The effect of damping on dynamic response of underground tunnel structures

The beam on elastic foundation model is used to simulate the underground tunnels structures;a vibration equation on two-parameter foundation considering the bending moment,axial force,shear deformation,external and internal damping is obtained.An approximate method for calculating of displacement of underground pipes is used to compute the displacement of underground tunnels structures,avoiding the trouble of integral transform.In numerical example involving the damping.it is convenient to use a special separated variable method to obtain natural frequencies and damping ratio,the attenuation of displacement considering damping.It is concluded that for underground structures,the effect of internal damping can be neglected.