The unification differential equation of buckling and motion of viscoelastic beam subjected to the uniformly distributed follower forces in time domain was established by differential operators including extension viscosity, shearing viscosity and moment of inertia. According to the unification differential equation, dynamic stability of three-parameter model of viscoelastic beams subjected to follower forces with clamped-free supported boundary condition was firstly analyzed by power series. The relations of the follower force versus vibration frequency and decay coefficient were obtained, so was the effect of viscous coefficient on the critical load of beams.

The vertical bearing capacity of a special pile group of platform in an offshore gas field has been studied. Large diameter d (2.134 m), deep penetration l (96 m), small spacing sa (3.507 m), and only one row piles are the usual characteristics of the pile group foundation in offshore engineering. According to the requirements of the related design code, the super pile group effect has to be considered. However, with the usual design code, when sa/d, the ratio of spacing to diameter, is less than 2.0, there is no way to consider the pile group effect. In this paper, considering the occlusion effect of soil plug of pipe pile, several methods have been introduced to study the super pile group effect of the vertical bearing capacity. These methods include linear elastic theory method, the method recommended by the Code of Pile Foundation in Port Engineering (JTJ254-98), and the method with virtue of the existing pile group model test results. Meanwhile, the plugged and unplugged conditions have been considered, respectively. Through the analysis, the factors of safety in extreme and normal operation states are obtained, and the results satisfy the design specifications.

The method of trigonometric series is one of widely used methods for calculating artificial ground motion. But using this method the speed of time, it was found that the zero line must exist the phenomenon of drift. This text fore person the foundation of the research up, a kind of more perfect model of differentiable nonsingular strength envelope function is proposed .a better resolve this problem. Passing the calculation proved that the new method is reasonable and effective.