Theoretical analysis and parametric design of rocking coupled wall with inerter system

A coupled wall can be transformed into a structural control device by the introduction of damped coupling and rocking mechanisms. To further enhance the structural control efficiency, inerter systems are proposed as the damped coupling devices in the rocking coupled wall. The theoretical model which can represent the key mechanism of the multi-pier rocking coupled wall with inerter systems is presented. The expression for the mechanical energy of each component is derived and then the corresponding equations of motion for the rocking coupled wall with inerter systems are established according to Lagrange’s equation. Closed-form expressions of stochastic seismic responses of the rocking coupled wall with inerter systems are derived subsequently. The demand-oriented design philosophy and the damping enhancement maximization principle of the inerter system are adopted as guidance to design the key parameters of the rocking coupled wall with inerter systems. A series of concise closed-form design formulae are derived to achieve the desired damping ratio and maximize the damping enhancement of inerter systems. Finally, the proposed mechanical model and formulae are validated by the design and analysis of a ten-story rocking coupled wall under seismic excitations. It is shown that the results of dynamic time-history analyses are in good agreement with the results of the theoretical formulae.