problem with arduino uno + L293D shield

hi everyone, i'm Michele from Italy.

i've got a strange problem:

i'm using Adafruit L293D shield motor with arduino uno to drive a double coil stepper motor.

the motor run correctly and it seems all right with my code but, if i disconnect my usb cable from pc after transferring code, the motor stop running and start to vibrate, if i reconnect usb cable to arduino and pc, all return to run correctly.

can some one explain me the reason?

thankyou all

When you disconnect the USB cable, what is supplying power to the Arduino and the motor shield?