There are quite a few visible errors in your breadboard layout.
You have pin 2 of the first 555 connected to the wrong side of the pushbutton. It is shorted to the 0V rail. This will keep the monostable permanently triggered; the button has no effect.
The wire from pin 3 of the first 555 doesn't seem to connect to anything. It looks like it should connect to pin 4 of the second 555, but there's a gap, with a brown link in between that doesn't connect to either wire.
The trimpot connected to the first 555 isn't connected properly. When a pot or trimpot is drawn as a variable resistor on a schematic, i.e. only two connection points, you need to use one (either one) of the end pins and the wiper pin. (The other end pin may be connected to the wiper as well; this makes no difference.) You have three separate connections to the three terminals of the trimpot. The capacitor needs to be connected to the wiper, not the other end, i.e. it needs to be connected to pins 6 and 7 of the 555.
The trimpot on the second 555 may be wrong as well. You have the top right pin connected to pin 7, which is right, and the wiper connected to pins 2 and 6, which is right, but you have a black link wire connected to the top left pin. I can't see where it goes - it's obscured by the electrolytic, which (I hope) connects to the wiper of the trimpot. That black link shouldn't go anywhere.
The third trimpot is wrong as well. The top right pin is OK, it's connected to pin 7 of the third 555. The wiper is connected to pins 2 and 6, which is right too. But the 10 nF capacitor appears to be connected to the top left end of the trimpot (which shouldn't be connected to anything) instead of to the wiper.
Also make sure you have the right kind of piezo device. There are two kinds. You need the simplest kind, which contains just a piezoelectric transducer element and must be driven with an audio-frequency AC voltage (this is generated by the third 555 in your circuit). For example:
http://www.digikey.com/product-detail/en/CEB-20D64/102-1126-ND/412385 (this one has no plastic enclosure) or
http://www.digikey.com/product-detail/en/PT-2207/433-1058-ND/1245312 (this one has a plastic enclosure and two pins).
The other kind includes an oscillator, and must be powered from a DC supply. Its frequency is fixed. For example:
http://www.digikey.com/product-detail/en/PK-12N40PQ/458-1066-ND/969793