Applied Mechanics Rigid Body Mechanics Statics Dynamics Kinematics

Applied Mechanics Rigid Body Mechanics Statics Dynamics Kinematics Kinetics Deformable Body Mechamics Elasticity Plasticity Viscoelasticity Fluid Mechanmics Liquids Gases

Statics Vs. Deformable Body Mechanics Statically Determinant Statically Indeterminant How is the problem different if the beam is rock? Wood? Bone? Tooth Enamel?

Elasticity The beam can bend to conform to the constraints of the supports. (You have done these types of problems in ENGR 220).

Elasticity vs. Plasticity Elastic: You can bend it, but it will come right back when you remove the external force (like a spring). Plastic: You can bend it, and it will stay where it left off (like soldering wire). Some materials tend to behave elastically, some plastically, but…. Almost all materials will have both behaviors. Small deflection – elastic. Large deflection – plastic.

Stress-Strain Curve (or Force-Deflection)

Elasticity vs. Viscoelasticity Elastic: Force is proportional to deflection (e. g. a spring). Viscoelastic: Force is proportional deflection AND to rate of deflection (e. g. silly putty). Viscous: Force is proportional to deflection only (e. g. a shock absorber or a fluid).

Mechanical Analogy F = kx spring (Think of k as Young’s Modulus) (Circuits: q = CV or V = q/C) F = C dx/dt shock absorber (dashpot) (Circuits: V=i. R, or V = R dq/dt) What about F = m d 2 x/dt 2 ? Same as F = ma – Newton’s law of motion. (Circuits: V = L di/dt = L d 2 q/d 2 t) Mass is inductance

If we know something about how circuits behave, we know something about how mechanical systems behave. One major difference: Circuits tend to be discrete. Mechanical systems tend to be distributed. We must deal with spatial relationships.

Styrofoam Cup Is a styrofoam cup elastic, plastic or viscoelastic? Place your answer here: YES

Important Stuff from Chapter 1 Units must match Hierarchy of Mechanical Measures

Important Stuff from Chapter 1 Energy and Torque (Same units, but … Torque is a vector, Energy is a scalar. Torque is instantaneous, Energy happens over time.

Important Stuff from Chapter 1 Know your greek letters:

Modeling and Approximation “In general, it is always best to begin with a simple basic model that represents the system. Gradually, the model can be expanded on the basis of experience …” But … Do not throw out the baby with the bath water.

Generalized Procedure 1. 2. 3. 4. 5. 6. 7. 8. 9. Select the system Postulate characteristics Simplify with approximations Relate body parts to mechanical elements Construct the mechanical model Apply principles of mechanics Solve for unknowns Compare to experiments Repeat from step 3

From Chapter 2 You need to know how to manipulate vectors. Vectors are the only way to represent systems in space. Review: Dot product, cross product, how to calculate them, and what they mean. For distributed systems:

Vector Arithmetic Add Head to tail Subtract – reverse direction and then add A A+B B A-B