Control vibration in engineering systems and apply your knowledge to everything from consumer product development, manufacturing, aerospace systems, and more.
Engineers with skills in vibration engineering contribute to creating manufacturing production systems, aerospace systems, automotive engineering, medical product development, consumer product development, and a host of industrial equipment and process systems in which vibration must be minimized or controlled. Students utilize sophisticated software tools, analytical techniques, and experimental methods to design, develop, and implement solutions for vibration control and minimization in engineering systems.
The advanced certificate in vibrations takes students beyond the preparation in vibration engineering that students typically complete during their undergraduate program of study. Students learn to use sophisticated software tools, analytical techniques and experimental methods to design, develop, and implement solutions for problems of vibration control and minimization in engineering systems. Students are exposed to modern technologies used in industry to ensure that they are prepared for their specialized job market. The curriculum answers a need for graduate level instruction for practicing engineers in a field of importance for the 21st century.
Plan of study
The advanced certificate requires students to successfully complete four required courses and one elective course. Students may apply the courses toward a master’s degree at a later date.
Is concerned with analytically finding the dynamic characteristics (natural frequencies and mode shapes) of vibratory mechanical systems (single-degree and multi-degrees of freedom systems), and the response of the systems to external excitations (transient, harmonic, and periodic). Application to vibration damping techniques (Dynamic Vibration Absorbers) is also covered. In addition, laboratory exercises are performed, and an independent design project is assigned.
This course trains students to utilize mathematical techniques from an engineering perspective, and provides essential background for success in graduate level studies. An intensive review of linear and nonlinear ordinary differential equations and Laplace transforms is provided. Laplace transform methods are extended to boundary-value problems and applications to control theory are discussed. Problem solving efficiency is stressed, and to this end, the utility of various available techniques are contrasted. The frequency response of ordinary differential equations is discussed extensively. Applications of linear algebra are examined, including the use of eigenvalue analysis in the solution of linear systems and in multivariate optimization. An introduction to Fourier analysis is also provided.
Advanced Engineering Mathematics
This is a course in partial differential equations focused primarily on separation of variable techniques, and teaches the necessary vector space theory so that the problem solving methodology may be understood completely. Algebraic vector space concepts, such as the basis, are extended to functions, and operator theory is introduced as a means of unifying the solution structure of linear algebraic and differential equation systems. Existence and uniqueness is examined by considering the null and range spaces of algebraic and differential operators, the adjoint operator, and Fredholm's Alternative. Eigenvalue analysis is extended to functions, including an examination of Sturm-Liouville theory. Solutions of Laplace's equation, the heat equation, the wave equation, and the biharmonic equation are examined in a variety of geometries.
Intermediate Engineering Vibrations
Is concerned with analytically finding the dynamic characteristics (natural frequencies and mode shapes) of continuous mechanical vibratory systems (strings, rods, and beams), and the response of the systems to external excitations (transient and harmonic). Solutions using the finite element method is also introduced.
Choose one of the following:
Random Signals and Noise
In this course the student is introduced to random variables and stochastic processes. Topics covered are probability theory, conditional probability and Bayes theorem, discrete and continuous random variables, distribution and density functions, moments and characteristic functions, functions of one and several random variables, Gaussian random variables and the central limit theorem, estimation theory , random processes, stationarity and ergodicity, auto correlation, cross-correlation and power spectrum density, response of linear prediction, Wiener filtering, elements of detection, matched filters.
Digital Signal Processing
In this course, the student is introduced to the concept of multi rate signal processing, Poly phase Decomposition, Transform Analysis, Filter Design with emphasis on Linear Phase Response, and Discrete Fourier Transforms. Topics covered are: Z- Transforms, Sampling, Transform Analysis of Linear Time Invariant Systems, Filter Design Techniques, Discrete Fourier Transforms (DFT), Fast Algorithms for implementing the DFT including Radix 2, Radix 4 and Mixed Radix Algorithms, Quantization Effects in Discrete Systems and Fourier Analysis of Signals.
This course is designed to introduce the student to advanced systems modeling techniques and response characterization. Mechanical, electrical, fluid, and mixed type systems will be considered. Energy-based modeling methods such as Lagrange’s methods will be used extensively for developing systems models. System performance will be assessed through numerical solution using MATLAB/Simulink. Computer projects using Matlab/Simulink will be assigned and graded in this course including concepts of data analysis and how it performs to parmeter estimation. Linearization of nonlinear system models and verification methods are also discussed.