we learned in the lecture, a continuous systems is an extension of multi-degree of freedom system when the number of DOF increases to infinity.

INSTRUCTIONS TO CANDIDATES

ANSWER ALL QUESTIONS

Vibrations and Dynamics of Aerospace Systems

As we learned in the lecture, a continuous systems is an extension of multi-degree of freedom system when the number of DOF increases to infinity.

In this exercise, you will develop a system of large degrees of freedom that mimics the behavior of a continuous string under vibration.

To  create this model,  we  are assuming that each element of the string can be modeled by a  tiny mass, and it is attached to the neighboring elements by  a rigid massless bar, as shown in   the figure

For our example,  we  assume that the string has a total length of L =  10 m,  total mass of M = 3 kg, and is under a constant tension of P = 100 N . Also, consider that the string was horizontal at t = 0 but the element on the middle, element (n + 1)/2th, is given a sudden vertical velocity of 1 m/s (for simplicity, assume n is always an odd number).

• Using the discrete model show in the figure above, find out the equivalent value for mi, and the the stiffness force fi−1 and fi+1 on each element as functions of x and i.

• Write the equation of motion for each element. Assume that element i is attached with a rigid massless bar with tension of P to elements i − 1 and i +  So, fi−1 and f1+1 should be functions of position of neighboring elements. Rearrange the equations in the form of an MDOF system.

 

• Write a MATLAB code that considers n = 9 mass elements and uses ODE45 to integrates the motion of the n-DOF Find the position of each element as a function of time.

• Plot the vertical position of each element at t = 1 s, t = 2 s, t = 6 s vs the location of the center of each element (plot of w x), all on the same figure. Use different color to distinguish the different time.

• use the analytical solution for the motion of the string with the same properties and IC, and solve for the analytical solution of the vibration of a continuous string. Plot the analytical response at t = 1 s, t = 2 s, t = 6 s similar to previous

• compare the results and write your

• increase n to 999 elements and repeat section c, d, and f.

Attachments:

Related Questions

. Introgramming & Unix Fall 2018, CRN 44882, Oakland University Homework Assignment 6 - Using Arrays and Functions in C

DescriptionIn this final assignment, the students will demonstrate their ability to apply two ma

. The standard path finding involves finding the (shortest) path from an origin to a destination, typically on a map. This is an

Path finding involves finding a path from A to B. Typically we want the path to have certain properties,such as being the shortest or to avoid going t

. Develop a program to emulate a purchase transaction at a retail store. This program will have two classes, a LineItem class and a Transaction class. The LineItem class will represent an individual

Develop a program to emulate a purchase transaction at a retail store. Thisprogram will have two classes, a LineItem class and a Transaction class. Th

. SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 1 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of

. Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of Sea Ports. Here are the classes and their instance variables we wish to define:

1 Project 2 Introduction - the SeaPort Project series For this set of projects for the course, we wish to simulate some of the aspects of a number of