  The periodic solutions of a type of nonlinear hyperbolic partial differential
equations with a localized nonlinearity are investigated. For instance, these
equations are known to describe several acoustical systems with fluid-structure
interaction. It also encompasses particular types of delay differential
equations. These systems undergo a bifurcation with the appearance of a small
amplitude periodic regime. Assuming a certain regularity of the oscillating
solution, several of its properties around the bifurcation are given:
bifurcation point, dependence of both the amplitude and period with respect to
the bifurcation parameter, and law of decrease of the Fourier series
components. All the properties of the standard Hopf bifurcation in the
non-hyperbolic case are retrieved. In addition, this study is based on a
Fourier domain analysis and the harmonic balance method has been extended to
the class of infinite dimensional problems hereby considered. Estimates on the
errors made if the Fourier series is truncated are provided.
