# Courses (2024-25)

Introduction to Mechatronics

Mechatronics is the multi-disciplinary design of electro-mechanical systems. This course is intended to give the student a basic introduction to such systems. The course will focus on the implementations of sensor and actuator systems, the mechanical devices involved and the electrical circuits needed to interface with them. The class will consist of lectures and short labs where the student will be able to investigate the concepts discussed in lecture. Topics covered include motors, piezoelectric devices, light sensors, ultrasonic transducers, and navigational sensors such as accelerometers and gyroscopes. Graded pass/fail.

Introduction to Robotics

This course examines the range of concepts and engineering approaches applicable to robotics. This includes tools from mechanical design and fabrication, mathematical analysis of mechanisms, a variety of sensors, programming at all levels, algorithms to interpret visual images, and planners to determine actions. Robots also act in a larger context, involving human-robot interactions, social cues, and even raising ethical questions. The course will explore these topics through hardware and software mini-projects. Lab work will combine instructor-led, mandatory sessions with additional self-paced times. Open only to first-year students. Sophomore students by permission of the instructor.

Thinking Like an Engineer

A series of weekly seminars by practicing engineers in industry and academia to introduce students to principles and techniques useful for Mechanical Engineering. The course can be used to learn more about the different areas of study within Mechanical Engineering. Topics will be presented at an informal, introductory level. Required for ME undergraduates. Graded pass/fail.

Thermal Science

An introduction to classical thermodynamics and transport with engineering applications. First and second laws; closed and open systems; properties of a pure substance; availability and irreversibility; generalized thermodynamic relations; gas and vapor power cycles; propulsion; mixtures; combustion and thermochemistry; chemical equilibrium; momentum and heat transfer including boundary layers with applications to internal and external flows. Not offered on a pass/fail basis.

Mechanics

An introduction to statics and dynamics of rigid bodies, deformable bodies, and fluids. Equilibrium of force systems, principle of virtual work, distributed force systems, friction, static analysis of rigid and deformable structures, hydrostatics, kinematics, particle dynamics, rigid-body dynamics, Euler's equations, ideal flow, vorticity, viscous stresses in fluids, dynamics of deformable systems, waves in fluids and solids. Not offered on a pass/fail basis.

Mechanical Prototyping

Enrollment is limited and is based on responses to a questionnaire available in the Registrar's Office. Introduction to the technologies and practices needed to fabricate mechanical prototypes. Students will acquire the fundamental skills necessary to begin using 3D Computer-Aided Design (CAD) software. Students will learn how to build parametric models of parts and assemblies and learn how to generate detailed drawings of their designs. Students will also be introduced to manual machining techniques, as well as computer-controlled prototyping technologies, such as three-dimensional printing, laser cutting, and water jet cutting. Students will receive safety-training, instruction on the theories underlying different machining methods, and hands-on demonstrations of machining and mechanical assembly methods. Several prototypes will be constructed using the various technologies available in the Mechanical Engineering Machine Shop.

Design and Fabrication

Enrollment is limited and is based on responses to a questionnaire available in the Registrar's office. Introduction to mechanical engineering design, fabrication, and visual communication. Principles of mechanical engineering design are taught through a series of lectures and short group-based design projects with an emphasis on formal design reviews and team competitions. Course lectures address the strength properties of engineering materials, statistical descriptions of stress and strength, design safety factors, static and variable loading design criteria, engineering case studies, and the design of mechanical elements. Group-based projects include formal design reviews and involve substantial use of the machine shop and maker-space facilities, for the construction of working prototypes. Not offered on a pass/fail basis.

CNC Machining

Enrollment is limited and is based on responses to a questionnaire available in the Registrar's office. Introduction to computer numerical control machining. Students will learn to create Gcode and Mcode using Computer-Aided Manufacturing (CAM) software; they will be instructed on how to safely prepare and operate the machine's functions; and will be taught how to implement programmed data into several different types of CNC equipment. The class will cover the parts and terminology of the equipment, fixturing materials, setting workpiece, and tool offsets. Weekly assignments will include the use of CAM software, machine operation demonstrations, and machining projects.

