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 vibration
Week 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 string
Week 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 techniques
Week 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 applications
Week 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 oscillator
Week 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 plates
Week 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 data
Week 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
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