FOLLOWING TOUCHDOWN FROM A NORMAL LANDING, AND DURING THE INITIAL PORTION OF THE LANDING ROLL, A RIGHT MAIN LANDING GEAR VIBRATION OF INCREASING AMPLITUDE OCCURRED. THE VIBRATION CONTINUED UNTIL THE RIGHT MAIN GEAR FAILED APPROXIMATELY 40 FEET BEFORE THE AIRCRAFT CAME TO A STOP. EXAMINATION REVEALED A FAILURE OF THE TORQUE LINK, SIDE BRACE, AND SHIMMY DAMPENER. THE RIGHT MAIN TIRES FAILED DUE TO FOREIGN OBJECT DAMAGE AND SKIDDING. THE LEFT MAIN TIRES FAILED DUE TO OVERHEAT. AN EMERGENCY EVACUATION WAS CONDUCTED USING THE TAIL CONE EXIT, WHICH WAS DEPLOYED MANUALLY. THERE WAS NO FIRE. Probable Cause: A RIGHT MAIN LANDING GEAR VIBRATION OF UNKNOWN ORIGIN, WHICH RESULTED IN A FAILURE OF THE RIGHT MAIN LANDING GEAR TORQUE LINK AND SIDE BRACE.