Investigating The Dynamic Buckling of A Column with Variable Section and Viscous Damper under Intermittent Axial Load

Document Type : Original Research

Authors
A. H. Taherkhani 1
M. Amin Afshar 2
1 Graduated Student, Department of Technology and Engineering, Imam Khomeini International University, Qazvin, P.O. Box 34148-96818, Iran
2 Assistant professor, Department of Technology and Engineering, Imam Khomeini International University, Qazvin, P.O. Box 34148-96818, Iran
10.22034/25.1.7
Abstract
The use of members with non-uniform cross-sections due to the reduction of the number of materials and the weight of the structure is widely used in industrial structures and metal bridges. Buckling is one of the major problems engineers face in the design of axial compression members (columns). For this reason, several researches have been conducted by researchers in the field of column buckling. Most of the previous research is limited to investigating stability and buckling in Non-prismatic elastic columns in the static state. During an earthquake, the structure is subjected to vertical and lateral earthquake loads. To evaluate the dynamic behavior of the structure during an earthquake, the stability and dynamic buckling of the column must be evaluated. The effect of the earthquake's vertical load and the dynamic axial load has an effect on the dynamic stability of the member in the form of the second-order effect of buckling. In this article, the dynamic buckling of a column with a variable section and viscous damper under alternating axial load is investigated in a comprehensive model. The alternating axial load effect is assumed as a cosine function and the viscous damping effect at the end of the member is assumed as a Dirac delta function. The changes in the moment of inertia along the length of the column are considered in three modes: linear, cubic, and fourth-order changes. The constituent differential equation includes column strain energy, second order effect of alternating axial load, inertia per unit length of the column, and damping of a viscous damper. To solve the constitutive equation, first the weak form of the governing differential equation is written. Lagrange interpolation functions are used as the shape function and the Fourier function (proposed by Bolotin) as the dynamic response of the equation. In the next step, the matrices of material hardness, geometric hardness, and mass are extracted. After extracting the above matrices, the eigenvalues (Buckling load factor, natural frequency) of the equation are checked. Muller root finding technique is used by coding in MATLAB software to calculate eigenvalues. For accuracy in calculations, the function of the form of the equation is checked by the Lagrange method with the number of thirty terms. Also, finding the roots of the equation to calculate the eigenvalue is done with a step of 0.05 using Mueller's method. The buckling load coefficient of the column is evaluated for different values of the expansion coefficient and the damping percentage of the viscous damper in different boundary conditions. The results show that the mentioned values have a significant effect on the changes in the buckling load factor in terms of excitation frequency and resonance frequency. Depending on the boundary conditions, increasing the opening factor causes the diagram to move to the right or left side of the dimensionless excitation frequency axis. Also, increasing the damping coefficient of the viscous damper causes the diagram to move to the left side of the dimensionless excitation frequency axis. Dimensionless parameters such as bar coefficient, excitation frequency, and opening coefficient have been used to report the dynamic behavior of the set in all the tables and figures. The results of this research can be generalized for the design of columns under periodic axial load. The results of this article are verified and compared with previous research. There is an acceptable agreement between the results of the present article and previous research.

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Modares Civil Engineering journal
Volume 25, Issue 1 - Serial Number 81
March and April 2025
Pages 7-20