In this module, students will learn about Lagrangeâs equation as a powerful method for analyzing mechanical systems. The application of this equation will be explored in relation to two-DOF systems and their dynamics.
This module provides an overview of the Mechanical Vibrations course, discussing its objectives, practical applications in engineering, and contemporary research trends. Students will gain foundational knowledge essential for further exploration of vibrational theories.
This module covers harmonic and periodic motions along with vibration terminology. Students will explore the differences between various types of vibrations and the context in which they occur, laying the groundwork for deeper analysis.
In this module, students will learn about vibration models and the equations of motion governing single-degree-of-freedom (DOF) systems. The natural frequency of free vibrations will be a focal point, providing insight into system behavior.
This module delves into energy methods and the principle of virtual work as applied to mechanical vibrations. Students will understand how these methods facilitate the analysis of vibrational systems and their responses to various forces.
This module focuses on viscously damped free vibrations, covering special cases such as oscillatory and non-oscillatory motions. Students will learn how to calculate damping coefficients through experimental means and understand the implications of hysteresis.
This module discusses logarithmic decrement and experimental methods for determining the damping coefficient. It also covers the hysteresis loop's role in understanding energy dissipation in vibrating systems.
This module introduces Coulomb damping and other damping models. Students will explore various damping mechanisms and their effects on vibrational behavior, laying the groundwork for understanding system stability and response.
This module covers forced harmonic vibration and the magnification factor, providing insights into how external forces affect vibrational systems. Students will understand the practical implications of these concepts in engineering applications.
In this module, students will learn about the Laplace transform and superposition theorem as tools for analyzing vibration systems. These concepts are crucial for solving complex vibrational problems and understanding system dynamics.
This module addresses rotor unbalance and the whirling of shafts, including the concept of transmissibility. Students will learn how these factors contribute to vibration in rotating systems and the importance of balancing techniques.
This module discusses support motion and vibration isolation techniques. Students will understand how these principles can mitigate unwanted vibrations in engineering systems and improve system performance.
This module covers the sharpness of resonance and introduces vibration measuring instruments. Students will gain insights into resonance phenomena and the technological tools used to measure and analyze vibrations in various applications.
This module introduces generalized and principal coordinates, providing the foundation for deriving equations of motion in two-degree-of-freedom systems. Students will gain a comprehensive understanding of how to apply these concepts in practical scenarios.
In this module, students will learn about Lagrangeâs equation as a powerful method for analyzing mechanical systems. The application of this equation will be explored in relation to two-DOF systems and their dynamics.
This module addresses coordinate coupling in mechanical systems, examining how interconnected coordinates influence the motion of coupled systems. Students will learn to identify and analyze these relationships effectively.
This module focuses on forced harmonic vibration in two-DOF systems, emphasizing the methods to analyze the response to periodic external forces. Students will learn to apply these concepts in various engineering contexts.
This module introduces the tuned absorber and methods for determining mass ratios, essential for minimizing vibrations in engineering systems. Students will explore the design considerations for effective vibration absorption.
In this module, students will learn about tuned and damped absorbers along with untuned viscous dampers. The comparative analysis of these systems will help in understanding their effectiveness in mitigating vibrations.
This module covers the derivation of equations of motion using the influence coefficient method. Students will gain insights into how these equations govern the behavior of multi-degree-of-freedom vibrational systems.
This module addresses the properties of vibrating systems, including flexibility and stiffness matrices, and the reciprocity theorem. Understanding these properties is critical for analyzing and designing mechanical systems effectively.
In this module, students will learn about modal analysis for undamped systems. The techniques covered will help in understanding the natural frequencies and mode shapes that characterize vibrational behavior.
This module focuses on modal analysis of damped systems, providing students with tools to analyze the effects of damping on vibrational behavior. The implications for real-world applications will be emphasized.
This module examines simple systems with one to three discs, including geared systems. Students will analyze the vibrational characteristics and dynamics of these systems in practical engineering scenarios.
In this module, students will learn about multi-degree-of-freedom systems through the transfer matrix method. The focus will be on analyzing branched systems and their vibrational behavior.
This module introduces the derivation of equations of motion based on Newton's and Hamilton's principle. Students will explore the foundational principles guiding the dynamics of mechanical systems.
In this module, the derivation of equations of motion will continue with a focus on Newton's and Hamilton's principle. Students will deepen their understanding of these essential dynamic principles.
This module covers the vibration of strings, examining the fundamental principles governing the oscillatory behavior of strings in tension. Students will analyze wave equations and their solutions in this context.
This module addresses longitudinal and torsional vibration of rods. Students will engage with the equations governing these types of vibrations and understand their application in engineering scenarios.
In this module, students will explore transverse vibrations of beams, focusing on the equations of motion and boundary conditions that govern their behavior. Practical implications for structural engineering will be emphasized.
This module continues the study of transverse vibration of beams, focusing on natural frequencies and mode shapes. Students will learn how these characteristics affect beam design and performance.
This module introduces Rayleigh's energy method for vibration analysis. Students will learn how to apply this technique to estimate natural frequencies and analyze vibrational systems effectively.
This module covers the matrix iteration method, a numerical approach for solving dynamic systems. Students will learn how to apply this method to derive system responses effectively.
This module addresses the Holzer method, Rayleigh-Ritz method, and Galerkin method for analyzing vibrational systems. Students will gain insights into the applicability of these techniques in engineering contexts.
This module introduces finite element formulation for rods, gears, and branched systems. Students will learn how to model these systems using finite element analysis to solve complex vibrational problems.
In this module, students will explore finite element formulation for beams using Galerkin's method. The focus will be on understanding how to create accurate models for vibrational analysis.
This module focuses on the global finite element assembly and the imposition of boundary conditions. Students will learn the procedures necessary for solving complex vibrational systems using finite element methods.
This module introduces vibration testing equipment, focusing on signal measurement techniques. Students will explore various tools used to assess vibrational characteristics in engineering systems.
In this module, students will explore vibration testing equipment used for signal analysis. The focus will be on understanding how to interpret data resulting from vibration tests to enhance system performance.
This module addresses field balancing of rotors, a critical process for reducing vibrations in rotating systems. Students will learn techniques and best practices for effective rotor balancing in engineering applications.