Abstract:

The dynamic motion equations of underground structure under horizontal seismic action are obtained. The transcendental equation for the determination of solution coefficients is deduced by using Laplace integral transform method and linking conditions of structure members. Using inverse Laplace integral transform method the equations for the determination of the displacements of the structure and the poles of the transformation parameters of the Laplace transform are obtained. The further study shows that a special relationship exists between the transformation parameters of Laplace transform and natural frequency of structure : . To avoid the difficulty in determining the coefficients of the solution and the poles of the transformation parameters of the Laplace transform in solving the transcendental equation, the authors suggest that the frequency of structural system is figured out firstly by numerical methods; then the structural displacement and internal forces are obtained by using the residue theorem of inverse Laplace transform.

Key words: dynamic analysis, Laplace transform, poles, resonance