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- Cylinders (1)
- Dispersion (1)
- Energy density fluctuation (1)
- Guided waves (1)
- Numerical method (1)
- Resonance-free ultrasound emitter (1)
- Spectral decomposition (1)
- Thermal inertia (1)
- Thermal sound generation (1)
- Thermo-acoustic effect (1)
In this paper, a method to determine the complex dispersion relations of axially symmetric guided waves in cylindrical structures is presented as an alternative to the currently established numerical procedures. The method is based on a spectral decomposition into eigenfunctions of the Laplace operator on the cross-section of the waveguide. This translates the calculation of real or complex wave numbers at a given frequency into solving an eigenvalue problem. Cylindrical rods and plates are treated as the asymptotic cases of cylindrical structures and used to generalize the method to the case of hollow cylinders. The presented method is superior to direct root-finding algorithms in the sense that no initial guess values are needed to determine the complex wave numbers and that neither starting at low frequencies nor subsequent mode tracking is required. The results obtained with this method are shown to be reasonably close to those calculated by other means and an estimate for the achievable accuracy is given.
In this work we experimentally verify the theoretical prediction of the recently published Energy Density Fluctuation Model (EDF-model) of thermo-acoustic sound generation. Particularly, we investigate experimentally the influence of thermal inertia of an electrically conductive film on the efficiency of thermal airborne ultrasound generation predicted by the EDF-model. Unlike widely used theories, the EDF-model predicts that the thermal inertia of the electrically conductive film is a frequency-dependent parameter. Its influence grows non-linearly with the increase of excitation frequency and reduces the efficiency of the ultrasound generation. Thus, this parameter is the major limiting factor for the efficient thermal airborne ultrasound generation in the MHz-range. To verify this theoretical prediction experimentally, five thermo-acoustic emitter samples consisting of Indium-Tin-Oxide (ITO) coatings of different thicknesses (from 65 nm to 1.44 lm) on quartz glass substrates were tested for airborne ultrasound generation in a frequency range from 10 kHz to 800 kHz. For the measurement of thermally generated sound pressures a laser Doppler vibrometer combined with a 12 lm thin polyethylene foil was used as the sound pressure detector. All tested thermo-acoustic emitter samples showed a resonance-free frequency response in the entire tested frequency range. The thermal inertia of the heat producing film acts as a low-pass filter and reduces the generated sound pressure with the increasing excitation frequency and the ITO film thickness. The difference of generated sound pressure levels for samples with 65 nm and 1.44 lm thickness is in the order of about 6 dB at 50 kHz and of about 12 dB at 500 kHz. A comparison of sound pressure levels measured experimentally and those predicted by the EDF-model shows for all tested emitter samples a relative error of less than ±6%. Thus, experimental results confirm the prediction of the EDF-model and show that the model can be applied for design and optimization of thermo-acoustic airborne ultrasound emitters.