There are many physical phenomena in nonlinear beam/plate vibration and structural-acoustic systems. The corresponding mathematical formulations are usually governed by a set of nonlinear differential equations associated with different boundary conditions. The exact solutions of these equations are sometimes unobtainable. Therefore, the development of approximate solution methods for nonlinear vibration has been a hot research focus for many years.
In this research, a new modified multi-level residue harmonic balance method was adopted to investigate the nonlinear beam/plate and nonlinear structural-acoustic problems. The main advantage of the proposed method is that a set of decoupled nonlinear algebraic equations is generated at each solution level. The computational time of using the new method is much less than that spent on solving the coupled nonlinear algebraic equations generated in the classical harmonic balance method. The new method can generate higher-level nonlinear solutions neglected by other modified harmonic balance methods. The new method was employed to study the dynamic responses of single beam/plate, double-beam, and panel-cavity systems.
On the other hand, although numerous nonlinear single beam/plate, linear double-beam, and linear panel-cavity problems have been solved, there have been few studies about nonlinear double-beam and nonlinear panel–cavity problems. The geometric nonlinear formulations for the aforementioned problems have been developed. The results from the proposed method agree reasonably well with those from the classical harmonic balance method. The effects of damping, axial force, aspect ratio, cavity depth, and excitation magnitude on the nonlinear behaviour are examined.