Analysis of Structural Vibration and Damping Mechanisms for Optimal Displacement/Deformation

Abstract

Structures are defined usually with respect to tolerable/permissible limiting conditions of displacement, deformation and stresses etc, which enables continuous load application and static equilibrium, otherwise the equilibrium becomes dynamical resulting in unstable structural system. This study aims to evaluate, effect of vibrations and damping on structural stability, and identified that vibration is mechanical phenomenon involving action of impact forces that produces oscillatory motion on the structure and characterized with oscillations, displacement, and frequency (f = w/2Л) about a static mean position of rest (ie, F = ma = 0). The research study entails review of literatures and work on structural vibration, stability and damping mechanism to restraint effect within permissible limits. Dampers are commonly used to constraint structures to infinitesimal displacement during load application, also the paper identify that vibratory systems are means of storing potential energy (mass), kinetic energy (spring) and means by which energy is gradually dissipated through oscillations (ie, F = ma). The motion can be optimized using principle of minimum potential energy and virtual work” expressing workdone on a system undergoing virtual displacement (W = Fδx = 0, because δx = 0). Vibration damping is an influence upon a system that prevents or reduces its oscillation, and is implemented by processes that dissipate energy stored in oscillations. The damping ratio describe the system parameters which varies from undamped (ξ = 0), underdamped (ξ < 1), critically damped (ξ =1) and overdamped (ξ > 1). Static equilibrium requires damping of structures between critically damped and overdamped to ensure minimal oscillatory amplitude as expected for stability and functional performance. Similarly, structural evaluation is implemented using virtual work method,analytically defined as total work done, W = F δs = 0 (ie, δs → 0 or negligible). In conclusion, the paper identify that dynamical tendency is characterized with instability while structural performance is identified with infinitesimal or limit state deformation and displacement; hence corresponding vibratory displacement and oscillations must be minimal using appropriate damping mechanism to reduce the cumulative effect on structural system and to provide stability and safety of structural systems.