# Syllabi

##### Rigid Body Dynamics (ESM 2304)

Reference: J.L. Meriam and L.G. Kraige, *Engineering Mechanics: Dynamics*, Fourth Edition, John Wiley & Sons, Inc., 1997.

Chapters 1 to 6.

Kinematics, Kinetics, Work & Energy, Impulse & Momentum

Particles and system of particles

Plane motion of rigid bodies

##### Mechanics of Deformable Bodies (ESM 2204)

Reference: F.P. Beer, and E.R. Johnston, Jr., *Mechanics of Materials*, Second Edition, McGraw-Hill, Inc. 1992.

Chapters 1 to 8, and 10.

Displacements, strains, and stresses in bars under axial loads, torque loads, pure bending and transverse loads.

Transformation of stress and strain, von Mises yield criterion

Energy methods

##### Structural Stability (AOE 4054)

Reference: George J. Simitses, *An Introduction to the Elastic Stability of Structures*, R.E. Kreiger, Malabar, Florida, 1986.

Chapters 1 to 3, and 5 to 7.

Stability of equilibrium: bifurcation and limit point buckling, imperfection sensitivity

Methods of stability analysis: Adjacent equilibrium, kinetic method, and energy method

Rayleigh-Ritz method

Applications to mechanical models, columns, rings and arches

##### Solid and Structural Mechanics (AOE 5024)

Reference: I.H. Shames and C.L. Dym, *Energy and Finite Element Methods in Structural Mechanics*, Hemisphere Publishing Corp., 1985. Chapters 1 to 5, 9 and 10.

Basic equations of elasticity in three and two dimensions.

Variational principles of elasticity: virtual work; complementary virtual work

Castigliano's theorems

Beam theory and St Venant torsion theory

Introduction to finite elements

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##### Vehicle Structural Dynamics (AOE 5034)

Reference: Roy R. Craig, Jr., *Structural Dynamics, an Introduction to Computer Methods*, Wiley, 1981.

__Chapter 1__: all (The science and art of structural dynamics)

The material in Chapters 2-6 is review of material nominally covered in AOE 3034, Systems and Control. However, the presentation in the textbook by Craig places much more emphasis on structural dynamics (as opposed to general "system" characteristics) than does the nominal presentation in AOE 3034.

__Chapter 2__: Introduction, Section 2.1 (Elements of lumped-parameter models), and Section 2.2 (Application of Newton's laws to lumped-parameter models)

__Chapter 3:__ Introduction (prototype SDOF system), Section 3.1 (free vibration of undamped SDOF systems), Section 3.2 (free vibration of viscous-damped SDOF systems, especially the underdamped case), and Section 3.3 (free-vibration measurement of SDOF natural frequency and damping__)__

__Chapter 4: Sections 4.1-4.3__ (SDOF response to steady sinusoidal excitation, especially the complex frequency response function method of Section 4.3) and Section 4.6 (frequency-response measurement of SDOF natural frequency and damping). Students should be aware that "structural" damping, as presented in Section 4.8, is generally a more realistic model for continuous structures than viscous damping. The viscous damping model is used predominantly in this and most other textbooks because it is more amenable to theoretical analysis.

__Chapter 5: Section 5.1 __(step response of viscous-damped SDOF systems), and Section 5.3 (response of undamped SDOF systems to ideal impulsive force)

__Chapter 6: Section 6.1__ (response of SDOF systems to ICs and general excitation, the convolution integral)

__Chapter 9: Section 9.1 __(Application of Newton's lawscontinuum PDE and BCs for a bar in axial deformation), Section 9.2 on (continuum PDE and BCs for a Bernoulli-Euler beam in bending deformation)

__Chapter 10: Section 10.1__ (vibration modes of continuous bars in axial deformation), Section 10.2 (vibration modes of continuous beams in bending deformation), Section 10.5 (orthogonality of continuous mode shapes, and the modal expansion theorem, for continuous beams in bending deformation)

__Chapter 11: Section 11.1__ (Application of Newton's laws to lumped-parameter models) and Sections 11.2-11.4 (Lagrange's equations and applications to lumped-parameter and continuous structural models, especially the global assumed modes method)

__Chapter 12: Section 12.1__ (Free vibration of 2-DOF systems).

__Chapter 13: Section 13.1 __(Important properties of natural frequencies and natural modes of MDOF structural models)

__Chapter 15: Section15.1__ (Introduction; principal coordinates), Sections 15.2 and 15.4 (mode-displacement solution for response of MDOF structures, with emphasis on steady-state frequency response)

__Chapter 16: Section 16.1__ (Introduction to the finite-element method), and Section 16.2 (Element stiffness & mass (both consistent and lumped) matrices and element consistent load vectors for bar, beam, and shaft elements).

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#### Applied Math and Numerical Methods

**Applied Math: (Math 4564 & 4574)**

References: Kreyszig, E., *Advanced Engineering Mathematics*, John Wiley and Sons, Inc., New York.

Part A: Ordinary Differential Equations

First-Order Differential Equations

Second-Order Linear Differential Equations

Higher-Order Linear Differential Equations

System of Differential Equations (Phase Plane and Stability)

Series Solution of Differential Equations, Special Functions

Laplace Transforms

Part B: Linear Algebra, Vector Calculus

Linear Algebra: Matrices, Vectors, Determinants

Vector Differential Calculus, Grad, Div, Curl

Vector Integral Calculus, Integral Theorems

Part C: Fourier Analysis

Fourier series, Integrals, and Transforms

**Numerical Analysis: (AOE 4404)**

Reference: Burden, R. L., and Faires, J. D., *Numerical Analysis*, Seventh edition, Brooks/Cole.

Solutions of Equations in One Variable (except 2.6)

Interpolation and Polynomial Approximation (except 3.5)

Numerical Differentiation and Integration

Initial Value Problems for Ordinary Differential Equations

Direct Methods for Solving Linear Systems

Iterative Techniques in Matrix Algebra

Approximating Eigenvalues

Numerical Solutions of Nonlinear Systems of Equations