the lightweight component is equipped with two cover layers , which are made of a wood material , for example , and a filling disposed in between said layers after cutting everything to size , having an edge support comprising thermoplastic material . this is done in that the edge support is anchored both in the first cover layer and in the second cover layer starting from the narrow side , wherein the anchoring is achieved in that the edge support is brought into contact with the respective cover layer and mechanical vibrations are coupled into the edge support by a sonotrode engaging from the narrow side , wherein the edge support at the same time is pressed against the cover layer such that in the region of a transition between the thermoplastic material and the wood material of the cover layer part of the thermoplastic material is liquefied and pushed into the cover layer material , thereby producing a positively engaged anchoring after hardening .