Dimensional and Data Analyses in Engineering

Experiments and Modeling in Mechanical Engineering

Engineering Design Laboratory

Multidisciplinary Systems Engineering

This course presents the fundamentals of modern multidisciplinary systems engineering in the context of a substantial design project. Students from a variety of disciplines will conceive, design, implement, and operate a system involving electrical, information, and mechanical engineering components. Specific tools will be provided for setting project goals and objectives, managing interfaces between component subsystems, working in design teams, and tracking progress against tasks. Students will be expected to apply knowledge from other courses at Caltech in designing and implementing specific subsystems. During the first two terms of the course, students will attend project meetings and learn some basic tools for project design, while taking courses in CS, EE, and ME that are related to the course project. During the third term, the entire team will build, document, and demonstrate the course design project, which will differ from year to year. First-year undergraduate students must receive permission from the lead instructor to enroll. Not offered 2024-25.

Senior Thesis: Major Design Experience

Senior Thesis

Special Topics in Civil Engineering

Special problems or courses arranged to meet the needs of first-year graduate students or qualified undergraduate students. Graded pass/fail.

Independent Studies in Mechanical Engineering

A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of undergraduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term of work.

Fluid Mechanics

Fundamentals of fluid mechanics. Microscopic and macroscopic properties of liquids and gases; the continuum hypothesis; review of thermodynamics; general equations of motion; kinematics; stresses; constitutive relations; vorticity, circulation; Bernoulli's equation; potential flow; thin-airfoil theory; surface gravity waves; buoyancy-driven flows; rotating flows; viscous creeping flow; viscous boundary layers; introduction to stability and turbulence; quasi one-dimensional compressible flow; shock waves; unsteady compressible flow; and acoustics.

Mechanics of Structures and Solids

Introduction to continuum mechanics: kinematics, balance laws, constitutive laws with an emphasis on solids. Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Wave propagation. Analysis of rods, plates and shells with applications in a variety of fields. Variational theorems and approximate solutions. Elastic stability.

States of Matter

Thermodynamics and statistical mechanics, with emphasis on gases, liquids, materials, and condensed matter. Effects of heat, pressure, and fields on states of matter are presented with both classical thermodynamics and with statistical mechanics. Conditions of equilibrium in systems with multiple degrees of freedom. Applications include ordered states of matter and phase transitions. The three terms cover, approximately, thermodynamics, statistical mechanics, and phase transitions.

Design for Freedom from Disability

This Product Design class focuses on people with Disabilities and is done in collaboration with Rancho Los Amigos National Rehabilitation Center. Students visit the Center to define products based upon actual stated and observed needs. Designs and testing are done in collaboration with Rancho associates. Speakers include people with assistive needs, therapists and researchers. Classes teach normative design methodologies as adapted for this special area. Not offered 2024-25.

Computational Mechanics

Numerical methods and techniques for solving initial boundary value problems in continuum mechanics (from heat conduction to statics and dynamics of solids and structures). Finite difference methods, direct methods, variational methods, finite elements in small strains and at finite deformation for applications in structural mechanics and solid mechanics. Solution of the partial differential equations of heat transfer, solid and structural mechanics, and fluid mechanics. Transient and nonlinear problems. Computational aspects and development and use of finite element code.

Special Laboratory Work in Mechanical Engineering

Special laboratory work or experimental research projects may be arranged by members of the faculty to meet the needs of individual students as appropriate. A written report is required for each term of work.

Sustainable Engineering

Examines the Earth's resources including fresh water, nitrogen, carbon and other biogeochemical cycles that impose planetary constraints on engineering; systems approaches to sustainable development goals; fossil fuel formation, chemical composition, production and use; engineering challenges and opportunities in decarbonizing energy, transportation and industry; global flows of critical elements used in zero-carbon energy systems; food-water-energy nexus; analysis of regional and local systems to model effects of human activities on air, water and soil.

