PART 5. PLANAR KINETICS FOR MULTI-BODY 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

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Textbook Chapter 5 (Lectures 32-35)

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

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Major Topics/WHAT YOU WILL LEARN

Recommended homework problems

32

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

33

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

34

Applications: vehicle suspension system, rotor-bearing 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

35

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 32-35

 

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