A process is provided for ultrasonically welding a rigid thermoplastic, such as acrylic, and a flexible thermoplastic, such a polyvinyl chloride (PVC) doped with plasticizers. The rigid piece includes an energy director where the joint is to be located. The energy director includes first and second ridges running the length of the joint and a groove running between the first and second ridges. The energy director is placed against one side of the flexible piece, and an ultrasonic horn against the other side opposite the energy director. The two pieces are then welded together using standard ultrasonic technology. The shape of the energy director promotes the melting and flow of both pieces as they are being welded together.