Engineer Arup has chosen its preferred solution to curb the wobble on the Millennium Bridge across the Thames.

The preferred solution, to be revealed in a report next week, is understood to consist of a passive damping system mounted beneath the deck of the £18m bridge, plus secondary bracing added at each end of the structure to stiffen it.

The passive damping system – much cheaper than the computer-controlled active system the engineers also investigated – involves fitting a series of steel boxes at intervals along the Foster and Partners-designed bridge's underside. Each box contains a weight "tuned" to respond to movement of a certain frequency. When the weight shifts, springs in the box absorb the movement and prevent the sway of the bridge.

The system will not prevent all swaying, since it can only be tuned to correct one frequency of movement. The bridge sways at different frequencies depending on the number of people crossing it, with the most severe movement occurring when large numbers use the bridge. It is thought the engineers will propose correcting only this extreme movement.

In addition, steel A-frames or cross-braces will be welded between the deck and the lateral cables at both ends of the bridge. This secondary bracing will give the structure added stiffness.

The proposals still have to be approved by the client, the Millennium Bridge Trust. Remedial work could delay the opening of the bridge until 2002.