Papers by Keyword: Non-Uniform Beam

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Authors: Wen Wen Jia, Deng Feng Wang
Abstract: To simplify the internal force evaluation of portal frame being composed of non-uniform members, the force method was used to solve internal force of every key section of the non-uniform beam in portal frame with single-span. Gauss numerical integration method was used to simplify the complex integration when the deformation energy was calculated. Under the precondition of satisfied accuracy, the direct expressions of bending momentshear force and axial force of every key section of beam were obtained. The research work can be used as reference for the evaluation and design of portal frame members.
Authors: Bo Qian
Abstract: Recursive and inexplicit differential equation of the second order with variable coefficients is derived from the fourth order linear homogeneous differential equation with variable coefficients of transverse vibration of non-uniform beam, which is about deflection and bending moment according to boundary conditions and order reduction. By finite difference method, numerical computation and accuracy are studied for natural frequency of transverse vibration for simply supported beam of non-uniform. Theoretical analysis and orthogonal computation examples show that numerical computation algorithm is very simple, and accuracy of computation depends on variety rate of gradually changed cross section in vertical direction and numbers of computation step, which is independent of width and length of beam; numerical accuracy of computation is estimable for given length or numbers of computation step; and reasonable length or numbers of computation step is determinable for given accuracy demand.
Authors: Zhi Gang Yu, Fu Lei Chu, Yue Cheng
Abstract: In this paper, a method is presented to facilitate the computation of dynamic properties of non-uniform beams with any number of cracks. Based on the Frobenius method, an analytical solution of vibration equation of non-uniform beams is obtained. In combination with the line spring model of crack, the transfer matrices for non-uniform beam element and crack are established respectively. Then the global transfer matrix can be simply formulated, from which the frequency equation in the form of 2×2 determinant is derived. Due to the decrease in the determinant order as compared with previously developed procedures, significant savings in the computational task would be achieved by the present method.
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