  We investigate wave mixing effects in a phononic crystal that couples the
wave dynamics of two channels -- primary and control ones -- via a variable
stiffness mechanism. We demonstrate analytically and numerically that the wave
transmission in the primary channel can be manipulated by the control channel's
signal. We show that the application of control waves allows the selection of a
specific mode through the primary channel. We also demonstrate that the mixing
of two wave modes is possible whereby a modulation effect is observed. A
detailed study of the design parameters is also carried out to optimize the
switching capabilities of the proposed system. Finally, we verify that the
system can fulfill both switching and amplification functionalities,
potentially enabling the realization of an acoustic transistor.
