Converting optical energy to electric energy is a huge business based on the photovoltaic effect. Is there an analogous effect for phonons? Are ther devices which convert phonon energy to electric energy
Yes. The Seebeck effect, for example, is the direct conversion of thermal gradient to electric voltage. It is used in the small scale in thermocouples to measure temperatures electronically, or in the larger scales in thermoelectric generators for power generation.
In fact, many of the long-range space probes launched by NASA get power this way. Radioactive material generates heat on decay, which gets converted to electricity, which then allows probes like Voyager 2 to have power faraway from the sun where solar power is not available.
How about the Piezo-electric effect?
if I'm not mistaken, pressure on the crystal is in essence equal to long-wavelength phonons.
They're don't seem to contain exactly what you're after (haven't read them thoroughly though), but are related nonetheless. At least they are a hint that a workable device to convert short-wavelength phonons to electrical energy is currently only available on the nano-scale.