GA SMA AFTER LNDG CROSSED PARALLEL RWY; AS IMPLIED BY GND CTLR INSTRUCTIONS; IN FRONT OF LNDG TRAFFIC AFTER TWR HAD INSTRUCTED TO HOLD SHORT.

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I RETURNED FROM A LCL TRNING FLT. PER TWR; WE LANDED ON RWY 4R AT MDW. SHORTLY AFTER OUR T/D; THE ACFT EXPERIENCED SEVERE NOSE SHIMMY VIBRATION. WE SLOWED DOWN AND TURNED LEFT AS PER TWR INSTRUCTIONS OFF OF RWY 4R. WE SWITCHED TO GND AND THEY TOLD US TO TAXI TO THE N RAMP. WE PROCEEDED TO DO SO. FIVE SECS LATER; GND ASKED US HOW DO WE HEAR. WE TOLD THEM LOUD AND CLEAR. AFTER 15 SECS GND TOLD US TO CALL THE TWR. WE DID AND TWR TOLD US WE XED AN ACTIVE RWY (4L) W/O THEIR PERMISSION. TWR SAID AS WE WERE LNDG HE TOLD US TO TURN LEFT AND HOLD SHORT OF RWY 4L AND REMAIN WITH HIM. WE OBVIOUSLY DID NOT HEAR HIM DUE TO THE EXTREME NOISE CAUSED BY THE NOSE SHIMMY. GND SHOULD NOT HAVE TOLD US TO TAXI TO THE N RAMP. TWR TOLD US ON THE PHONE THAT THERE WAS LNDG TFC ROLLING ON RWY 4L AT THE TIME WE XED RWY 4L. CALLBACK CONVERSATION WITH RPTR REVEALED THE FOLLOWING: TAPES WERE REVIEWED WITH THE TWR AND THE TWR DID TELL THE SMA TO HOLD SHORT AND STAY WITH HIM; BUT RPTR FIGURES THE NOISE FROM THE NOSE WHEEL VIOLENT SHIMMY WAS PROBABLY WHY THEY MISSED IT. STATED IT WAS VERY DARK AND WHEN HE CALLED GND CTL THEY APPARENTLY DIDN'T LOOK TOO CLOSELY AND FIGURED SINCE HE WAS ON GND FREQ; HE WAS ALREADY ACROSS THE LEFT RWY. HE ESTIMATED THE LNDG TFC ON THE LEFT RWY WAS 2500-3000' AWAY; ALTHOUGH HE DID NOT ACTUALLY SEE THE TFC. TWR CHIEF HAD SAID HE WOULD TURN THE INCIDENT OVER TO GADO; BUT HE HAS HEARD NOTHING FROM GADO TO THIS DATE; SO DOUBT IF AFTER A MONTH GADO IS GOING TO DO ANYTHING OR THE TWR MAY HAVE DECIDED NOT TO RPT TO GADO.