## Advanced Mechanical Vibration EGME 511, California State University, Fullerton

June 25, 2014

### 1 Introduction

I took this course in Spring 2009 at CSUF. Not part of a degree program

course description from catalog:

Textbook

### 2 classnotes

my class notes PDF

### 4 Exams

 Exam my score class average my solution ﬁrst midterm 80/100 61/100 PDF second midterm 90/100 68/100 PDF ﬁnal exam 95/100 NA PDF

### 5 HWs

 HW Description of HW link 1 1. Solve 2nd order ODE 2. Calculate maximum value of the peak response (magniﬁcation factor) for a system with some damping ratio given (Quadrature peak picking method) 3. Solve for the forced response of a single-degree-of-freedom system to a harmonic excitation 4. Discuss the stability of 2nd order ODE 5. Find range of values for PD controller in feedback for stability 6. Compute a feedback law with full state feedback 7. Find the equilibrium points of the nonlinear pendulum equation 2 1. Find EQM for mass-spring with dynmaic friction on incline (this is nonlinear EQM due to columb friction) 2. Modal analysis problem on 2 by 2 system 3. Find EQM using lagrangian, 2 pendulums attached by one spring between them 4. Another Modal analysis problem on 2 by 2 system 5. 2nd order system, subject to 2 impulses, ﬁnd response using convolution 6. Convolution problem. Underdamped system, force is half sin 3 1. Find EQM, one mass, 2 springs, diﬀerent k, springs only attached when hit 2. Find EQM using Lagrangian, pendulum, but string is rubber band with some stiﬀness. 3. Find exact solution to nonlinear pendulum EQM 4. nonlinear second order ODE. Find equilibrium points and stability at these. 5. nonlinear 2nd order. Find stability around equilibrium 6. similar to above, but ﬁnd stability conditions based on damping sign 7. columb damping and phase plane 8. Given phase plane equation (i.e. dy/dx), determine stability. i.e. go back from phase plane to the system matrix 9. Solve Van Der Pol using perurbation

### 6 Projects

1.
Impulse response of second order system which is not underdamped
2.
Stabilization of an inverted pendulum on moving cart using feedback control
3.
Eigen modal analysis notebook PDF

### 7 some notes

1.
possible error in key
2.
note on solving wave equation
3.
eigenvalue modal analysis