Free vibration analysis of a nonlinear panel coupled with extended cavity using the multi-level residue harmonic balance method

• In many previous works, the assumption of cavity length=panel length was adopted.
• The effects of cavity length≠panel length and nonlinear vibration are newly studied.
• A new harmonic balance method recently developed is adopted in this study.
• The results show that the natural frequency is very sensitive to the cavity length.

This article addresses the free vibration analysis of a nonlinear panel coupled with extended cavity. In practice, the cavity length of a panel-cavity system is sometimes longer than the panel length. Therefore, this study examines the effect of cavity length on the natural frequency of a nonlinear panel coupled with extended cavity. The multi-level residue harmonic balance method, which was recently developed by the author and his research partners, is used to solve this nonlinear problem. The present harmonic balance solution agrees reasonably well with the results obtained from a previous classical solution and shows that the cavity length is a very important factor that significantly affects the panel vibration and should not be ignored in the modelling process. The natural frequency of a panel-cavity system is very sensitive to the cavity length and decreases significantly when the cavity is longer, due to its larger volume or weaker stiffness. Moreover, when the cavity is very long and its resonant frequencies are close to that of the panel, multiple frequency solutions are obtained.