Vibro-acoustic coupling dynamics of a finite cylindrical shell under a rotor-bearing-foundation system׳s nonlinear vibration excitation

The vibro-acoustic coupling dynamics of a rotor-bearing-foundation-cylinder system are investigated. Using rotor dynamics, structure dynamics and acoustical theory, the vibro-acoustic coupling equation of a cylindrical shell under rotor-bearing-foundation system׳s nonlinear vibration excitations is derived based on variational principle. In order to solve the coupling equation, the influences of the shell׳s vibration to the rotor-bearing system are neglected, and then the dynamical equation is reduced. The nonlinear forces transmitted to the cylinder are fitted in the Fourier series by the fast Fourier translation and the harmonic balance method, and then the analytical solution of the vibro-acoustic coupling equation of the cylinder is derived. Based on inherent assumption, the analytical expressions of the acoustic radiation power and the surface velocity are given. Then bifurcation diagrams, phase diagrams, time history diagrams and spectrum graphs are employed to study the nonlinear vibration characteristics and the acoustic radiation characteristics. It is inferred that the present work proposes a semi-analytical and semi-numerical method for the nonlinear vibro-acoustic coupling system. The motions of the forces transmitted to the cylinder are periodic motions, quasi-periodic motions, and so on. The vibro-acoustic characteristics of shell are dominated by the rotation frequency of the rotor, while there are some harmonic components dominating the vibro-acoustic characteristics at resonant frequencies.