Mechanical Behavior of Materials

Introduction to the mechanical behavior of solids, emphasizing the relationships between microstructure, architecture, defects, and mechanical properties. Elastic, inelastic, and plastic properties of crystalline and amorphous materials. Relations between stress and strains for different types of materials. Introduction to dislocation theory, motion and forces on dislocations, strengthening mechanisms in crystalline solids. Nanomaterials: properties, fabrication, and mechanics. Architected solids: fabrication, deformation, failure, and energy absorption. Biomaterials: mechanical properties of composites, multi-scale microstructure, biological vs. synthetic, shear lag model. Fracture in brittle solids and linear elastic fracture mechanics.

Energy Technology and Policy

Energy technologies and the impact of government policy. Fossil fuels, nuclear power, and renewables for electricity production and transportation. Resource models and climate change policies. New and emerging technologies.

Classical Thermodynamics

Fundamentals of Classical Thermodynamics. Basic laws of thermodynamics, work and heat, entropy and available work, and thermal systems. Equations of state, compressibility functions, and the Law of Corresponding States. Thermodynamic potentials, phase equilibrium, phase transitions, and thermodynamic properties of solids, liquids, and gases. Examples will be drawn from fluid dynamics, solid mechanics, energy systems, and thermal-science applications.

Heat and Mass Transfer

Transport properties, conservation equations, conduction heat transfer, convective heat and mass transport in laminar and turbulent flows, phase change processes, thermal radiation.

Combustion Fundamentals

Experimental Robotics

Robotics

The course develops the core concepts of robotics. The first quarter focuses on classical robotic manipulation, including topics in rigid body kinematics and dynamics. It develops planar and 3D kinematic formulations and algorithms for forward and inverse computations, Jacobians, and manipulability. The second quarter transitions to planning, navigation, and perception. Topics include configuration space, sample-based planners, A* and D* algorithms, to achieve collision-free motions. Course work transitions from homework and programming assignments to more open-ended team-based projects.

Robotic Systems

This course builds up, and brings to practice, the elements of robotic systems at the intersection of hardware, kinematics and control, computer vision, and autonomous behaviors. It presents selected topics from these domains, focusing on their integration into a full sense-think-act robot. The lectures will drive team-based projects, progressing from building custom robotic arms (5 to 7 degrees of freedom) to writing all necessary software (utilizing the Robotics Operating system, ROS). Teams are required to implement and customize general concepts for their selected tasks. Working systems will autonomously operate and demonstrate their capabilities during final presentations.

Computational Methods for Flow in Porous Media

Graduate Engineering Seminar

Students attend a graduate seminar each week of each term and submit a report about the attended seminars. At least four of the attended seminars each term should be from the Mechanical and Civil Engineering seminar series. Students not registered for the M.S. and Ph.D. degrees must receive the instructor's permission. Graded pass/fail.

Dynamics and Vibration

Equilibrium concepts, conservative and dissipative systems, Lagrange's equations, differential equations of motion for discrete single and multi degree-of-freedom systems, natural frequencies and mode shapes of these systems (Eigenvalue problem associated with the governing equations), phase plane analysis of vibrating systems, forms of damping and energy dissipated in damped systems, response to simple force pulses, harmonic and earthquake excitation, response spectrum concepts, vibration isolation, seismic instruments, dynamics of continuous systems, Hamilton's principle, axial vibration of rods and membranes, transverse vibration of strings, beams (Bernoulli-Euler and Timoshenko beam theory), and plates, traveling and standing wave solutions to motion of continuous systems, Rayleigh quotient and the Rayleigh-Ritz method to approximate natural frequencies and mode shapes of discrete and continuous systems, frequency domain solutions to dynamical systems, stability criteria for dynamical systems, and introduction to nonlinear systems and random vibration theory.

