Daraio Research Group Caltech

AM/CE. 9 units (2-1-6); second term. 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.

Mechanics. 9 units (3-0-6); third term. Prerequisites: Sophomore standing required; ME 11 abc, may be taken concurrently. 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 .

AM/CE. 9 units (3-0-6); second terms. 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 (Eigen value 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.

Ae/AM/ME 225. 9 units (3-0-6); second term. Prerequisite Ae/AM/ME 102abc or permission of the instructor.

The course will cover the basic principles of linear and nonlinear wave propagation in periodic media. It will introduce examples of periodic structural configurations at different length-scales and their relation to wave propagation. The course will cover the fundamental mathematical principles used to describe linear wave propagation and will describe the fundamentals of weakly nonlinear and highly nonlinear approaches. Selected recent scientific advancements in the dynamics of periodic media will also be discussed.

AE 244. 9 units (3-0-6); third term.

Basics of the mechanics of nanomaterials, including the physical and chemical synthesis/processing techniques for creating nanostructures and their relation with mechanical and other structural properties. Overview of the properties of various types of nanomaterials including nanostructured metals/ceramics/composites, nanowires, carbon nanotubes, quantum dots, nanopatterns, self-assembled colloidal crystals, magnetic nanomaterials, and biorelated nanomaterials. Innovative experimental methods and microstructural characterization developed for studying the mechanics at the nanoscale will be described. Recent advances in the application of nanomaterials in engineering systems and patent-related aspects of nanomaterials will also be covered. Open to undergraduates with instructor's permission.

Ae/AM/CE/ME 102 ab. 9 units (3-0-6); first, second, third terms. Prerequisite: ME 35 abc or equivalent.

Static and dynamic stress analysis. Two- and three-dimensional theory of stressed elastic solids. Analysis of structural elements with applications in a variety of fields. Variational theorems and approximate solutions, finite elements. A variety of special topics will be discussed in the third term such as, but not limited to, elastic stability, wave propagation, and introductory fracture mechanics.

ME65a. 9 units (3-0-6); first term. Prerequisites: ME 35 abc, Ma 2 ab.

Introduction to continuum mechanics, principles of elasticity, plane stress, plane strain, axisymmetric problems, stress concentrations, thin films, fracture mechanics, variational principles, frame structures, finite element methods, composites, and plasticity. Taught concurrently with Ae/AM/CE/ME 102.

ME 35c. 9 units (3-0-6); first, second, third terms. Prerequisites: Ma 1 abc, Ph 1 abc.

Introduction to statics and dynamics of rigid and deformable bodies. Equilibrium of force systems, principle of virtual work, distributed force systems, friction, static analysis of rigid and deformable structures, kinematics, particle dynamics, rigid-body dynamics, dynamics of deformable systems, and vibrating systems.

The course is an advanced introduction to nonlinear problems of elastic continuum media. It will start with a review of basic principles and equations for linear elasticity in continuum media under the small strains assumptions. It will then introduce slender structures, i.e. rods and plates and analyze buckling and instabilities introduced by the geometric nonlinearity of their kinematics. Bringing kinematic nonlinearities to three dimensional to continuum structures will naturally lead to finite strains and nonlinear elasticity. The theoretical topics will be illustrated by work-out examples and experiments using rods, strings, rubber balloons and sheets. The concepts are introduced using precise mathematical deductions and physical assumptions and will be discussed in depth. However, calculations will be kept to a minimum by using symbolic and numeric computations to solve different problem settings. The presented method can be applied for various engineering applications, e.g. the prediction of the failure of structures by buckling and instability, the design of novel materials with architectured microstructures or the analysis of soft biological materials.

For the mechanical design of systems, knowledge about basic concepts of continuum mechanics are indispensable. These include mechanical stress, deformations, etc. which are demonstrated on simple examples resulting in an understanding which is both mathematically correct and intuitive. In this course students learn the basic concepts of the mechanics of deformable media that they will later apply in other courses that are closer to real engineering applications.

The course provides an introduction to the mechanics of nano- and micro-materials and devices, in the quasi-static and dynamic domains. It reviews scale effects in materials, surveys available characterization techniques and describes the effects of surfaces and micro-scale contacts. Recent applications of nano- and micro-materials in engineering systems will also be discussed.

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).