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#### MEE 519 Projects 5 parts I, II, & III: Damped Spatial Pendulum Part I: Model a spatial pendulm made up of 6 cables suspending a steel ball (sphere) with the diameter of 5

###### Mechanical Engineering

MEE 519
Projects 5 parts I, II, & III: Damped Spatial Pendulum
Part I: Model a spatial pendulm made up of 6 cables suspending a steel ball (sphere) with the diameter of 5.2 m. Tune the pendulum to the frequency of 0.18 Hz.
Each cable can be created using two bodies connected by a revolute joint and one end. The other ends of the two bodies are attached to the ceiling and the mass using two universal joints (one at each end). Alternatively, a cable can be created using one body with a U joint at one end and a spherical (S) joint at the other, but the former joint arrangement simulates the behavior of a cable more realistically. Creating a ‘cable’ library item and using it in the model is recommended.
Simulate the motion of the pendulum for 50 seconds, by subjecting the base of the pendulum (the ceiling) to a sinusoidal motion with the same frequency as that of the tuning frequency of the pendulum, i.e., resonate the pendulum. Keep the input on for 30 sec and off for the remaining of the simulation time; display the motion of the pendulum mass on an oscilloscope. To a) prevent the motion of the undamped pendulum from becoming chaotic and b) account of the inherent friction in the joints, add a small amount of damping (e.g., 100 Nsec/m) to the U joints of the cables.
Part II: Add substantial amount of damping to the pendulum using 6 long-stroke viscous dampers, similar to hydraulic cylinders, to the pendulum mass. The viscous dampers are made up of two bodes with a U joint at each end and a Cylindrical (C) joint in between (connecting the two bodies) resulting in a UCU joint arrangement1.
a) With the base of the dampers (the floor) fixed, repeat the simulation of Part 1 and plot the resulting displacements of the mass to a base perturbation trace with and without the dampers in place. Comparison of the two traces should show the impact of adding viscous damper legs to the pendulum.
b) With the base of the dampers (the floor) subject to the same perturbation as the base of cables (ceiling), interface the model of the damped pendulum with the model of the structure stored in the attached mat-file. Subject the structure to a perturbing force and examine the motion of the structure with and without the damped pendulum appended to it.
Part III: The state space model of a tall building is constructed using its first 3 modes. The attached m-file and the accompanying mat file, contain the necessary information about the building. Note that the proximity of the center of rigidity and center of mass of the floors in this building makes the first 3 modes somewhat decoupled from each other.
Tune your pendulum (as a Pendulum Tuned Mass Damper, PTMD) to the first 3 modes of the building, one mode at a time, and show the effectiveness of the PTMD in adding damping to its target modes, by plotting the suitable time responses and frequency response functions of the top floor of the building with and without the PTMD in place.

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