## AE 715/433: Vibrations and Structural Dynamics

Single degree of freedom system vibrations, Free and Forced Undamped and Damped Vibrations. Periodic and General Excitations : Duhamel Integral Approach. Introduction to Vibration Isolation. Discrete systems with multiple degrees of freedom, elastic and inertia coupling, Natural frequencies and modes, free vibration response, orthogonality of natural modes, modal analysis, Forced vibration response, special and general cases of damping, matrix formulations, solution of the eigen value problem. Vibration of continuous systems, differential equations and boundary conditions, Free and forced longitudinal, flexural and torsional vibrations of one-dimensional structures, Elements of analytical dynamics, generalized coordinates, Principle of Virtual Work, Hamilton Principle, Lagrange equations, applications. Modal analysis. Approximate methods based on Lagrange equation and assumed modes. Structural damping.

## AE 639: Continuum Mechanics

1. Continuum mechanics: an introduction 2. Mathematical Preliminaries 2.1 Vector spaces 2.2 Index notations 2.3 Tensor algebra 2.4 Tensor calculus 3. Kinematics 3.1 Motion of a body: referential and spatial descriptions 3.2 The deformation gradient 3.3 Stretch, strain and rotation 3.4 Spin, circulation and vorticity 3.5 Deformation of volume and area 3.6 Discussion on frames of reference 4. Basic Thermo-mechanical Principles 4.1 Conservation of mass 4.2 Surface tractions, body forces and stress tensor 4.3 Conservation of linear and angular momentum 4.4 Conservation of energy 4.5 Clausius-Duehm inequality 5. Constitutive Relations 5.1 Principle of material objectivity 5.2 Thermoelastic materials: isotropic, transversely isotropic and orthotropic 5.3 Inviscid fluids 5.4 Viscous fluids 6. Typical boundary value problems 6.1 Bending of beams 6.2 Torsion of a circular cylinder 6.3 Fluid flow: Poiseuille flow and Couette flow

## AE 102: Data Analysis and Intrepretation

Chapter 1: The Role of Statistics 1. Reasons to study statistics 2. The nature and role of variability 3. Statistics and data analysis 4. Types of data and some simple graphical displays

Chapter 2: The data analysis process and collecting data sensibly 1. Data collection 2. The data analysis process 3. Population and sampling 4. Inferential statistics

Chapter 3: Graphical methods for describing and summarizing data 1. Displaying categorical data: comparative bar charts and pie charts 2. Displaying numerical data: stem-and-leaf displays, boxplots 3. Displaying numerical data: Frequency distributions and histograms 4. Displaying bivariate numerical data: scatterplot

Chapter4: Numerical methods for describing and summarizing data 1. Describing the center of data set (mean, median) 2. Describing variability in a data set (range, quartile, IQR, SD) 3. Describing bivariate data (measure of dependence and linear relation, Pearson's correlation coefficient)

Chapter 5: Probability, Random variables and Discrete and Continuous Distributions (Normal) 1. Interpreting probabilities and basic probability rules 2. Probabilities as a basis for making decisions 3. Random variables and discrete probability models 4. The binomial and Poisson distributions 5. Other discrete distributions 6. Continuous random variables and probability distributions 7. Population models for continuous variables 8. Normal distributions; interpreting center and variability: empirical rule, z scores

Chapter 6: Continuous Distributions, CLT and Basic Estimation Techniques, Confidence Interval, Hyp. Test, Simple Linear Reg. 1. Other continuous distributions 2. Sampling variability and sampling distributions a. Statistics and sampling variability b. The sampling distribution of sample mean, central limit theorem 3. Estimation using a sigle sample a. Point estimation 4. Confidence interval for a population mean and population 5. Hypothesis testing using a single sample a. Hypotheses and test procedures and errors in hypothesis testing b. Hypothesis tests for a population mean and population proportion 6. Comparing two populations for treatments a. Inferences concerning the difference between two population or treatment means using independent samples b. Inferences concerning the difference between two population or treatment means using paired samples c. Tests for independence in two-way

Chapter 7: Simple Linear Regression and Correlation 1. The simple linear regression model 2. Inferences about the slope of the population regression line