58:153 Fundamental of VibrationsElective Program Course, 3 s.h., Fall Semester 2000(Catalog) Description: Analysis and evaluation of the vibration of linear discrete and continuoussystems. Modeling techniques and simulations for vibration response, variousexcitations, modal analysis and engineering applications.Pre(Co)requisites: 57:019 Mechanics of Deformable Bodies (P)Textbook: S. Rao, Mechanical Vibrations, 3ed. Addison Wesley Longman, 1995.Course Objectives: After taking this course students will be able to:• gain an understanding of the fundamentals of vibrations• become familiar with the modeling of single degree of freedom systems• become familiar with the modeling of multi-degree of freedom systems• become familiar with the modeling of continuous systemsTopics (class hours):• Introduction, vibration, degrees of freedom, discrete and continuous systems, equation of motion2• Free vibration analysis of SDOF systems6• Steady-state response to harmonic excitation6• Vibration under general excitations4• Modeling of multidegree of freedom systems6• Determination of natural frequencies and mode shapes4• Modeling of continuous systems6• Numerical integration methods in vibration analysis4• Vibration measurement and control4Total42Computer Usage: Students are expected to use one of these software for solving HW problems;Matlab, Mathematica, Maple.Laboratory Project: NoneContribution to Criterion 4 "Professional component":_ Mathematics and Basic_ Engineering Science_ Engineering Design_ General Educationx Other (e.g., elective)53:132/58:155 Fundamentals of VibrationsSpring Semester 2002Instructor: M. Asghar Bhatti# Date Lecture topic(s)1 22-Jan-02 Introduction, Spring-mass systems2 24-Jan-02 Damping in dynamic systems3 29-Jan-02 Coulomb & Hysteretic damping4 31-Jan-02 Free vibrations of mdof systems5 5-Feb-02 Free vibration of damped systems6 7-Feb-02 Response due to harmonic loading7 12-Feb-02 Vibration isolation8 14-Feb-02 Impulse response, Duhamels integral9 19-Feb-02 Newmark's method10 21-Feb-02 Response spectra11 26-Feb-02 Equivalent spring-mass systems12 28-Feb-02 Earthquake response spectra13 5-Mar-02 Human sensitivity to vibration14 7-Mar-02 Midterm examination, 7:00-9:00pm15 12-Mar-02 Midterm solution, Modal superposition16 14-Mar-02 Rayleigh damping, Rigid-body modes17 19-Mar-02 Spring break18 21-Mar-02 Spring break19 26-Mar-02 Continuous systems20 28-Mar-02 Continuous systems21 2-Apr-02 Energy method22 4-Apr-02 Rayleigh-Ritz method23 9-Apr-02 Rayleigh-Ritz method24 11-Apr-02 Finite element method, Axial vibrations25 16-Apr-02 Finite elements, Trusses26 18-Apr-02 Finite elements, Beams27 23-Apr-02 Introduction to Ansys28 25-Apr-02 Dynamic analysis using Ansys29 30-Apr-02 Guyan reduction30 2-May-02 Inverse iteration31 7-May-02 Subspace iteration32 9-May-02 ReviewFinal examination: 2:15 p.m., Friday, May