Abstract
A generalized elastic coordinate method (GECM) is proposed for the vibrational (elastic) response analysis of unconstrained structural dynamics. Firstly, the generalized rigid body and elastic coordinates are defined to describe the overall motion of a discrete unconstrained structure. Secondly, the corresponding equations of motion for generalized elastic coordinates are established with a tiny computational cost, and the stiffness matrix is still sparse. Finally, the elastic deformation in physical space can be exactly caught by the proposed equations of motion after determining the rigid body modes and the coordinate system of the rigid body motion. Different from directly solving the original semi-positive definite system in physical space, in which the overall displacement can only obtain, and the direct modal projection, the modal truncation error problem can be effectively overcome based on the established positive definite system when the modal order reduction is carried out. In light of this, the modal truncation error correction of the elastic displacement for the transient time domain and steady-state frequency domain of unconstrained structures is directly realized, summed the above as GECM, and the validity and practicability are illustrated through the numerical examples.
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