How does this oscillator work under a constant DC voltage?
In real life, an oscillator will start up by amplifying transistor/resistor noise, and/or from the circuit power-on transient.

In a simulator, noise may well be absent in a simple transistor model, and the initial DC bias point analysis will leave all the components with nice quiescent voltages on them. The transistor will then just sit there amplifying nothing into nothing.

The easiest way to kick an oscillator into life is to use the simulator's initial conditions control on one of the capacitors in the tank circuit. This means that the AC simulation will start with something other than 'nothing' to amplify. 

Most simulators have a way of setting the voltage on a capacitor to a specific value, either a 'use initial conditions' checkbox in the component dialogue, or a text directive included in the circuit. Read the manual for your simulator. If it doesn't have initial conditions, then switch to a better simulator. LTSpice is good, if clunky, and comes at the right price.