Continuum Mechanics of Fluids and Solids

Elements of Cartesian tensors. Configurations and motions of a body. Kinematics-study of deformations, rotations and stretches, polar decomposition. Lagrangian and Eulerian strain velocity and spin tensor fields. Irrotational motions, rigid motions. Kinetics-balance laws. Linear and angular momentum, force, traction stress. Cauchy's theorem, properties of Cauchy's stress. Equations of motion, equilibrium equations. Power theorem, nominal (Piola-Kirchoff) stress. Thermodynamics of bodies. Internal energy, heat flux, heat supply. Laws of thermodynamics, notions of entropy, absolute temperature. Entropy inequality (Clausius-Duhem). Examples of special classes of constitutive laws for materials without memory. Objective rates, corotational, convected rates. Principles of materials frame indifference. Examples: the isotropic Navier-Stokes fluid, the isotropic thermoelastic solid. Basics of finite differences, finite elements, and boundary integral methods, and their applications to continuum mechanics problems illustrating a variety of classes of constitutive laws. part b not offered 2024-25

Structural and Earthquake Engineering

Matrix structural analysis of the static and dynamic response of structural systems, Newmark time integration, Newton-Raphson iteration methodology for the response of nonlinear systems, stability of iteration schemes, static and dynamic numerical analysis of planar beam structures (topics include the development of stiffness, mass, and damping matrices, material and geometric nonlinearity effects, formulation of a nonlinear 2-D beam element, uniform and nonuniform earthquake loading, soil-structure interaction, 3-D beam element formulation, shear deformations, and panel zone deformations in steel frames, and large deformation analysis), seismic design and analysis of steel moment frame and braced frame systems, steel member behavior (topics include bending, buckling, torsion, warping, and lateral torsional buckling, and the effects of residual stresses), reinforced concrete member behavior (topics include bending, shear, torsion, and PMM interaction), and seismic design requirements for reinforced concrete structures. Not offered 2024-25.

Imperfections in Crystals

The relation of lattice defects to the physical and mechanical properties of crystalline solids. Introduction to point imperfections and their relationships to transport properties in metallic, covalent, and ionic crystals. Kroeger-Vink notation. Introduction to dislocations: geometric, crystallographic, elastic, and energetic properties of dislocations. Dislocation reactions and interactions including formation of locks, stacking faults, and surface effects. Relations between collective dislocation behavior and mechanical properties of crystals. Introduction to computer simulations of dislocations. Grain boundaries. The structure and properties of interfaces in solids. Emphasis on materials science aspects of role of defects in electrical, morphological, optical, and mechanical properties of solids. Not offered 2024-25.

Mechanics of Composite Materials and Structures

Finite Elasticity

Finite theory of elasticity: constitutive theory, semi-inverse methods. Variational methods. Applications to problems of current interest. Not offered 2024-25.

Fracture of Brittle Solids

The mechanical response of brittle materials (ceramics, glasses and some network polymers) will be treated using classical elasticity, energy criteria, and fracture mechanics. The influence of environment and microstructure on mechanical behavior will be explored. Transformation toughened systems, large-grain crack-bridging systems, nanostructured ceramics, porous ceramics, anomalous glasses, and the role of residual stresses will be highlighted. Strength, flaw statistics and reliability will be discussed.

Mobile Robots

Mobile robots need to perceive their environment and localize themselves with respect to maps thereof. They further require planners to move along collision-free paths. This course builds up mobile robots in team-based projects. Teams will write all necessary software from low-level hardware I/O to high level algorithms, using the robotic operating system (ROS). The final systems will autonomously maneuver to reach their goals or track various objectives.

Mechanics of Rocks

Basic principles of deformation, strength, and stressing of rocks. Elastic behavior, plasticity, viscoelasticity, viscoplasticity, creep, damage, friction, failure mechanisms, shear localization, and interaction of deformation processes with fluids. Engineering and geological applications. Not offered 2024-25.

Climate Change Impacts, Mitigation and Adaptation

Climate change has already begun to impact life on the planet, and will continue in the coming decades. This class will explore particular causes and impacts of climate change, technologies to mitigate or adapt to those impacts, and the economic and social costs associated with them - particular focus will be paid to distributional issues, environmental and racial justice and equity intersections. The course will consist of 3-4 topical modules, each focused on a specific impact or sector (e.g. the electricity or transportation sector, climate impacts of food and agriculture, increasing fires and floods). Each module will contain lectures/content on the associated climate science background, engineering/technological developments to combat the issue, and an exploration of the economics and the inequities that exacerbate the situation, followed by group discussion and synthesis of the different perspectives.

