ABOUT THE COURSE: All structures or mechanical systems are in fact, continuous having their physical parameters, external forces and their response are distributed in space. The dynamic behavior of the structures or machine components, can only be truly reflected in the continuous systems. The slenderness of the structures necessitates the adoption of continuous modelling. The exact solutions that can be obtained from continuous models provide true physical behavior in addition to yielding various bench mark results for testing the efficacy of many numerical methods used in discrete approaches. Keeping this in mind, the present course has been framed to teach the students about the formulation and solution of vibration problems of the continuous systems by exact method as well as by numerical techniques with application of MATLAB tool box. The course is designed for 12 modules in which each module will consist of 3 or 4 lecture hours. INTENDED AUDIENCE: B.E Final year/M.Tech/ PhD students/Industrial personsPREREQUISITES: BE/B.Tech in Civil/Mechanical/Aerospace Engg/ Marine Engg.INDUSTRY SUPPORT: Aeronautics Research & Development Board, Delhi; Indian Space Research Org.,
Vibration of Continuous Systems
Indian Institute of Technology Guwahati and NPTEL via Swayam
This course may be unavailable.
Overview
Syllabus
Week 1: Introduction to continuous system:
1. Modelling of undamped and damped system
2. Concepts of time domain and frequency domain approach
3. Generalized approach for forced vibrationWeek 2:Different approaches for problem formulation
1. Equation of motion of continuous system by force balance
2. Energy approach and Hamilton’s principle
3. Lagranges equations and their applications.Week 3:One dimensional wave equation:
1. D,Alembert solution of the wave equation
2. Transverse vibration of stretched string
3. Modal analysis and dynamic response of flexible stringWeek 4:Axial and torsional vibration of bar:
1. Development of equation of motion by force balance and energy principle
2. Free vibration problems in axially loaded bar and torsional system,
3. Dynamic response of Shaft subjected to distributed couple or concentrated couple.Week 5:Flexural vibration of beams:
1. Equation of motions of slender beams
2. Eigen value problems in beams
3. Forced vibration analysis using mode superposition techniquesWeek 6:Vibration of beams subjected to moving load:
1. Formulation of problems in vibration of beams subject to moving load
2. Solution of Problems using mode superposition principles
3. Some practical applicationsWeek 7:Combination of continuous and lumped parameter system:
1. Exact solution of beam vibration with a concentrated mass
2. Semi-analytical approach for vibration of beams with several concentrated masses
3. Beam vibration problem with moving oscillatorWeek 8:Vibration of membranes and plates:
1. Equation of motion for the vibration of stretched membranes
2. Vibration of rectangular plates
3. Practical applications of vibration of platesWeek 9:Approximate methods in vibration of continuous system:
1. Rayleigh-Ritz method
2. Gallerkin’s approach
3. Finite difference method in vibration of beams and plates.Week 10:Vibration isolation:
1. Continuous system subject to support excitation
2. Force transmission and vibration isolation
3. Tuned mass damper for vibration reduction.Week 11:Transient vibration analysis:
1. Unit impulse and response to arbitrary excitation
2. Response to step, ramp and pulse excitation 3. Dynamic analysis using ground motion dataWeek 12:Numerical techniques with MATLAB applications:
1. Eigenvalues and eigen vector computation including state space form
2. Direct integration methods
3. Spectral analysis of structures for earthquake excitation
1. Modelling of undamped and damped system
2. Concepts of time domain and frequency domain approach
3. Generalized approach for forced vibrationWeek 2:Different approaches for problem formulation
1. Equation of motion of continuous system by force balance
2. Energy approach and Hamilton’s principle
3. Lagranges equations and their applications.Week 3:One dimensional wave equation:
1. D,Alembert solution of the wave equation
2. Transverse vibration of stretched string
3. Modal analysis and dynamic response of flexible stringWeek 4:Axial and torsional vibration of bar:
1. Development of equation of motion by force balance and energy principle
2. Free vibration problems in axially loaded bar and torsional system,
3. Dynamic response of Shaft subjected to distributed couple or concentrated couple.Week 5:Flexural vibration of beams:
1. Equation of motions of slender beams
2. Eigen value problems in beams
3. Forced vibration analysis using mode superposition techniquesWeek 6:Vibration of beams subjected to moving load:
1. Formulation of problems in vibration of beams subject to moving load
2. Solution of Problems using mode superposition principles
3. Some practical applicationsWeek 7:Combination of continuous and lumped parameter system:
1. Exact solution of beam vibration with a concentrated mass
2. Semi-analytical approach for vibration of beams with several concentrated masses
3. Beam vibration problem with moving oscillatorWeek 8:Vibration of membranes and plates:
1. Equation of motion for the vibration of stretched membranes
2. Vibration of rectangular plates
3. Practical applications of vibration of platesWeek 9:Approximate methods in vibration of continuous system:
1. Rayleigh-Ritz method
2. Gallerkin’s approach
3. Finite difference method in vibration of beams and plates.Week 10:Vibration isolation:
1. Continuous system subject to support excitation
2. Force transmission and vibration isolation
3. Tuned mass damper for vibration reduction.Week 11:Transient vibration analysis:
1. Unit impulse and response to arbitrary excitation
2. Response to step, ramp and pulse excitation 3. Dynamic analysis using ground motion dataWeek 12:Numerical techniques with MATLAB applications:
1. Eigenvalues and eigen vector computation including state space form
2. Direct integration methods
3. Spectral analysis of structures for earthquake excitation
Taught by
Prof. Sudip Talukdar
