Basic Information
Brief Introduction to Nonlinear Phenomena, Asymptotic Formalism, Asymptotic Expansions. Asymptotic Analysis of Odes, Pdes., Multi-scale Expansion, Dispersive and Non-dispersive Waves, Nonlinearity and Wave Breaking, Inviscid Burger S Equation, Shock Waves. Second Order Linear Wave Equation, Dynamics of Linear Lattice Models# Mono-atomic Chains, Poly-atomic Chains, Dynamics of Weakly Non-linear Lattices# Solitary Waves, Kdv Equation, Kdv Soliton And Multi-soliton Solutions, Effect of Nonlinearity On The Stability Of Weakly Non-linear Lattices# Solitary Waves, Kdv Equation, Kdv Soliton And Multi-soliton Solutions, Effect of Nonlinearity On The Stability Of Plane Waves (modulation Instability), Nonlinear Schrodinger Equation and Its Properties, Bright and Dark Solitons. Primary Response of The Uncompressed Granular Chains, Nesterenko Compact-like Soliton Solution. K (n.m) - Equation and Rozenau Compacton Solution. Friesecke - Wattis Theorem On Existence of Solitary Waves On Lattices. Olitary Waves in a General Type of Nonlinear Chains Subject to a State Of a Sonic Vacuum. Approximate Analytical and Semi-analytic Techniques For The Analysis of Solitary Waves On Lattices. Nonlinear Wave Phenomena Emerging in The Real Mechanical Models Will Be Emphasized. Learning Outcomes# at The End of The Course The Student Will Know# 1. to Identify and Describe Nonlinear Wave Phenomena in Weakly Nonlinear, Discrete Mechanical Structures. 2. to Perform The Stability Analysis of Waves in Periodic, Discrete Mechanical Chains. 3. to Apply The Numerical, Analytical and Semi-analytical Methods To Describe The Essentially Nonlinear. Wave Solutions Supported By Discrete Nonlinear Medium in a State of Sonic Vacuum.
Faculty: Mechanical Engineering
|Pre-Academic
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