People generally refer to the sign of the effective damping coefficient, the multiplier of the mechanical surface displacement rate; when the coefficient is positive then it is referred to as positive damping or otherwise. In this case, the mechanical work done by the air on the mechanical structure is negative, that is the air force on the structure resists the motion of the structure hence, negative mechanical work is done by the structure system on the surrounding external air. But because the structure as a system exports external work (does work on the surroundings) in this way, that work is thermo-dynamically generally defined as a positive system work in an energy equilibrium equation. NOTE: Mechanical work and system work always have opposite signs. The mechanical definition of work is the traditional definition or calculation of incremental work done as the dot product of a force vector with the incremental displacement vector. That should tell you why I just made the preceeding statement about mechanical work and system work being of opposite signs!

Thank you Hayrani Oz

You mean that sign of effective damping coefficient is positive when the air resist the moving of the building by exerting negative mechanical work.

But how negative damping coefficient could produce especially when building surrounded with air from all direction, so any building movement will absorb work producing +ve damping

It depends on the phase angle between the work producing force and displacement components. Opposing sense force component extracts work from the system, nonopposing/supporting sense force component adds work to the system. Systemwise, the former is positive work, the latter is negative work. The surrounding air as a system does the opposite work of these. In an aero-structure environment both can happen. I also rephrased my previous answer above.

thank you Hayrani Oz