Experimental Methods in Earthquake Engineering

Laboratory work involving calibration and performance of basic transducers suitable for the measurement of strong earthquake ground motion, and of structural response to such motion. Study of principal methods of dynamic tests of structures, including generation of forces and measurement of structural response. Not offered 2024-25.

Advanced Work in Civil Engineering

A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of graduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term.

Advanced Work in Mechanical Engineering

A faculty mentor will oversee a student proposed, independent research or study project to meet the needs of graduate students. Graded pass/fail. The consent of a faculty mentor and a written report is required for each term of work.

Advanced Topics in Civil Engineering

The faculty will prepare courses on advanced topics to meet the needs of graduate students.

Advanced Topics in Mechanical Engineering

The faculty will prepare courses on advanced topics to meet the needs of graduate students.

Mechanics and Materials Aspects of Fracture

Analytical and experimental techniques in the study of fracture in metallic and nonmetallic solids. Mechanics of brittle and ductile fracture; connections between the continuum descriptions of fracture and micromechanisms. Discussion of elastic-plastic fracture analysis and fracture criteria. Special topics include fracture by cleavage, void growth, rate sensitivity, crack deflection and toughening mechanisms, as well as fracture of nontraditional materials. Fatigue crack growth and life prediction techniques will also be discussed. In addition, "dynamic" stress wave dominated, failure initiation growth and arrest phenomena will be covered. This will include traditional dynamic fracture considerations as well as discussions of failure by adiabatic shear localization. Not offered 2024-25

Computational Solid Mechanics

This course focuses on the analysis of elastic thin shell structures in the large deformation regime. Problems of interest include softening behavior, bifurcations, loss of stability and localization. Introduction to the use of numerical methods in the solution of solid mechanics and multiscale mechanics problems. Variational principles. Finite element and isogeometric formulations for thin shells. Time integration, initial boundary value problems. Error estimation. Accuracy, stability and convergence. Iterative solution methods. Adaptive strategies. Not offered 2024-25.

Dynamic Behavior of Materials

Fundamentals of theory of wave propagation; plane waves, wave guides, dispersion relations; dynamic plasticity, adiabatic shear banding; dynamic fracture; shock waves, equation of state. Not offered 2024-25

Statistical Mechanics

Overview of probability and statistics, and the Maxwell-Boltzmann distribution. Overview and elements of Quantum Mechanics, degenerate energy states, particles in a box, and energy-state phase space. Statistics of indistinguishable elementary particles, Fermi-Dirac and Bose-Einstein statistics, partition functions, connections with classical thermodynamics, and the Law of Equipartition. Examples from equilibrium in fluids, solid-state physics, and others. Not offered 2024-25

Space Structures

This course examines the links between form, geometric shape, and structural performance. It deals with different ways of breaking up a continuum, and how this affects global structural properties; structural concepts and preliminary design methods that are used in tension structures and deployable structures. Geometric foundations, polyhedra and tessellations, surfaces; space frames, examples of space frames, stiffness and structural efficiency of frames with different repeating units; sandwich plates; cable and membrane structures, form-finding, wrinkle-free pneumatic domes, balloons, tension-stabilized struts, tensegrity domes; deployable and adaptive structures, coiled rods and their applications, flexible shells, membranes, structural mechanisms, actuators, concepts for adaptive trusses and manipulators. Not offered 2024-25

Effective properties of heterogenous and meta-materials

Heterogenous materials. Notion of effective properties. Homogenization theory and applications to linear conductivity, elasticity and viscoelasticity. Effective properties in non-linear setting and instabilities. Wave propagation and meta-materials. Bandgaps.

Plasticity

Theory of dislocations in crystalline media. Characteristics of dislocations and their influence on the mechanical behavior in various crystal structures. Application of dislocation theory to single and polycrystal plasticity. Theory of the inelastic behavior of materials with negligible time effects. Experimental background for metals and fundamental postulates for plastic stress-strain relations. Variational principles for incremental elastic-plastic problems, uniqueness. Upper and lower bound theorems of limit analysis and shakedown. Slip line theory and applications. Additional topics may include soils, creep and rate-sensitive effects in metals, the thermodynamics of plastic deformation, and experimental methods in plasticity. Not offered 2024-25

Multifunctional Materials

Multiscale view of materials and different approaches of introducing functionality; Electronic aspects and multiferroic materials; Symmetry breaking phase transformations, microstructure: shape-memory alloys, ferroelectrics, liquid crystal elastomers; Composite materials and metamaterials: multifunctional structures. Not offered 2024-25.

