3. Single-Degree-of-Freedom Systems

Structural dynamics is the study of systems that are designed to oscillate under the influence of applied loads. The essential features of the response of an oscillating system can be observed in simplest form in a single-degree-of-freedom (SDOF) oscillator. Hence, we start our exploration of structural dynamics here, both to refresh our understanding of how to solve the differential equations that govern these types of systems and to see some of the basic behavioral features of oscillating systems. Among those features, we will find that a linear SDOF system possesses a natural frequency, which is determined by the physical properties of the system, and the system will resonate if excited by a sinusoidal force with a driving frequency equal to the natural frequency. We will examine the effects of viscous damping on the response of the system and consider various loading conditions, including earthquake excitation. Finally, we will extend the formulation to include nonlinear response of the restoring force elements and develop a framework for the numerical analysis of nonlinear systems that will be useful throughout the book.