Homework Format:Assistance/Collaboration Policy:School of Engineering Attendance and Lateness Policy:Content/ActivityENGR 431 Mechanical VibrationsA study of periodic motion in single and multiple degrees of freedom systems with and without damping. Free, forced, and transient vibrations. Vibration instrumentation. Three hours lecture a week. (3 credits). FallPREREQUISITES: ENGR220, MATH317TEXTBOOK: Engineering Vibrations (2nd or 3rd Edition) by Daniel J. Inman. Prentice Hall. ISBN: 013726142X or ISBN 013228173-2INSTRUCTOR: Dr. Matthew R. Stein, SE106 254-3489. [email protected] WEB PAGE: http://faculty.rwu.edu/mstein/ENGR431COURSE OBJECTIVES: By the end of this course, students should be able to1. Employ fundamental techniques for analyzing mechanical vibrations2. Model dynamic systems using differential equations 3. Solve these equations using classical techniques4. Predict the free response of an linear second order damped and undamped system5. Predict the forced response of an linear second order damped and undamped system6. Use numerical integration techniques for solving non-linear differential equations7. Analyze the underlying causes of nonlinearity and predict nonlinear behavior8. Model undamped multiple degree of freedom systems9. Model damped multiple degree of freedom system10. Use Scilab to perform sophisticated engineering analysisTOPICS COVERED:1. Review of dynamics and modeling dynamic systems using differential equations.2. Solution to the single degree of freedom undamped and damped free vibrating system.Modeling nonlinear effects and numerical solution techniques.3. Forced vibration of undamped and damped system. Resonance, beating and phase shift.4. Impulse response and response to cyclical and arbitrary inputs.5. Two degree of freedom vibrating systems. Modes of vibration and vibration suppression.6. Multiple degree of freedom systems and modal analysis.CLASS SCHEDULE: Class meets three times weekly for 50 minutes. CONTRIBUTION OF COURSE TO MEETING PROFESSIONAL COMPONENT:As an engineering elective, this course presents an opportunity for advanced study suitable for upperclassmen with prerequisite mathematical advancement. The course includes sophisticatedmathematical treatment of complex mechanical phenomenon. Inherent to this study are object lessons in subtle issues such as convergence and reliability of numerical methods. At the end of this class students will be able to use sophisticated engineering tools to anayze complex, multiple-degree-of-freedom systemsRELATIONSHIP OF COURSE TO PROGRAM OBJECTIVES: This class specifically responds to some degree to all program outcomes. a. an ability to apply knowledge of mathematics, science, and engineeringb. an ability to design and conduct experiments, as well as to analyze and interpret datae. an ability to identify, formulate and solve engineering problemsi. a recognition of the need for, and an ability to engage in lifelong learningk. an ability to use the techniques, skills and modern engineering tools necessary for engineering practiceGRADING: Percent of totalMidterm Exams 300 points 93.33% AFinal Exam 250 points 90% A-Homework 150 points 86.67% B+Data Analysis Projects 300 points 83.33% BDesign Project 500 points 80% B-Total 1500 points 76.67% C+Table represents the minimum grade that will be 73.33% Cassigned. Instructor reserves the right to “curve” 70% C-grades upwards, when appropriate, but will notassign grades lower than those listed in this table. <70% FHOMEWORK FORMAT:Most homework assignments will be submitted electronically via BlackBoard. DISABILITY STATEMENT: Students with disabilities who wish to receive academic accommodations for this course must register with Disability Support Services (DSS) in order to begin the accommodation process. The DSS office will provide registered students with the specific information they will need to share with each instructor. DSS is located on the second floor of the library.ASSISTANCE/COLLABORATION POLICY:Students may work in designated groups of two students for all homework and project submissions. Direct copying or duplication between groups, is plagairism and could result in disqualification of assignments and/or disciplinary action.SCHOOL OF ENGINEERING ATTENDANCE AND LATENESS POLICY:Regular attendance in classes is expected of all students. Faculty members are in no position to assess the validity of excuses and the Student Health Service will not provide notes or vouch for student health. Three absences, or one week of class, are allowed to all students for any and all reasons. No explanation is necessary for these three absences. Absences above three affect thefinal course grade according to the following schedule.Unexcused absences:Up to 3 absences No effect on final grade4 Absences Final grade lowered by ½ letter grade.5 Absences Final grade lowered by 1 letter grade.6 or more absences Final grade of 0 assigned (Official withdrawal recommended).Attendance is typically monitored using "sign-in sheets" for each class meeting. It is the responsibility of the student to sign-in during each class attended. A student is considered absent of his or her signature does not appear on the sign-in sheet. Forgery of signatures on sign-in sheets is a violation of university Academic Integrity Policies and subject to disciplinary action.Tardiness: Each three instances of excessive tardiness (e.g. > 10 minutes) will count as one absence.Late assignments: Assignments are submitted via Blackboard and date-stamped on submission. Students may submit one assignment late without penalty and one assignment for 50% credit. All late assignments must be turned in within three weeks of the due date.DETAILED CLASS SCHEDULE:# Date Homework due Homework due Reading Content/Activity1 Aug 26 (W) 2nd Edition 3rd Edition Review of Dynamics2 Aug 28 (F) Springs, friction and dampers3 Aug 31 (M) Review of Differential Equations4 Sep 2 (W) Scilab Tutorial (10 Pts) Scilab Tutorial (10 Pts) 1.1-1.5 The 2nd order ODE5 Sep 4 (F) Solution to the ODE6 Sep 9 (W) Solution to the ODE7Sep 11 (F)HW1: 1.2,4,6,11HW1: 1.2,4,8,13Review of Scilab8 Sep 14 (M) Alternative Solution & Terminology9 Sep 16 (W) Viscous Damping10Sep 18 (F)HW2:1.18,19,23,24,27HW2:1.20,21,26,28,311.6-1.10Solution to the ODE11 Sep 21 (M)Discriminant and 12 Sep 23 (W) Damped responses13 Sep 25 (F) HW3:1.37,42,43,63,64,85 HW3:1.42,47,48,72,73,96 Free Response