Structural Dynamics Fundamentals And Advanced Applications

[Klacee Sawatzky]

Thiscourse is designed to give beginning students the basic preparation in mathematical methods required for graduate Structural Engineering courses. Topics include: linear algebra; systems of ordinary differential equations; diffusion and wave propagation problems; integral transforms; and calculus of variations. Prerequisites: graduate standing or approval of instructor.

Application of advanced analytical concepts to structural engineering problems. Analysis of frame structures using matrix methods and introduction to the finite element method. Displacement-based and force-based beam element formulations. Development of computer programs for structural analysis. Use of computer resources. Prerequisites: graduate standing.

The course emphasizes the principles behind modern nonlinear structural analysis software. It deals with the theory, computer implementation, and applications of methods of material and geometric nonlinear analysis. Emphasis is on 2D and 3D frame structures modeled using 1D (beam-column) elements. Use of computer resources. Prerequisites: SE 201A or equivalent, or consent of instructor.

Static, dynamic, and energy-based techniques and predicting elastic stability. Linear and nonlinear analysis of classical and shear deformable beams and plates. Ritz, Galerkin, and finite element approaches for frames and reinforced shells. Nonconservative aerodynamic (divergence flutter) and follower forces. Recommended preparation: SE 101A-C and SE 110A or equivalent background in solid mechanics and structural dynamics. Prerequisites: graduate standing.

Response of discrete linear structural systems to harmonic, periodic and transient excitations. Lagrangian mechanics. Linearization of the equations of motion. Free and forced vibrations of multi degree-of-freedom structures. Normal mode, frequency response and numerical methods. Continuous systems. Prerequisites: graduate standing or consent of instructor.

Free-and forced-vibration of continuous systems such as axial and torsional vibrations of bars and transverse vibrations of various beams, membranes, and plates. Euler-Lagrange formulation using variational calculus. Rayleigh-Ritz method for approximation. Applications in vibration suppression/isolation. Prerequisites: graduate standing.

Advanced analytical techniques to understand nonlinearity in mechanical vibration. Phase plane analysis instability, and bifurcations. Application in nonlinear structural resonance. Introduction to chaotic dynamics, advanced time series analysis, and using chaotic dynamics in applications such as structural damage assessment. Prerequisites: SE 203 or consent of instructor; graduate standing.

Introduction to probability theory and random processes. Dynamic analysis of linear structural systems subjected to stationary and nonstationary random excitations. Reliability studies related to first excursion and fatigue failures. Applications in earthquake engineering, offshore engineering, wind engineering, and aerospace engineering. Use of computer resources. Recommended preparation: basic knowledge of probability theory (SE 125 or equivalent). Prerequisites: SE 203; graduate standing.

Properties of reinforcing steels; concrete technology; creep, shrinkage and relaxation; Mohr-Coulomb failure criteria for concrete; confinement, moment curvature and force-displacement responses; plastic design; code compliant seismic design philosophy; code compliant seismic design of structural walls. Use of computer resources. Recommended preparation: SE 151A and SE 151B or equivalent background in basic RC/PC design. Prerequisites: department approval or consent of instructor.

Load and Resistance Factor Design (LRFD) philosophy. Behavior and design of steel elements for global and local buckling. Background of seismic codes. Ductility requirements and capability design concept. Seismic design of steel moment frames and braced frames. Recommended preparation: SE 130A and SE 150A, or equivalent course, or consent of instructor.

Analysis and design of unreinforced and reinforced masonry structure using advanced analytical techniques and design philosophies. Material properties, stability, and buckling of unreinforced masonry. Flexural strength, shear strength, stiffness, and ductility of reinforced masonry elements. Design for seismic loads. Prerequisites: SE 151A or equivalent basic reinforced concrete course, or consent of instructor; graduate standing.

The course deals with cable structures from a structural mechanics point of view. The theoretical and practical aspects of the application of cables to moorings, guyed structures, suspension bridges, cable-stayed bridges, and suspended membranes are discussed. Prerequisites: graduate standing or consent of instructor.

