The Beach Boys are one of the biggest mirages in rock history. From the jangly surfing-and-hot-rod ditties of their nascent years to the glorious, gossamer harmonies they became famous for, their songs always sounded soaked in California sunshine. Behind the harmonic aura of summer fun, however, the offstage dynamics were often dissonant — and the vibrations often anything but good.

The six-decade saga of the band — particularly the founding nucleus of brothers Brian, Carl and Dennis Wilson and cousin Mike Love — has been wrought with tragic overtones: the alleged early abuse and outright theft the Wilsons suffered at the hands of their father-manager; drummer Dennis’s Manson family entanglement and drowning at age 39; guitarist Carl’s succumbing to lung cancer at age 51; and, of course, the well-publicized psychological torments of songwriter and musical polymath Brian.Lead singer Love, the bearer of one of rock’s most recognizable names, has emerged as the enduring standard bearer of the Beach Boys brand, billed on its website as The Beach Boys/Mike Love. The original frontman is still at the forefront, the lone, surviving feel-good story of a band that, despite it all, is still all about feeling good — and after 64 years, still touring, including a show at the Broward Center on March 1 and two shows at the Kravis Center in West Palm Beach on March 6.

It didn’t come easy for Love. In the ’90s, he sued Brian Wilson claiming he’d been frozen out of songwriti.