Dynamic Analysis of SDoF&MDoF Systems Subjected to Sinusoidal, Step & Ramp Loading Using MATLAB

Abstract

Impulsive force is a force of large magnitude that acts over a short time interval. In practice, vehicles and cranes are subjected to impulsive loads. In this chapter, the response of the single-degree-of freedom system with or without damping subjected to impulsive loads is considered. The concept of response spectrum, which is a very useful tool in the design, is also illustrated. Structural engineers are familiar with the analysis of structures for static loads in which a load is applied to the structure and a single solution is obtained for the resulting displacements and member forces. When considering the analysis of structures for dynamic loads, the term dynamic simply means “time-varying.” Hence, the loading and all aspects of the response vary with time. This results in possible solutions at each instant during the time interval under consideration. From an engineering standpoint, the maximum values of the structural response are usually the ones of particular interest, especially when considering the case of structural design. Two different approaches, which are characterized as either deterministic or nondeterministic, can be used for evaluating the structural response to dynamic loads. If the time variation of the loading is fully known, the analysis of the structural response is referred to as a deterministic analysis. This is the case even if the loading is highly oscillatory or irregular in character. The analysis leads to a time history of the displacements in the structure corresponding to the prescribed time history of the loading. Other response parameters such as member forces and relative member displacements are then determined from the displacement history. If the time variation of the dynamic load is not completely known but can be defined in a statistical sense, the loading is referred to as a random dynamic loading, and the analysis is referred to as nondeterministic. The nondeterministic analysis provides information about the displacements in a statistical sense, which results from the statistically defined loading. Hence, the time variation of the displacements is not determined, and other response parameters must be evaluated directly from an independent nondeterministic analysis rather than from the displacement results. Methods for nondeterministic analysis are described in books on random vibration.