pjwhitlow welcome to the forum. Where are you flying to from Frankfurt? What time of year? What airline? What are your other layover options? By the time your incoming Dubrovnik flight lands and gets you to the terminal (sometimes you have to be bussed in at FRA), your onward flight will already be well into the boarding process. That process often includes additional security screening at the gate. Flights usually close the door to boarding 15 min. before flight leaves (sometimes earlier, depends on airline). I myself wouldn't risk it, but if the airline sells it then it's a "legal" connection. I'd also suggest having a robust plan B and researching your passenger rights if you miss the flight to the US.