EN 137: ADVANCED ENGINEERING MECHANICS

Tentative Course Outline

Division of Engineering

Brown University

Spring Semester, 2005-2006

Rod Clifton

1.  Introduction and Review

            1.1  Overview of the objectives and methods of mechanics

                        Mechanical systems; issues; discrete and continuous approximations of a system.

            1.2  Kinematics of particles

                        Position, velocity, acceleration; rotating frames

            1.3  Dynamics of particles (direct approach)

                        Inertial frames, Newton’s 2^nd Law, kinetic energy, potential energy

2.  Analytical mechanics

            2.1  Generalized description of mechanical systems

            2.2  Virtual work and generalized forces

            2.3  Lagrange’s equations for holonomic conservative systems

            2.4  Extensions of Lagrange’s equations

                        Non-conservative systems; Lagrange multipliers

            2.5  Hamilton’s Principle

3.  Dynamics of rigid bodies

            3.1  Angular momentum and kinetic energy in terms of angular velocity

            3.2  Calculating inertial properties of homogeneous solids

                        Inertia tensor; principal axes and moments of inertia; parallel axis theorem

            3.3  Equations of motion for rigid bodies

            3.4  Euler’s equations

                        Derivation; how to use the equations; applications to free motion of rigid bodies;

                        stability of rotations

            3.5  Gyroscopes; precession rate

            3.6  Euler’s angles

                        Angular velocity, kinetic energy of rotation, angular moments

            3.7  Lagrange’s equations

                        Free motion of a rigid body, axi-symmetric bodies, spinning tops, rolling disk                             (non-holonomic system)

4.  Vibration of linear, single-degree-of-freedom systems

            4.1  Equations of motion

            4.2  Free vibration

                        Solutions of the equations of motion; damped systems

            4.3  Forced harmonic response of linear 2^nd order systems

                        Forcing function for rotating machinery; transient and steady state response

5.  Vibration of linear systems with several degrees of freedom

            5.1  Equations of motion in matrix form

            5.2  Free vibration of conservative, multi-degree-of-freedom (MDOF) systems

                        Natural frequencies, normal modes

            5.3  Forced vibration of MDOF systems

                        Vibration isolation

            5.4  Forced vibration of damped MDOF systems

6.  Introduction to vibrations and waves in continuous systems

            6.1  Equations of motion for conservative, one-dimensional, continuous systems

            6.2  One-dimensional wave propagation in bars

            6.3  Longitudinal vibration of bars

                        Natural frequencies, normal modes