DYNAMIC ANALYSIS OF A CRACKED BEAM UNDER MOVING LOAD BASED ON MODIFIED ADOMIAN DECOMPOSITION METHOD

Abstract

It is well known that continuous system motion equations are based on partial differential equations. Their solutions are more difficult than discrete systems’ equations of motions, especially if the equations of motions are non-linear. Different efforts have been implemented to solve non-linear partial differential equations for a long time. Researchers have tried to use different methods for this purpose. Modified Adomian Decomposition Method (MADM) is a promising method and has been applied to solve non-linear partial differential equations obtained in engineering systems. In this article, MADM is used to investigate the forced vibration of the Euler-Bernoulli (EB) cracked beams under a moving load. For this purpose, MADM was used to create the mentioned vibration response. This model consists of moving load acting on two continuous segments where the crack is modeled as a rotational spring with sectional flexibility. For this purpose, the equations of motion with a fourth order have been used. They are non-homogenous partial differential equations, which were used for mathematical modeling. Dynamic response was analyzed to understand the cracked supported beam beneath the moving load, which revealed the impact of concentrated force on crack location as well as extension. Some numerical results were presented by using MATLAB software to compute the vibration analysis and plot the deflection. The solution and its methodology were verified with the help of some studies. Results have shown that MADM is effective and accurate for vibration analysis of cracked beams under a moving load.