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Two simplified methods are introduced in the paper, in which periods and mode shapes are obtained through solving the story lateral stiffness of frameshear wall structures, the method of solving the differential equation and the method of substructure. On the basis of assumption for structure, the assembling strategy of mass matrix and stiffness matrix are discussed specially. The periods and mode shapes can be acquired through both methods and the results are compared and analyzed with PKPM and ANSYS. The computation programs are very convenient and can gain the periods and mode shapes quickly. The methods will create some degree of errors, but it is in the scope of acceptance. They are of great reference to structural designers and scientific researchers. Introduction With the rapid development of computation theory, the computation methods for high-rise buildings have gained great progress, from the initial vibration analysis of plane frame structure to current space finite element analysis[1],the method of analysis is more and more accurate and complex[2,3]. In actual engineering, there is some degree of difficulty to perform a finite element analysis (FEA) for the whole structure, and FEA is only carried out for parts where there is complex stress distribution. Matrix displacement method is used in the analysis in the high-rise building analysis software, but it is improved. Wall element is introduced in many software, the bar element is still adopted for frame column and beam, but the shear wall is not modeled by thin-wall column, but by shell element which will make the computing results more accurate. The modal reduction is used in the Matrix displacement method for the assembling of lateral stiffness matrix, but modal reduction is complex when the sum of structural elements is large. In the paper, two simplified methods developed based on Fortran are introduced and checked by PKPM and ANSYS, which can be used for solving the dynamic characters, guarantee the validity of computing results and obtain periods and mode shapes quickly and accurately. Basis of structural dynamics Finite element analysis (FEA) is the theoretical basis of the two methods, its basic procedure is: discretization of structure, determination of displacement pattern, analysis of element characteristics and establish and solve equation. Eigen-equation of un-damped free vibration is expressed as[4,5] { } 2 | [ ] [ ] | 0 K M ω δ − = (1) Where, [ ] K and [ ] M is stiffness and mass matrix, ω is circular frequency; { } δ is eigenvector. Basic assumptions. The stiffness is rigid in the floor plane and the stiffness is ignored outside the plane. All lateral structures are connected with the rigid floors and the floors can be seen as a horizontal hinged link between the lateral structures. The influence of torsion is not considered and the horizontal displacement of lateral structure at the same floor is equal. 0749 2nd International Conference on Electronic & Mechanical Engineering and Information Technology (EMEIT-2012) Published by Atlantis Press, Paris, France. © the authors The plane stiffness of the lateral structure is infinite and its out-of-plane stiffness is very small and can be ignored. The shear walls can be united into an equivalent shear wall, its synthesized bending stiffness is the total of synthesized bending stiffness of each shear wall. All the frames can be united into an equivalent frame and its synthesized lateral stiffness is the total of synthesized lateral stiffness of each frame. All the coupling beams can be united into a total coupling beam, the restraining moment of the total coupling beam is the sum of restraining moment of each coupling beam. Method of solving the differential equation. The shear wall and frame are seen as an elastic foundation beam and elastic foundation effectively, the deformation of the shear wall and frame are compatible along with the height. Setup of differential equation. The relation of the shear wall between the load and internal force, which is a rigid system, is 2 2 W W d y M EI dx = (2) 3 3 W W d y V m EI dx − = − (3)

Study on simplified calculation method for the vibration characters of frame-shear wall structures