Vibration Analysis and the Minimization of Structural Response in High Impact Lateral Loading Environment

Lateral loads act transversely to longitudinal axis of high-rise structures including offshore platforms, and dams etc, the line of action together with that of gravity load produces a resultant line of action, characterized with impending motion (∑F = ma ≠ 0) and finite displacement (ie, θ and ∆) which produces vibration of the structural system, an undesirable effect on structural performance and stability. The paper identifies the loading intensity acting on structural system that influence on stability and the importance of accurately predicting structural responses that enables stability within permissible limits and static equilibrium state for performance. Vibration is dynamical structural phenomenon that produce oscillatory motion, expressed by equations, F = -kx = m , and -kx/m =  . Solution of the equation is a sinusoidal position function x(t) = A cos(wt-φ), where A is the amplitude (or maximum displacement. The study identified that motion of vibratory system can be optimized using principle of minimum potential energy and virtual work method, which express that work done on system undergoing virtual displacement is negligible, ie, W = F ∂x ≈ 0, since ∂x ≈ 0, an infinitesimal displacement. Damping mechanism are often required to reduce the motion potential, and defined as influence upon a system to reduce oscillation to minimal and insignificant state, which was further enumerated with concept of wave interference (W₁ + W₂ = 0, ie, destructive interference). Similarly, damping ratio is the system parameters that varies from undamped (ξ = 0), underdamped (ξ < 1), critically damped (ξ =1) and overdamped (ξ > 1). In conclusion, the paper indicated that dynamical tendency is characterized with instability of structural systems with impending motion, hence corresponding vibratory displacement and amplitude of oscillations must be very minimal within structural code permissible limits.