Tried securing moulding, loose plastic parts, etc. near firewall under hood close to windshield, on passenger side, but didn't stop the fluttering sound. Sounds like it's in or near the firewall or vent system on the passenger side. The faster I go, the more it seems to flutter. I have heard similar complaints from other owners, but see no answers yet. It happens whenever traveling between 35mph and faster. Happens with convertible top up and with top down. Do not think convertible has anything to do with it.
I have a fluttering noise at 35mph and faster from passger side of my '03 solara on 2003 Toyota Solara
It is common for that engine to crack the exhaust manifold and make that fluttering type of sound. Real easy to see on the front manifold a little harder at the rear. Look for what looks like a gray or black pencil mark around one of the runners of the exhaust manifold.
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I think you should check the tire that side for rocks caught in the threads of the tire and check the flap around the finder if its not that it could be the wheel seal in the housing