| In the detection of prestressed structure, it is an important method that evaluates the health situation of prestressed structure by the actual prestressing force. It has intrinsic relation between the natural frequency and actual prestressing force in prestressed structure. The natural frequency will increase as the increasing of the prestressing force. It is not agree with the classical theory. To analyze the natural frequency of the prestressed structure by using the finite element programming which based on classical theory is not appropriate. Because of the limitation of commercial finite element software, it is necessary to develop finite element program about prestressed structure. This test develop finite element modal analysis program about bonded prestressed simple supported concrete beam based on the basic theory of finite element and prestressed concrete. The up-to-date research findings are used and the contribution to stiffness matrix of prestressing force is considered.In this test, the dynamic finite element program of bonded prestressed concrete beam is designed. The concrete element is simulated by quadrilateral isoperimetric element. And the steel is distributed to concrete. The linear elastic constitutive relationship is used. The contribution of prestressed force of steel is considered as amendment to stiffness matrix according to correlation documentation. The generalized Jacobi method and subspace interaction method were used to solve the eigenvalue problem. The algorithm of generalized eigenvalue problem and standard eigenvalue problem is considered. And the contribution of lumped mass matrices and uniform mass matrices is considered.At last, base on the experiment of three bonded prestressed concrete simple supported beam, the natural frequency of the beam is calculated by the program. Comparing with the experimental result, the precision of the program is verified. And the test paved the way for further research... |
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