PART 5. PLANAR KINETICS FOR MULTIBODY RIGID BODY SYSTEMS
Motion and Deformation of Mechanical
Systems with 2 or more Degrees of Freedom (DOF) – combining translation and
rotational displacements as independent variables
Textbook Chapter 5 (Lectures 3235)
Acronyms: M:
mass, K: stiffness, C: damping, EOM: equation of motion, SEP: static
equilibrium position, DOF: degree of freedom, FBD: free body diagram, CME:
Principle of Conservation of Mechanical Energy
Lecture (get me) 
Major Topics/WHAT
YOU WILL LEARN 
Recommended homework
problems 
Torsional
vibrations of rotating assemblies.
Motion of disks connected with flexible shafts: FBDs,
identification of elastic moments, derivation of multiple DOF EOMs,
eigenvalue analysis and determination of natural frequencies and mode shapes.
Interpretation of natural modes of motion 
5.44, 5.45,
5.47 

Lateral
vibrations of rigid body connected to an elastic beam. Brief review of lateral deflections of
elastic beams. Definition of lumped stiffness (K) for cantilever beam. Derive
EOM for mass supported at beam end: identification of system natural
frequency. Analysis for development of beam stiffness matrix from
force/moment relationships to beam displacement/rotation. Applications
to building and bridge frames – 2DOF examples: eigen analysis – natural frequencies and
interpretation of mode shapes 
5.49, 5.51, 5.56, 5.57c 

Applications:
vehicle suspension system, rotorbearing system, rolling w/o
slipping: FBDs,
identification of constraints and reaction forces, geometric approach to
derive mechanism kinematics, derivation of EOMs from rigid body force and
moment equations 
5.59, 5.60, 5.63, 5.64 

More
applications: pendulum
& cart suspended system. An extremely brief introduction to
Lagrange's method to derive EOMs. Applying a recipe for success (or not) 
5.62,
5.70, 5.71, 5.85 




Get all: Lectures 3235_{}
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