Analytical solution of vibration of simply supported beam under eccentric axial compressive loading.

A Pushrod is acting as a slender beam under axial loading and has a variety of applications, like in the automobile industry. For study purposes, a pushrod has been considered which is made of a superelastic shape memory alloy of a circular cross-section. The behavior of the pushrod is scrutinized during the applied force of vibration acting uniformly and eccentrically upon it. These dynamic loadings render a significant impact on its elastic behavior and a constructive formula for the deflection of the beam from its neutral axis is introduced. With this equation, the elastic curve deviations from its initial position are analyzed and its response to the increase in the number of modes is evaluated. The deflection of the beam is highest when the mode number is 1 and with the raise of modal shapes, the deflection tends to get decreased. A comparison with the static beam under affiliated force depicts that the deflection escalates in the beam under dynamic loading. With the change of force functions, different deflection curves have been calculated and from their comparison, the characteristics of this slender pushrod have divulged its other features too. For engineering structure study and design, vibration analysis has been marked as a must-to-do list. [ABSTRACT FROM AUTHOR]