Nonlinear Interactions of Acoustic Fields with Bodies Under Harmonic Excitations.

The multidimensional finite amplitude waves produced in a lossless fluid by the harmonic pulsations of a body in the flow field are examined. The pulsations are assumed to be such that they are expandable in a Fourier series in time and the independent coordinates describing the surface of the body. The analysis is applicable to isentropic gases and nondissipative liquids. The equations describing the dimensionless velocity potential and the fluid pressure are derived along with the boundary conditions at the surface of the body. The first problem considered is the interaction of an acoustic field with a plate undergoing near resonant flexations. The method of renormalization is used to obtain uniformly valid expansions for the velocity components and the pressure by coordinate strainings in two dimensions. The technique is applied to the finite amplitude waves produced by the pulsations of an infinite circular cylinder, a finite circular cylinder, and a sphere.