The longitudinal vibration transducer has the characteristics of high efficiency and high power.The bending vibration radiator has the characteristics of low radiation impedance and large radiation area.Therefore,the longitudinal bending composite ultrasonic radiation system composed of the longitudinal vibration transducer and the bending vibration radiator is widely used in practice.The radiators at the front end of the longitudinal bending composite ultrasonic radiation system mainly include two types of the circular thin plate and the rectangular thin plate.The radiation is excited by the transducer to generate a vibration response.It will cause the surrounding air to fluctuate,forming the sound wave and the sound field.This is the sound radiation.The radiated sound field includes the near field and the far field.The near field is near the sound source,and the sound pressure is different from the phase of the particle velocity.In the near-field region,the relationship between the sound pressure of the sound source radiation and the distance is very complicated.Because the near-field distribution of the radiated sound field is not uniform,the sound pressure fluctuations vary greatly.Therefore,studying the distribution law of near-field sound field is of great significance for the application of ultrasonic technology,and it is also an important theoretical basis for the design and practical application of ultrasonic radiation system.The steady-state plane wave solution of the wave equation consists of two parts of the ordinary plane wave and the evanescent wave.Near-field acoustic holography is measured in the near-field region of the sound source which the propagating wave component can be obtained,and the evanescent wave component can also be obtained.Inspired by this,the acoustic field of the circular piston and the rectangular piston is calculated by the angular spectrum method in this paper.The distribution of near-field sound pressure is obtained by superposition of the propagating wave the and evanescent wave,and the correctness of the theory is verified by experiments.The specific work is as follows:(1)The theory of the plane wave and the evanescent wave is introduced.The physical concept of the propagating wave and the evanescent wave is illustrated simply and clearly.On this basis,the basic principle of the angular spectrum method is introduced.Solving the Helmholtz equation in the frequency domain,we can get the plane wave solution including ordinary plane wave which is the propagating wave and the evanescent wave.The phase velocity of the propagating wave is larger than the sound velocity.The propagating wave can be obtained by superposition of ordinary plane waves,which is the supersonic sound wave.The phase velocity of the evanescent wave is smaller than the sound velocity,which is the subsonic sound wave.The amplitude of the evanescent wave in the process of propagation decays exponentially with the distance.The evanescent wave decays to a small extent within a range of wavelengths and is negligible.Therefore,in the near-field detection,the propagating wave component can be obtained,and the evanescent wave component can be obtained,and in the far-field detection,only the propagating wave component can be obtained.The basic idea of the angular spectrum method is to decompose the wave into countless plane waves,and calculate the propagation of the sound field by superposition of plane waves.According to the basic idea of the angular spectrum method,the sound pressure at a certain point in the sound field can be expressed uniquely and completely by the superposition of plane waves and evanescent waves.(2)The radiated sound field of the circular piston and the rectangular piston is calculated by the angular spectrum method.The calculation method of the near-field sound pressure is obtained by superposition of the plane propagating wave and the evanescent wave.Combined with the numerical analysis method,the sound source radius and frequency are selected,the near-field sound pressure distribution curve of the circular piston sound source is obtained.The results show that the near-far field boundary points calculated by the angle spectrum method and the point source combination method are consistent.The amplitude of sound pressure increases with the increase of the sound source radius,and the critical distance of near-far field increases with the sound source radius.The amplitude of sound pressure increases with the increase of radiation frequency,and the critical distance of near-far field increases with the increase of radiation frequency.(3)The radiation of the stepped plate should theoretically be equal to the radiation of the corresponding piston which the stepped plate is the piston radiator.In this paper,the sound pressure distribution along the near-field is tested by using the stepped plate instead of the circular piston.Firstly,the frequency equation of the single-step circular plate is obtained by calculation.Secondly,programming procedure to obtain the size parameters of a single stepped circular plate.A single-step circular plate of 45#steel was designed.The longitudinal vibration transducer was excited by an ultrasonic generator,the center of the stepped circular plate was connected with the transducer,and the stepped circular plate was making bending vibration.Recording the sound pressure level at different distances from the center of the stepped circular plate,and converting it to its sound pressure value,the near-field sound pressure distribution on the acoustic axis of the stepped circular plate can be obtained.After testing,the trend of the experimental test results are basically consistent with the trend of theoretical calculation results.