At a press briefing last Thursday to reveal its £5m solution to excessive movement in the bridge, the firm admitted that its reputation depended on its coming up with the right answer.
Arup is proposing to install a passive damping system, which it will test by installing a limited number of dampers beneath the bridge. These will be used to check the bridge's actual movement against computer predictions.
Work started on installing the dampers this week and their effect is due to be tested over Christmas. Bob Emerson, chairman of Arup, said: "The installation of the prototype will be completed before Christmas although the tests themselves might run into the middle of January."
It is understood that the bridge, in central London, will be tested first by a mechanical shaker and then by a group of 300 pedestrians.
Michael Willford, Arup's director responsible for dynamic modelling on the bridge, admitted that the firm was under extreme pressure.
He said: "This solution has got to work. There must be no further surprises in store."
A decision has yet to be made over who will foot the full bill for the modifications. Emerson added: "Arup is in discussion with the main parties on payment for the final solution."
Specialist steel fabrication and bridge building contractor Cleveland Bridge was due to begin installing dampers on the centre span of the bridge this week. It will fit four
V-shaped steel braces, two viscous dampers and one tuned-mass damper beneath the deck of the bridge's centre span.
This solution has got to work. There must be no further surprises
Michael Willford, Arup
The full solution will involve the installation of both types of dampers beneath the entire deck of the bridge.
A planning application for the modifications was lodged last week.
Millennium Trust chairman David Bell said work would take six months once tests were complete.
Viscous dampers work like shock absorbers in a car. They comprise a piston that moves in and out of an oil-filled cylinder. Those being fitted to the bridge are high-specification versions originally developed for use on military and space exploration vehicles. These are being used to cut down on maintenance.
These dampers will be attached to a series of opposed V-shaped braces fitted beneath the deck of the bridge.
The bracing will act to limit horizontal movement in the bridge by transmitting energy to the viscous dampers.
Tuned mass dampers will also be fitted beneath the deck. These are large weights that provide additional horizontal movement control.
Foster and Partners had weekly meetings with Arup while the solution was being developed.
A rival bridge designer said: "It is a robust solution. Using the system will allow Arup to fine-tune the solution by adjusting the dampers."