hwk07 - ME563 – Fall 2011 Purdue University West...

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: ME563 – Fall 2011 Purdue University West Lafayette, IN Homework Set No. 7 Assignment date: Friday, October 7 Due date: Friday, October 14 Please attach this cover sheet to your completed homework assignment. Name PUID Problem 7.1 Problem 7.2 Problem 7.3 TOTAL Homework 7.1 Consider the three systems shown below: (a) longitudinal motion of a homogeneous rod, (b) transverse motion of a homogeneous string, and (c) torsional motion of a homogeneous shaft. Derive the boundary conditions for each of the three systems. For each x = L boundary condition, you must draw an appropriate free body diagram consistent with the sign conventions for corresponding problem. You will not receive credit for your work without correct free body diagrams. Homework 7.2 Choose one of three systems described in Problem No. 7.1. For the system of your choice: 1. Derive the characteristic equation. Write this characteristic equation in terms of appropriate non-dimensional stiffness and mass parameters. 2. Make a sketch of the characteristic function for numerical values for the non-dimensional stiffness and mass parameters of your choice. 3. Based on your sketch above, provide lower and upper bounds for the first four natural frequencies of the system. Homework 7.3 Consider the transverse motion w(x, t) for the thin bending beam shown below. Both ends of the beam are clamped to ground. 1. Derive the characteristic equation. 2. Make a sketch of the characteristic function. 3. Based on your sketch above, provide lower and upper bounds for the first four natural frequencies of the system. 4. Determine numerical values for the first four natural frequencies using a numerical solver such as the Matlab function “fsolve”. 5. Determine the first four modal functions for the problem. Make a sketch of these modal functions vs. x. ...
View Full Document

This document was uploaded on 12/23/2011.

Ask a homework question - tutors are online