Structural Dynamics

This book offers a base course in Structural Dynamics and serves the Master’s Degree curriculum for structural engineers. It offers an in-depth analysis and original solutions for many design and analysis scenarios. In this sense, it could also be useful for Ph.D. students or civil and structural engineering professionals who would like to enrich their own knowledge in the field of Structural Dynamics.

The first chapter is an introduction to Structural Dynamics wherein the basic concepts and ideas are introduced.

The second chapter is devoted to the dynamic analysis of one Degree of Freedom (DOF) system. In it the topics of free and forced vibrations are discussed in detail. Here I also present how to model the internal frictional resistance using an appropriate viscous resistance proportional to the first degree of the velocity.

The third chapter deals with the dynamics of systems with a finite number of DOFs solved according to the classical method of structural dynamics. The following basic issues are considered here: the modal analysis, or how to determine the natural frequencies and modal shapes; how to identify the systems’ resistance properties; how to determine the amplitude dynamic diagrams for the cross-sectional forces, and so forth.

The fourth chapter deals with the dynamics of frame structures modeled as systems with an infinite number of DOFs. Discussed are here the method of initial parameters and its application in the deformation method of structural dynamics.

The fifth chapter is devoted to the most frequently used method for dynamic analysis of frame structures, namely the Finite Elements Method (FEM) for displacements.

The sixth chapter is an introduction to Seismic Mechanics – one of the most important parts of structural dynamics. The topic of how to determine the seismic forces is clarified here. Some sample cases are solved based on the Bulgarian codes for design in areas affected by seismic activity.

The Appendices contain several algorithms for the most popular methods for numerical integration of ordinary differential equations: the Simpson method for the numerical solution of the Duhamel integral; the Central differences method; the methods of Runge-Kutta, Hubolt, Wilson, and Newmark.