Since the beginning of 1980s, Adomian has introduced the so called Decomposition Method for solving linear and nonlinear, ordinary and partial differential and integro-differential equations in physics. Using ADM, solution is obtained as sum of an infinite series with elegantly computable components which rapidly converges to the true solution with high accuracy. In recent years, researchers have shown a great interest in ADM for its application to a wide range of problems in applied sciences. In this paper, this technique is applied to solve free longitudinal vibration of a uniform rod with various boundary conditions. At first, the frequency equation is obtained analytically and then ADM is used to calculate the natural frequencies and mode shapes. Also the effect of mass and spring stiffness at the boundary on natural frequencies is evaluated.

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