Master the principles of structural dynamics with this comprehensive and self-contained textbook, with key theoretical concepts explained through real-world engineering applications.

• The theory of natural modes of vibration, the finite element method, and the dynamic response of structures is balanced with practical applications to give students a thorough contextual understanding of the subject.

• Enhanced coverage of damping, rotating systems, and parametric excitation provides students with superior understanding of these essential topics.

• Examples and homework problems, closely linked to real-world applications, enrich and deepen student understanding.

• Curated mathematical appendices equip students with all the tools necessary to excel, without disrupting coverage of core topics.

• Containing all the material needed for a one- or two-semester course, and accompanied online by MATLAB/Python code, this authoritative textbook is the ideal introduction for graduate students in aerospace, mechanical, and civil engineering.

Master the principles of structural dynamics with this comprehensive and self-contained textbook, with key theoretical concepts explained through real-world engineering applications.

• The theory of natural modes of vibration, the finite element method, and the dynamic response of structures is balanced with practical applications to give students a thorough contextual understanding of the subject.

• Enhanced coverage of damping, rotating systems, and parametric excitation provides students with superior understanding of these essential topics.

• Examples and homework problems, closely linked to real-world applications, enrich and deepen student understanding.

• Curated mathematical appendices equip students with all the tools necessary to excel, without disrupting coverage of core topics.

• Containing all the material needed for a one- or two-semester course, and accompanied online by MATLAB/Python code, this authoritative textbook is the ideal introduction for graduate students in aerospace, mechanical, and civil engineering.

Master the principles of structural dynamics with this comprehensive and self-contained textbook, with key theoretical concepts explained through real-world engineering applications.

• The theory of natural modes of vibration, the finite element method, and the dynamic response of structures is balanced with practical applications to give students a thorough contextual understanding of the subject.

• Enhanced coverage of damping, rotating systems, and parametric excitation provides students with superior understanding of these essential topics.

• Examples and homework problems, closely linked to real-world applications, enrich and deepen student understanding.

• Curated mathematical appendices equip students with all the tools necessary to excel, without disrupting coverage of core topics.

• Containing all the material needed for a one- or two-semester course, and accompanied online by MATLAB/Python code, this authoritative textbook is the ideal introduction for graduate students in aerospace, mechanical, and civil engineering.

Master the principles of structural dynamics with this comprehensive and self-contained textbook, with key theoretical concepts explained through real-world engineering applications.

• The theory of natural modes of vibration, the finite element method, and the dynamic response of structures is balanced with practical applications to give students a thorough contextual understanding of the subject.

• Enhanced coverage of damping, rotating systems, and parametric excitation provides students with superior understanding of these essential topics.

• Examples and homework problems, closely linked to real-world applications, enrich and deepen student understanding.

• Curated mathematical appendices equip students with all the tools necessary to excel, without disrupting coverage of core topics.

• Containing all the material needed for a one- or two-semester course, and accompanied online by MATLAB/Python code, this authoritative textbook is the ideal introduction for graduate students in aerospace, mechanical, and civil engineering.

Master the principles of structural dynamics with this comprehensive and self-contained textbook, with key theoretical concepts explained through real-world engineering applications.

• The theory of natural modes of vibration, the finite element method, and the dynamic response of structures is balanced with practical applications to give students a thorough contextual understanding of the subject.

• Enhanced coverage of damping, rotating systems, and parametric excitation provides students with superior understanding of these essential topics.

• Examples and homework problems, closely linked to real-world applications, enrich and deepen student understanding.

• Curated mathematical appendices equip students with all the tools necessary to excel, without disrupting coverage of core topics.

• Containing all the material needed for a one- or two-semester course, and accompanied online by MATLAB/Python code, this authoritative textbook is the ideal introduction for graduate students in aerospace, mechanical, and civil engineering.

Groundwater flow varies spatiotemporally under many real-world situations, different from the natural gradient experiments in Chapter 10. This chapter presents field experiments that explore the role of velocity variation at the local- and large-scale solute migration in the aquifer and reveal difficulties in characterizing the aquifer, monitoring, and predicting solute transport even in a small-scale aquifer.

Widely used, parsimonious, practical well-mixed models are presented in this chapter for lakes water quality analyses. In addition, the volume-average, ensemble average, and stochastic concepts implicitly rooted in these models are explained and emphasized.

Chapter 4 introduces the molecular diffusion concept and Fick’s Law to explain the mixing phenomena at a small-scale CV in the distributed models rather than the large CV of the well-mixed model. For this purpose, it begins with describing diffusion phenomena, then formulating Fick’s law and developing the diffusion equation. Subsequently, examining the random velocity of Brownian particles and their pure random walk, we articulate the probabilistic nature of the molecular diffusion process and the reason why Fick’s Law is an ensemble mean law. Next, analytical solutions to the diffusion equation for various types of inputs are introduced. The advection-dispersion equation (ADE) formulation then follows, which couples the effect of fluid motion at fluid continuum scale and random motion of fluid molecules at the molecular scale to quantify solute migration. Likewise, we present analytical solutions to the ADE for several input forms and discuss snapshots and breakthroughs for different input forms.

This chapter discusses two different approaches to describing fluid flow: a Lagrangian approach (following a fluid element as it moves) and a Eulerian approach (watching fluid pass through a fixed volume in space). Understanding each of these descriptions of flow is needed to fully understand the dynamics of fluids. This chapter is devoted to diving into the differences between the two descriptions of fluid motion. Understanding this chapter will help tremendously in the understanding of the upcoming chapters when the Navier–Stokes equations and energy equation are discussed. This chapter will introduce the material derivative. It is extremely important to understand this derivative before the Navier–Stokes equations themselves are tackled.

Field tracer experiments in Borden aquifer in Canada and the Macrodispersion Experiment (MADE) Site, Mississippi, are reviewed. Both experiments injected tracers in aquifers and monitored their movements over fields at ten to hundred meters under natural gradient conditions. The behaviors of the tracer plumes at these two sites are distinctly different because the Borden aquifer is statistically homogeneous, and the aquifer of MADE is statistically heterogeneous. As a result, the validity of the classical ADE and non-Fickian dual-domain models becomes a contentious debate and deserves articulation of the differences between the ensemble mean nature of the models and the observations in one realization. The two experiments provided opportunities for understanding the limitations of applying solute transport theories and mathematical models based on soil-column experiments to real-world scenarios where heterogeneity is multi-scales, and groundwater flow varies spatiotemporally. Ignorance of the differences in scale of dominant heterogeneity and the observation, model, and interest scales is to blame. We explore and discuss the strengths and weaknesses of the theories and models.

In the previous chapter, the forces acting on a moving fluid element were exhaustively studied. Using Newtons second law of motion, the Navier–Stokes equations for both compressible and incompressible flows were obtained. This chapter uses an alternative approach to developing the Navier–Stokes equations. Namely, by starting from a Eulerian description (as opposed to a Lagrangian description), the integral form and conservation form of the Navier–Stokes equations are developed. The continuity and Navier–Stokes equations in its various forms are tabulated and reviewed in this chapter. This chapter ends by solving some very simple, yet common, problems involving the incompressible Navier–Stokes equations.

This chapter introduces numerical methods, including 1) Finite Difference Approach, 2) Methods of characteristics (Eulerian-Lagrangian), and 3) Finite Element Approach for solving the ADE applicable to multidimensional, variable velocity, irregular boundary, and initial conditions. However, only one- and two-dimension examples are illustrated for convenience. Once the algorithms are understood, they can be expanded to other situations with ease.