Abstract: Assembling of two workpieces by the ultrasonic staking or riveting method comprises the providing of a first thermoplastic workpiece having an upstanding stud, an apertured second workpiece juxtaposed on the first workpiece so that the stud protrudes through the aperture of the first workpiece, and a horn applying ultrasonic energy to the upstanding, free end of the stud by forced contact between the stud end and the horn. The improvement comprises the application of ultrasonic energy to the horn during brief time periods which alternate with brief time periods during which the horn, while still in contact with the stud end, is substantially inactive.