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Welcome to Explorable Explanations

The best way to understand complex concepts is to interact with them.

This suite of applets and interactive lectures provides a unique, hands-on approach to learning key principles in engineering and materials science.

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Active Learning through Virtual Exploration

These applets are designed to help students:

Solid Mechanics & Structures

Vector Algebra — Forces as Vectors Y1 Free Body Diagrams (FBD) Y1 Internal Load Diagrams (SFD, BMD) Y1 Static and Kinetic Friction Y1 Second Moment of Area Y1 Pulley Systems Y1 Truss Analysis Y1 Basics of Stress Analysis Y2 Strains and Deformations Y2 Bending of Asymmetric Sections Y2 2D Stress Transformations and Failure Criteria Y2 Macaulay's Method Y2 Elastic Instability (Buckling) Y2 Composites Y3 3D Stress Transformations Y3 Plasticity in Bending and Residual Stresses Y3 Stress-based Fatigue Y3 Fracture Mechanics Y3 Stress Concentration Y3 Beam Strain and Deflection LAB

Dynamics & Vibrations

Kinematics of Linear Motion Y1 Circular Motion Y1 Kinematics of Parabolic Motion Y1 Kinematics of Relative Motion Y1 Rotational Dynamics Y1 Principle of Work and Energy Y1 Principle of Impulse and Momentum Y1 SDOF Free/Forced Vibrations Y2 SDOF Base Excitation Y2 Balance of Rotating Masses Y2 Gear Trains Y2 Kinematics of Mechanisms Y2 Balance of Reciprocating Masses Y2 Gyroscopic Effects Y2 2DOFs Free Undamped Vibration Y3 Tuned Mass Damper Y3 MDOFs Free Damped Vibration Y3 Random Vibrations Y3 Modal Testing Y3

Nonlinear Dynamics

Nonlinear Dynamics Y3 Lagrangian & Hamiltonian Mechanics Y3 Predator–Prey Dynamics & Limit Cycles Y3 Resilience & Sustainability Y3

Fluid Mechanics

Hydrostatics Y1 Bernoulli's Equation Y1 Friction in Pipes (Concentrated & Distributed Losses) Y1 Impact of Jets Y1 Viscosity and Vorticity Y2 Boundary Layer and Turbulence Y2 Drag and Lift: Aerodynamic Forces Y2 Navier-Stokes Equations Y3 Turbomachinery Y3

Thermodynamics & Heat Transfer

(Closed/Open/Isolated) Systems Y1 Thermodynamic State Variables Y1 Thermodynamic Processes Y1 Phase Changes of Water Y1 Thermodynamic Cycles Y2 Entropy Y2 Real Gases (Van der Waals & Redlich-Kwong) Y2 Heat Transfer Y2

Computational Methods & Controls

Fourier Series Y2 Laplace Transforms Y2 Control Systems Y2 PID Controllers Y2 Frequency Response & Bode Plots Y2 ODE Numerical Methods Y2 Finite Element Methods Y3 FEM Formulations (1D-2D-3D Elements) Y3 FEM Nonlinear Solvers Y3 PDE Numerical Methods Y3

Automotive & Robotics

Drive and Dragged Wheels Y1 Differential Gears Y2 Tire–Road Forces Y2 Vehicle Ride and Handling Y3 Vehicle Dynamics Y3 Engine Powertrain Performance Y3 Robot Kinematics (Forward/Inverse) Y3 Carbody Bounce: SDOF Free Vibration Rail Base Excitation and Resonance Speed Rail Bounce and Pitch Modes Rail Hunting Wheelset and Critical Speed Rail Flexible Carbody and Seat Comfort Rail Nonlinear Damper Playground Rail Clickety-clack: Hear the Rail Joints Rail

Renewable Energy

Betz Limit for Wind Turbines Energy Solar Cell Bandgap Limit Energy Wave Energy Absorption Limit Energy Pelton Wheel Optimum Speed Energy

Materials Science

Emergent Material Properties MatSci Nucleation of Polycrystals and Vacancies MatSci Crystal Lattices MatSci Miller Indices MatSci Phase Diagrams MatSci Dislocations MatSci Diffusion MatSci Corrosion MatSci

Games!!!

☄️ Asteroids 🧱 Borkout 🐦 Flappy Bork 💎 Match3 🎯 Parabolic Master 🏹 Parabolic Master 99 🏢 TMD Tuner 🔨 Resonance Hunter 🏎️ Apex Motorsport 🏓 Pong 🐍 Snake 🟦 Tetris 🔗 Word Connections ⚙️ Word Quest ENG 🧬 Word Quest BIO