Concepts, advantages, and limitations of seismic isolation techniques; fundamentals of dynamic response under seismic excitation; spectral analysis; damping; energy approach; application to buildings and structures. Prerequisites: SE 221 or consent of instructor.

Introduction to plate tectonics and seismology. Rupture mechanism, measures of magnitude and intensity, earthquake occurrence and relation to geologic, tectonic processes. Probabilistic seismic hazard analysis. Strong earthquake ground motion; site effects on ground motion; structural response; soil-structure interaction; design criteria; code requirements. Use of computer resources. Prerequisites: SE201A or SE 203; graduate standing.

Influence of soil conditions on ground motion characteristics; dynamic behavior of soils, computation of ground response using wave propagation analysis and finite element analysis; evaluation and mitigation of soil liquefaction; soil-structure interaction; lateral pressures on earth retaining structures; analysis of slope stability. Recommended preparation: SE 181 or equivalent. Prerequisites: department approval and graduate standing.

Modal analysis. Nonlinear response spectra. Performance based seismic design. Nonlinear time history analyses. Capacity design. Structural walls. Coupled walls. Rocking walls. Base isolation. Recommended preparation: grade of B+ or higher in SE 211 and SE 201B. Prerequisites: department approval and graduate standing.

Review of probability theory and random processes. Fundamentals of structural reliability theory. First- and second-order, and simulation methods of reliability analysis. Structural component and system reliability. Reliability sensitivity measures. Bayesian reliability analysis methods. Bases for probabilistic design codes. Use of computer resources. Recommended preparation: basic knowledge of probability theory (e.g., SE 125). Prerequisites: graduate standing.

This course will treat quantitative aspects of the flow of uncontaminated groundwater as it influences the practice of geotechnical engineering. We will cover flow through porous media, generalized Darcy's law, groundwater modeling, confined and unconfined systems, well hydraulics, land subsidence, and construction dewatering. Prerequisites: SE 241 or consent of instructor; graduate standing.

Provides background and tools to apply machine learning to solve problems in computational mechanics and engineering. An overview of the basic principles of machine learning will be provided, including supervised and unsupervised learning, regression, classification, and generative algorithms versus discriminative algorithms. Focus will be given to deep neural networks, convolutional neural networks, recurrent neural networks, physics-informed machine learning and implementation in Python. Recommended preparation: knowledge of computer programming, probability theory, linear algebra, and solid mechanics. Prerequisites: graduate standing or consent of instructor.

Cross-listed with MAE 235. Practical application of the finite element method to problems in solid mechanics. Elements of theory are presented as needed. Covered are static and dynamic heat transfer and stress analysis. Basic processing, solution methods, and postprocessing are practiced with commercial finite element software. Students may not receive credit for SE 233 and MAE 235.

Wave propagation in elastic media with emphasis on waves in unbound media and on uniform and layered half-spaces. Fundamental aspects of elastodynamics. Application to strong-motion seismology, earthquake engineering, dynamics of foundations, computational wave propagation, and nondestructive evaluations. Prerequisites: graduate standing or consent of instructor.

Propagation of elastic waves in thin structural elements such as strings, rods, beams, membranes, plates, and shells. An approximate strength-of-materials approach is used to consider propagation of elastic waves in these elements and obtain the dynamic response to transient loads. Prerequisites: graduate standing or consent of instructor.

Advanced treatment of topics in soil mechanics, including state of stress, pore pressure, consolidation and settlement analysis, shear strength of cohesionless and cohesive soils, mechanisms of ground improvement, and slope stability analysis. Concepts in course reinforced by laboratory experiments.

Application of soil mechanics to the analysis, design, and construction of foundations for structures. Soil exploration, sampling, and in-situ testing techniques. Stress distribution and settlement of structures. Bearing capacities of shallow foundations and effects on structural design. Analysis of axial and lateral capacity of deep foundations, including drilled piers and driven piles. Prerequisites: graduate standing or consent of instructor.

Advanced treatment of the dynamic interaction between soils and structures. Dynamic response of shallow and embedded foundations. Kinematic and inertial interaction. General computational and approximate analytical methods of analysis. Prerequisites: SE 200 and SE 203; graduate standing.

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