Special Topics in Solid Mechanics

Subject matter changes depending on staff and student interest. Not offered 2024-25

Computational Fluid Dynamics

Development and analysis of algorithms used in the solution of fluid mechanics problems. Numerical analysis of discretization schemes for partial differential equations including interpolation, integration, spatial discretization, systems of ordinary differential equations; stability, accuracy, aliasing, Gibbs and Runge phenomena, numerical dissipation and dispersion; boundary conditions. Survey of finite difference, finite element, finite volume and spectral approximations for the numerical solution of the incompressible and compressible Euler and Navier-Stokes equations, including shock-capturing methods.

Advanced Robotics: Planning

Advanced topics in robotic motion planning and navigation, including inertial navigation, simultaneous localization and mapping, Markov Decision Processes, Stochastic Receding Horizon Control, Risk-Aware planning, robotic coverage planning, and multi-robot coordination. Course work will consist of homework, programming projects, and labs. Given in alternate years.

Advanced Robotics: Kinematics

Advanced topics in robot kinematics and robotic mechanisms. Topics include a Lie Algebraic viewpoint on kinematics and robot dynamics, a review of robotic mechanisms, and a detailed development of robotic grasping and manipulation. Given in alternate years. Not offered 2024-25.

Stable Isotopes: Ecological and Environmental Applications

Closed Loop Flow Control

This course seeks to introduce students to recent developments in theoretical and practical aspects of applying control to flow phenomena and fluid systems. Lecture topics in the second term drawn from: the objectives of flow control; a review of relevant concepts from classical and modern control theory; high-fidelity and reduced-order modeling; principles and design of actuators and sensors. Third term: laboratory work in open- and closed-loop control of boundary layers, turbulence, aerodynamic forces, bluff body drag, combustion oscillations and flow-acoustic oscillations. Not offered 2024-25

Linear and Nonlinear Waves in Structured Media

The course will cover the basic principles of wave propagation in solid media. It will discuss the fundamental principles used to describe linear and nonlinear wave propagation in continuum and discrete media. Selected recent scientific advancements in the dynamics of periodic media will also be discussed. Students learn the basic principles governing the propagation of waves in discrete and continuum solid media. These methods can be used to engineer materials with predefined properties and to design dynamical systems for a variety of engineering applications (e.g., vibration mitigation, impact absorption and sound insulation). The course will include an experimental component, to test wave phenomena in structured media. Not offered 2024-25.

Static and Dynamic Failure of Brittle Solids and Interfaces, from the Micro to the Mega

Linear elastic fracture mechanics of homogeneous brittle solids (e.g. geo-materials, ceramics, metallic glasses); small scale yielding concepts; experimental methods in fracture, fracture of bi-material interfaces with applications to composites as well as bonded and layered engineering and geological structures; thin-film and micro-electronic components and systems; dynamic fracture mechanics of homogeneous engineering materials; dynamic shear dominated failure of coherent and incoherent interfaces at all length scales; dynamic rupture of frictional interfaces with application to earthquake source mechanics; allowable rupture speeds regimes and connections to earthquake seismology and the generation of Tsunamis. Not offered 2024-25

Fracture and Frictional Faulting

Introduction to elastodynamics and waves in solids. Fracture theory, energy concepts, cohesive zone models. Friction laws, nucleation of frictional instabilities, rupture of frictional interfaces. Radiation from moving cracks. Thermal effects during dynamic fracture and faulting. Interaction of faulting with fluids. Applications to engineering phenomena a physics and mechanics of earthquakes.

Research in Civil Engineering

Research in the field of civil engineering. By arrangements with members of the staff, properly qualified graduate students are directed in research.

Research in Mechanical Engineering

Research in the field of mechanical engineering. By arrangement with members of the faculty, properly qualified graduate students are directed in research.