This study investigates the response frequency conversion characteristic of a nonlinear curved panel mounted with a centre mass and the sound radiations. A set of coupled governing differential equations is set up and used to generate the nonlinear vibration responses, which are used to calculate the corresponding radiated sounds. The vibration, sound levels, and the ratio of the antisymmetrical to symmetrical mode responses are plotted against the excitation level and compared with a set of experimental data. The frequency conversion characteristic is investigated from the frequency spectrums of the vibration responses.

Previous studies of various nonlinear vibration/oscillation systems have been studied over recent decades [

Figure ^{−2}. The transverse displacement is expressed in terms of the mode shapes and given by

Side view of a curved panel mounted with a mass.

The residual can be found by substituting (

The experimental setup, which was the same as that in [

Experimental setup.

In Figure

(a) Relative total vibration level

Figure

(a) Relative total vibration level (

Figure

Ratio of the antisymmetrical to symmetrical responses, (dB scale).

The nonlinear curved panels mounted a centre mass and the sound radiations have been studied. The results indicate that if the resonant frequency ratio is more far from two and the excitation and the structure are symmetrical, a higher excitation level is required to induce the antisymmetrical mode vibration. In the frequency spectrums, it can be seen in some cases studied that the response frequency of the dominant mode, which is the first antisymmetrical mode, is much lower than the excitation frequency. This can be considered as “high-frequency excitation input-low-frequency response output.” Besides, as the radiation efficiency of the antisymmetric mode is much lower than the others, the overall sound radiation is thus much smaller.

The harmonic balance method was employed for solving the Duffing equation, which represents the large amplitude free vibration of a beam in a previous study, and the result agreed well with the elliptic solution in [

The solution of a nonlinear system is assumed to be of the form of a Fourier series:

For example, one constant and two harmonic terms are considered in (

If the initial centre deflection,

The Hamiltonian in (

The work described in this paper was fully supported by a grant from the Research Grants Council of the Hong Kong, China [Project no. 9041496 (CityU 116209)]. The author would like to express his sincere gratitude and appreciation to Dr. WY Poon, Dr. CF Ng, and Ms. CK Hui for experimental hardware tuning and data acquisition.