What was found
AT FL380, DESCENDED TO FL240. DISCONNECTED THE AUTOTHROTTLES & PULLED THE ENGS TO IDLE. ACFT STARTED TO SHAKE WITH A LOW FREQUENCY. IMMEDIATELY CHECKED IF SPOILERS DEPLOYED AS IT FELT LIKE AN INTENSIFIED SPOILER DEPLOYMENT. THERE WAS NO SPOILER DEPLOYMENT. GOT A RED LT ENGINE TGT ICAS MESSAGE & SAW NEEDLE IN RED ARC WHILE BOTH ENGS AT IDLE. PERFORMED APPLICABLE CHKLIST & PERFORMED AN ENGINE SHUTDOWN OF LT ENG. DECLARED AN EMERGENCY WITH ATC. ONCE ENG SHUTDOWN & SECURED, AIRCRAFT FLEW NORMAL FOR SINGLE ENG OPS. NO VIBRATION. CONTINUED TO KVNY AS WE HAD ALREADY PASSED KLAS AND I WOULD HAVE DONE A SLOW AND STABLE DESCENT INTO VAN NUYS. ONCE LANDED, FIRE TRUCKS WERE WAITING. TAXI’D INTO FBO WITHOUT INCIDENT. AFTER PAX DISEMBARKED, CHECKED THE EXCEEDANCES PAGE & NONE LISTED. LOOKED AT HP FAN BLADES & SEEMED OK. THERE WAS NO OIL THAT WAS ABNORMAL UNDERNEATH ENG OR ANY FUEL LEAKS.