Formula for Forced Vibration Analysis of Structures Using Static Factored Response as Equivalent Dynamic Response

Abstract

This Paper proposed and examined a formula for forced vibration analysis of structures using static factored response as equivalent dynamic response. Some methods of dynamic analysis are based on using static factored response as equivalent dynamic response thereby excluding the formulation of the equations of motion for forced vibration. These methods obtain dynamic response by the magnification of static response using the dynamic magnification factor or a modified form of the dynamic magnification factor. Dynamic response obtained by such methods give stress values which differ greatly from the actual. The flaw of these methods consist in magnifying stress values with factors obtained from displacement consideration on a false assumption of direct linear variation in the stress-displacement relationship. Based on the flexible frame model and stiffness formulation a formula for forced vibration analysis of structures using static factored response as equivalent dynamic response was developed with forced vibration equations and appropriate stress-displacement relationship. Though the use of this formula excludes the formulation of the equation of motion for forced vibration, the results obtained by its application to an MDOF Frame agree with that of the exact method using the flexible frame model. The formula can be used in practice for forced vibration analysis of structures or serve as control for the exact methods.