In this course we're going to study the response of single-degree-of-freedom systems in forced vibration.Learn how structures respond when an excited by an external force, or by ground motion.Content summary:- Equation of motion.- Forced undamped vibration.- Forced viscously damped vibration.- Applications of forced vibration.- Energy balance.An important course in structural dynamicsThe response of single-degree-of-freedom systems in forced vibration constitutes an important course in the field of structural dynamics. Through this mainly theoretical treatment you will learn the important concepts of the response factor, the phase angle, the transient and steady-state motion, and the energy balance in the system. This theory is used in the subsequent courses of this series, to examine the response to more complex types of loading and structures. In addition, applications of the forced vibration theory are presented that can be used in experiments to evaluate the dynamic properties of the structure.Content and overviewIn this course we're going to study first the definition of the harmonic force. Then we are going to learn how to form the equation of motion for the case that an external force is acting directly on the system, and for the case that the system is excited by the earthquake motion of the ground.Subsequently, we're going to study the response of single-degree-of-freedom systems to forced vibration. We're going to derive the solution to the equation of motion, so as to obtain the response equations, for both undamped and viscously damped systems. We're going to learn that the response has two components: the transient response, and the steady-state response. We're also going to introduce the definitions of the response factors, which state the degree of amplification of the system response, as a result of dynamic loading. In both cases, the phase angle between the excitation and the response are examined. The phenomenon of resonance, which occurs when the exciting frequency is equal to the natural frequency of the system, is also studied.In the next section we're going to study the forced vibration test, using which the resonant frequency and the damping ratio of the structure can be estimated. The forced vibration theory is then applied in the evaluation of the transmissibility function, which gives the degree of amplification due to the dynamic application of the load. We're going to learn that the transmissibility function can be used to evaluate the response of the structure to earthquake ground motion. We're also going to use the transmissibility function to learn how the earthquake forces induced to the structure can be reduced using vibration isolation.In the last section we're going to study the energy balance in the system during forced vibration. We're going to learn how to evaluate the energy input and the energy dissipation, and we're going to learn that the energy in the system has two components: the kinetic energy, and the potential energy. We're going to examine the steady-state response from the perspective of the energy balance in the system, and then we're going to visualize the energy dissipation using the hysteresis loop. Lastly, we're going to learn how to calibrate the viscous damping model using experimental data.By completing this course you will cover an important part of the structural dynamics theory, and understand some important concepts. This theory is used in subsequent courses to study the response to other types of loading, and other types of structures.

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