Course content

PART I: VIBRATIONS

Chapter I: General Introduction to Vibrations

This unit provides an overview of the fundamental concepts related to mechanical vibrations. It introduces oscillatory motion, vibrating systems and key parameters such as natural frequency, damping, and dynamic response. It establishes the foundational knowledge required for the analysis of vibrating systems.

Chapter II: Linear Systems with One Degree of Freedom

This unit focuses on the study of simple vibrating systems characterized by a single degree of freedom. It covers the equations of motion, analytical solutions for free and forced vibrations, with and without damping, as well as resonance phenomena. Learning activities are designed to develop skills in modeling and interpreting dynamic responses.

Chapter III: Linear Systems with Multiple Degrees of Freedom

This unit extends the analysis to more complex systems involving multiple degrees of freedom. It introduces matrix methods, modal analysis, natural frequencies, and mode shapes. The objective is to understand dynamic interactions between system components.

PART II: MECHANICAL WAVES

Chapter IV: Generalities on Mechanical Waves

This unit presents the fundamental principles governing the propagation of mechanical waves. It introduces concepts such as disturbances, propagation media, wave velocity, and different types of waves (progressive and standing waves). It establishes the connection between vibrational phenomena and wave propagation.

Chapter V: Transverse Waves on a String

This unit examines the propagation of transverse waves along a stretched string. It covers the wave equation, boundary conditions, and the formation of standing waves. Emphasis is placed on practical applications and resonance phenomena in string systems.

Chapter VI: Longitudinal Waves in Fluids

This unit addresses the propagation of longitudinal waves in fluid media, particularly sound waves. It introduces concepts such as acoustic pressure, speed of sound, and reflection/refraction mechanisms. It provides a foundation for understanding physical acoustics.

Chapter VII: Elastic Waves in Solids

This unit deals with wave propagation in elastic solid media. It distinguishes between different types of waves (compressional, shear, and surface waves) and highlights their relevance in analyzing the mechanical properties of materials. It forms an essential basis for applications in civil engineering and materials science.