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Earthquakes, a plucked string, ocean waves crashing on the beach, the sound waves that allow us to recognize known voices. Waves are everywhere, and the propagation and classical properties of these apparently disparate phenomena can be described by the same mathematical methods: variational calculus, characteristics theory, and caustics. Taking a medium-by-medium approach, Julian Davis explains the mathematics needed to understand wave propagation in inviscid and viscous fluids, elastic solids, viscoelastic solids, and thermoelastic media, including hyperbolic partial differential equations and characteristics theory, which makes possible geometric solutions to nonlinear wave problems. The result is a clear and unified treatment of wave propagation that makes a diverse body of mathematics accessible to engineers, physicists, and applied mathematicians engaged in research on elasticity, aerodynamics, and fluid mechanics. This book will particularly appeal to those working across specializations and those who seek the truly interdisciplinary understanding necessary to fully grasp waves and their behavior. By proceeding from concrete phenomena (e.g., the Doppler effect, the motion of sinusoidal waves, energy dissipation in viscous fluids, thermal stress) rather than abstract mathematical principles, Davis also creates a one-stop reference that will be prized by students of continuum mechanics and by mathematicians needing information on the physics of waves.

Wave-motion, Theory of. --- Acoustic impedance. --- Adiabatic condition. --- Adjoint operators. --- Bessel's equation. --- Boundary layer. --- Brachistochrome problem. --- Bulk modulus. --- Canonical transformations. --- Caustic or focal curves. --- Characteristic coordinates. --- Characteristic line element. --- Characteristics, method of. --- Critical sound speed. --- Cyclic coordinates. --- Deformation. --- Direction field. --- Doppler effect. --- Eigenfunctions. --- Eigenvalues. --- Epicycloid. --- Fermat's principle. --- Finite bar. --- Friction, internal. --- Generalized force. --- Generalized velocity. --- Hamilton-Jacoby theory. --- Hamiltonian. --- Ideal or perfect gas. --- Integral surfaces. --- Isothermal condition. --- Jacobian. --- Kinetic energy. --- Lagrangian function. --- Lame constants. --- Laminar flow. --- Memory function. --- Minimizing curve. --- Monge axis. --- Monge cone. --- Navier equations. --- Oseen approximation. --- Physics of propagating waves. --- Plane elastic waves. --- Poiseuille flow. --- Progressing wave. --- Quantum mechanics. --- Radially symmetric waves. --- Regressing wave. --- Reynold's law. --- Self-adjoint operator. --- Sinusoidal waves. --- Undulatory theory --- Mechanics

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The problem of solving complex engineering problems has always been a major topic in all industrial fields, such as aerospace, civil and mechanical engineering. The use of numerical methods has increased exponentially in the last few years, due to modern computers in the field of structural mechanics. Moreover, a wide range of numerical methods have been presented in the literature for solving such problems. Structural mechanics problems are dealt with using partial differential systems of equations that might be solved by following the two main classes of methods: Domain-decomposition methods or the so-called finite element methods and mesh-free methods where no decomposition is carried out. Both methodologies discretize a partial differential system into a set of algebraic equations that can be easily solved by computer implementation. The aim of the present Special Issue is to present a collection of recent works on these themes and a comparison of the novel advancements of both worlds in structural mechanics applications.

History of engineering & technology --- direction field --- tensor line --- principal stress --- tailored fiber placement --- heat conduction --- finite elements --- space-time --- elastodynamics --- mesh adaptation --- non-circular deep tunnel --- complex variables --- conformal mapping --- elasticity --- numerical simulation --- numerical modeling --- joint static strength --- finite element method --- parametric investigation --- reinforced joint (collar and doubler plate) --- nonlocal elasticity theory --- Galerkin weighted residual FEM --- silicon carbide nanowire --- silver nanowire --- gold nanowire --- biostructure --- rostrum --- paddlefish --- Polyodon spathula --- maximum-flow/minimum-cut --- stress patterns --- finite element modelling --- laminated composite plates --- non-uniform mechanical properties --- panel method --- marine propeller --- noise --- FW-H equations --- experimental test --- continuation methods --- bifurcations --- limit points --- cohesive elements --- functionally graded materials --- porosity distributions --- first-order shear deformation theory --- shear correction factor --- higher-order shear deformation theory --- equivalent single-layer approach --- n/a