ME 340

Dynamic modeling of mechanical components and systems; time-domain and frequency-domain analyses of linear time-invariant systems; multi-degree-of-freedom systems; linearization of nonlinear systems. Course Information: Credit is not given toward graduation for ME 340 and either SE 320 or AE 353. Prerequisite: MATH 285 or MATH 286 or MATH 441; TAM 212; credit or concurrent registration in MATH 257 or MATH 415; credit or concurrent registration in ECE 205. Class Schedule Information: Students must register for one lab and one lecture section.

• Sections AL1 and OL1
• Sections AL2 and OL2

Dynamic modeling of mechanical components and systems; time domain and frequency domain analysis of linear time invariant systems; multi-degree of freedom systems; linearization of nonlinear systems. Prerequisite: TAM 212, MATH 285 and concurrent registration in ECE 205/206, and MATH 415. 3.5 undergraduate hours. Students may not receive credit for this course and any of the following: GE 320 and AAE 353.

TOPICS:

1. Laplace transformation: properties, inverse transformation, solutions of differential equations by Laplace transform, transfer functions - poles and zeroes.

2. Modeling of dynamic systems: principles of conservation - mass, energy, fluid flow, heat transfer, mechanical/electromechanical systems, state(phase) space representation.

3. Dynamic system classification, linearization of nonlinear systems, dynamic simulation.

4. Time domain analysis of linear time invariant systems: first and second order systems, time constant, damping ratio and natural frequency, impulse response and convolution integral.

5. Frequency domain analysis: frequency response, application to vibration isolation, base excitation, measurement systems, Fourier series analysis.

6. Multi-degree-of-freedom systems: natural frequencies and normal modes, applications to beat generation and vibration absorbers.

LABORATORY PROJECTS:

1. Mathematical preliminaries. Complex numbers; partial fractions; eigenvalues and eigenvectors; MATLAB computations and graphing of real- and complex-valued functions.

2. First-order systems. Exponentially decaying signals; free and step responses of linear, time-invariant first-order systems; time constant; system identification; physical experiments with a leaking tank and a hydraulic motor.

3. Block diagrams and simulation. Time- and frequency-domain block diagrams with integrators amplifiers; Laplace transforms and transfer functions; SIMULINK realizations; numerical experiments with a mechanical suspension, a nonlinear pendulum, and a quarter-car model.

4. Second-order systems. Exponentially decaying harmonic signals; free, step, and unit impulse responses of linear, second-order time-invariant systems; natural frequency and damping ratio; under-, critically-, and over-damped systems; system identification; physical experiments with a single-degree-of-freedom spring-mass-damper system.

5. Mode shapes and resonance. Natural frequencies and modal oscillations; harmonic excitation; steady-state response; physical experiments with a two-degree-of-freedom spring-mass-damper system.

6. Continuous systems. Boundary-value problems for cantilevered and clamped-clamped beams; natural frequencies and modal oscillations; modal decompositions; harmonic excitation and resonance; physical experiments with a cantilevered beam; simulations with a finite-element model.

7. Nonlinear systems. Lagrange’s equations; equilibrium configurations; linearization and stability; simulation and physical experiments with a double pendulum.

ME: Required.

EM: TAM 412 required instead.

1/21/2021