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MECH-330 Dynamic Systems I
2005 Catalog Data: Credit: (4-0-4) Four-Lecture-Hours Prerequisites: MATH-204, Differential Equations & Laplace Transforms, MECH-310, Mechanics III, MECH-231, Signal Analysis for Mechanical Systems, OR EE-210, Circuits I, OR EE-212, Applied Electrical Circuits MECH-312, Design of Mechanical Components I Corequisites: MECH-322, Fluid Mechanics, MATH-305, Numerical Methods & Matrices OR MATH-307, Matrix Algebra
A study of mathematical modeling of mechanical, electrical, hydraulic and multidiscipline engineering system using bond-graph-technique, yielding state space equations. Derivation of the Equations of Motion (EOM) of single Degree of Freedom (SDOF) and 2DOF using Lagrange Equation and/or Newton Second Law (NSL). Determine transfer functions and frequency transfer function response for first and second order systems. A study of linear mechanical vibrations for SDOF and 2DOF systems, and of their vibration isolation. Determine characteristic equation, stability eigenvalues of systems. Develop computer code in order to simulate, analyze real engineering systems in the time and frequency domain using Matlab.
Textbook: Barak, P., Mathematical Modeling of Mechanical and Multidiscipline Systems , John Wiley & Sons, Inc.
References: Karnop, Dean C., Margoles, Donald L., and Rosenberg, Ronald C., System Dynamics – Modeling and Simulation of Mechatronic Systems, 3 rd^ Edition, John Wiley & Sons.
Thomson, William T. and Dillou Dableh, Marie, Theory of Vibration with Applications , 5th^ Edition, Prentice Hall.
Strum and Ward , Laplace Transform Solution of Differential Equations, Prentice-Hall
Kreyszig, Advanced Engineering Mathematics , John Wiley & Sons, Inc.
Coordinator: Pinhas Barak, Room 2-217 C.S. Mott Engineering & Science Center, (810) 762-7840, pbarak@kettering.edu.
Course Learning Objectives: Upon completion of this course, “Dynamics Systems I”, the student will be able to:
- identify system components, their symbols, terminology, attributes, constitutive equations and interactions based on a unified approach [ME PO’s A, C, P]
- model mechanical, electrical, hydraulic and multidiscipline systems using bond-graph technique [ ME PO’s A, B, C, E, P, S]
- derive the Equations of Motion (EOM) in state space form from bond-graph models of mechanical, electrical, hydraulic and multidiscipline systems with Multi-Input-Multi- Output (MIMO) variables[ME PO’s A, B, C, L, S]
- derive the equations of motion of Single Degree of Freedom (SDOF) and a 2DOF mechanical system using Lagrange equation and/or Newton Second Law (NSL)[ME PO A]
- determine transfer functions of first and second order systems using Laplace transformation pairs from the t-domain to the s-domain[ME PO A]
- derive the characteristic equation of a first and second order system, solve for the eigenvalues, natural frequency (if any) and evaluate the stability of the system[ME PO’s A, B, C, L, S]
- estimate the value of a function f(t) at t→0, and t→∞ using the Initial Value Theorem (IVT) and the Final Value Theorem (FVT)[ ME PO A]
- evaluate the time response to deterministic inputs for first and second order systems[ ME PO’s A, B, C, E, J]
- investigate and analyze the vibration isolation of SDOF and 2DOF mechanical systems in the time and frequency domain[ ME PO’s A, B, C, E, S]
- develop a computer code to simulate and analyze and design real engineering systems using Matlab software[ME PO’s A, B, C, E, L, P, S]
- take the second course in systems engineering entitled “MECH 430 – Dynamic Systems II” dealing with more advanced multi-domain systems and closed-loop control systems.
Prerequisites by Topic:
- Differential equations
- Laplace Transform and it’s application to the solution of differential equations
- Electrical circuit, charge, force, potential, current, capacitors, resistors and inductors
- Fundamentals of mechanical and mechatronics design, sensors and actuators
- Principle of superposition for linear system and application of Cramer’s Rule to the solution of a set of linear algebraic equations
- Application and basics of Newtonian mechanics and physical laws
- Kinematics and kinetics of a particle and a rigid body in 2-D
- Concept of kinetic and potential energy
Corequisites by Topic:
- Matrices and determinants and application to the solution of linear systems
- Fluid motion, fluid properties, flow regimes, pressure variation
equation via EOM of a SDOF, transmissibility ratio: fixed base, base motion, rotating unbalance, examples. 10 Fundamentals in Linear Mechanical Vibrations. 2 DOF deriving the EOM using Lagrange equation, characteristic equation, eigenvalues, natural frequencies, eigenvectors, mode of vibrations, examples. Review, concluding remarks. 11 Comprehensive Final Exam.
Schedule: Two sessions per week of 120 minutes each.
Computer Usage: Basic computer skills and Matlab Professional Edition 6.5 (or higher).
Recommended Laboratory Projects: Laboratory project #1: Matlab. Supervised simple case study for first and second order system; 2 hours per student, up to 5% of final grade. Laboratory project #2: Comprehensive case study using Matlab, teams of no more than two students (to be collected), up to 10% of final grade.
Relationship to Professional Component: This course is 90% engineering science and 10% engineering design.
Prepared by: Pinhas Barak, Professor of Mechanical Engineering
