Most people settling into their seat for a jukebox musical know what they're in for: a rundown of songs from a certain band, artist or era, linked by a storyline. It doesn't have to be theatre's most complex or compelling storyline – although some shows manage it – but it helps if you can trace enough of a narrative to invest in at least the main characters. Sadly, American Idiot doesn't manage this, and the results are bewildering.

Part of the problem stems from the material on which the show is based – punk band Green Day's 2004 rock opera-cum-concept album of the same name. Both a damning study of post-9/11 America and a call for the disaffected youth to rise up against media indoctrination and President Bush, it seethes with political rage. But as for plot – well, it's called a ‘concept' album for a reason.

The show follows suit. While we see angry young man Johnny leave suburbia in search of city lights and something to believe in, the show's minimal dialogue and unclear lyrics (lost to frenetic performance and an excellent but overpowering five-piece band) make this less a story than a broad portrait of rage and disillusionment. A concept musical if you will.

The concept itself is masterfully realised. The cast has a raw, incensed energy about them, which they maintain indisputably throughout. Racky Plews's direction is endlessly inventive, transforming Sarah Perks's grim, graffitied set from bedsit to bus to supermarket with the use of just a few props. And Plews's choreography is a brilliantly rowdy mash-up of air guitar, simulated sex and middle-finger salutes, which the cast performs with wild-eyed defiance. But one does begin to feel exhausted by the show's pacing. Quieter moments, which could position the thrashing punk-rock set pieces as welcome highs, are few and far between. As such, the score becomes a relentless onslaught of drums and anarchy.

The show has two star turns to tempt audiences: singer-songwriter, Newton Faulkner, as Johnny, and 2011 X Factor finalist, Amelia Lily, as his love interest Whatsername. Both have great voices – Faulkner's in particular shines during the rare acoustic numbers – but they are too often outperformed by the more experienced supporting cast. And with no dialogue and no duets on which to build their relationship, the connection between them remains unconvincing.

For keen Green Day fans or those looking for a jolt of anarchic energy and some head-bangingly good punk rock, American Idiot will of course prove a great night out. But if you're looking for a story to accompany your air guitar, you may want to look elsewhere.

American Idiot runs at the Arts Theatre until 25 September.