A continuous-discrete approach for the free vibration analysis of coupled shear walls based on foundations flexible in rotational, vertical and horizontal directions is proposed in this paper. The coupled shear wall structural system is treated as a continuous system (or continuous medium) and a discrete system (or lumped mass system) at different stages of dynamic analysis. The advantages of the two types of analytical systems are fully utilised. The accuracy and efficiency of the methodology is verified by comparing the frequencies of a pair of cantilever walls (a special case of coupled shear walls) obtained by the proposed approach with those obtained by classical methods. The minimum number of lumped masses needed in the proposed approach to obtain an acceptably accurate value of natural frequency for any vibration mode of coupled wall structures on flexible foundations is discussed. Numerical studies are carried out with the hybrid approach to investigate the effects of foundation flexibility on the free vibration characteristics of coupled shear wall systems.

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