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Resonant Ultrasound Spectroscopy
Resonant ultrasound spectroscopy (RUS) is a laboratory technique used in geology and material science to measure fundamental material properties involving elasticity. This technique relies on the fact that solid objects have natural frequencies at which they vibrate when mechanically excited. The natural frequency depends on the elasticity, size, and shape of the object—RUS exploits this property of solids to determine the elastic tensor of the material. The great advantage of this technique is that the entire elastic tensor is obtained from a single crystal sample in a single rapid measurement. At lower or more general frequencies, this method is known as acoustic resonance spectroscopy. History Interest in elastic properties made its entrance with 17th century philosophers, but the real theory of elasticity, indicating that the elastic constants of a material could be obtained by measuring sound velocities in that material, was summarized only two hundred of years later. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Geology
Geology (). is a branch of natural science concerned with the Earth and other astronomical objects, the rocks of which they are composed, and the processes by which they change over time. Modern geology significantly overlaps all other Earth sciences, including hydrology. It is integrated with Earth system science and planetary science. Geology describes the structure of the Earth on and beneath its surface and the processes that have shaped that structure. Geologists study the mineralogical composition of rocks in order to get insight into their history of formation. Geology determines the relative ages of rocks found at a given location; geochemistry (a branch of geology) determines their absolute ages. By combining various petrological, crystallographic, and paleontological tools, geologists are able to chronicle the geological history of the Earth as a whole. One aspect is to demonstrate the age of the Earth. Geology provides evidence for plate tectonics, the ev ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Surface
In physics, a free surface is the surface of a fluid that is subject to zero parallel shear stress, such as the interface between two homogeneous fluids. An example of two such homogeneous fluids would be a body of water (liquid) and the air in the Earth's atmosphere (gas mixture). Unlike liquids, gases cannot form a free surface on their own. Fluidized/ liquified solids, including slurries, granular materials, and powders may form a free surface. A liquid in a gravitational field will form a free surface if unconfined from above. Under mechanical equilibrium this free surface must be perpendicular to the forces acting on the liquid; if not there would be a force along the surface, and the liquid would flow in that direction. Thus, on the surface of the Earth, all free surfaces of liquids are horizontal unless disturbed (except near solids dipping into them, where surface tension distorts the surface in a region called the meniscus). In a free liquid that is not affecte ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Variational Method
The calculus of variations (or variational calculus) is a field of mathematical analysis that uses variations, which are small changes in functions and functionals, to find maxima and minima of functionals: mappings from a set of functions to the real numbers. Functionals are often expressed as definite integrals involving functions and their derivatives. Functions that maximize or minimize functionals may be found using the Euler–Lagrange equation of the calculus of variations. A simple example of such a problem is to find the curve of shortest length connecting two points. If there are no constraints, the solution is a straight line between the points. However, if the curve is constrained to lie on a surface in space, then the solution is less obvious, and possibly many solutions may exist. Such solutions are known as ''geodesics''. A related problem is posed by Fermat's principle: light follows the path of shortest optical length connecting two points, which depends upo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Normal Mode
A normal mode of a dynamical system is a pattern of motion in which all parts of the system move sinusoidally with the same frequency and with a fixed phase relation. The free motion described by the normal modes takes place at fixed frequencies. These fixed frequencies of the normal modes of a system are known as its natural frequencies or resonant frequencies. A physical object, such as a building, bridge, or molecule, has a set of normal modes and their natural frequencies that depend on its structure, materials and boundary conditions. The most general motion of a linear system is a superposition of its normal modes. The modes are normal in the sense that they can move independently, that is to say that an excitation of one mode will never cause motion of a different mode. In mathematical terms, normal modes are orthogonal to each other. General definitions Mode In the wave theory of physics and engineering, a mode in a dynamical system is a standing wave st ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Free Body
In physics and engineering, a free body diagram (FBD; also called a force diagram) is a graphical illustration used to visualize the applied forces, moments, and resulting reactions on a free body in a given condition. It depicts a body or connected bodies with all the applied forces and moments, and reactions, which act on the body(ies). The body may consist of multiple internal members (such as a truss), or be a compact body (such as a beam). A series of free bodies and other diagrams may be necessary to solve complex problems. Sometimes in order to calculate the resultant force graphically the applied forces are arranged as the edges of a polygon of forces or force polygon (see ). Free body A body is said to be "free" when it is singled out from other bodies for the purposes of dynamic or static analysis. The object does not have to be "free" in the sense of being unforced, and it may or may not be in a state of equilibrium; rather, it is not fixed in place and is thus "f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Elastic Wave
Linear elasticity is a mathematical model of how solid objects deform and become internally stressed by prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics. The fundamental assumptions of linear elasticity are infinitesimal strains — meaning, "small" deformations — and linear relationships between the components of stress and strain — hence the "linear" in its name. Linear elasticity is valid only for stress states that do not produce yielding. Its assumptions are reasonable for many engineering materials and engineering design scenarios. Linear elasticity is therefore used extensively in structural analysis and engineering design, often with the aid of finite element analysis. Mathematical formulation Equations governing a linear elastic boundary value problem are based on three tensor partial differential equations for the balance of linear momentum and six infini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Differential Of A Function
In calculus, the differential represents the principal part of the change in a function y = f(x) with respect to changes in the independent variable. The differential dy is defined by dy = f'(x)\,dx, where f'(x) is the derivative of with respect to x, and dx is an additional real variable (so that dy is a function of x and dx). The notation is such that the equation dy = \frac\, dx holds, where the derivative is represented in the Leibniz notation dy/dx, and this is consistent with regarding the derivative as the quotient of the differentials. One also writes df(x) = f'(x)\,dx. The precise meaning of the variables dy and dx depends on the context of the application and the required level of mathematical rigor. The domain of these variables may take on a particular geometrical significance if the differential is regarded as a particular differential form, or analytical significance if the differential is regarded as a linear approximation to the increment of a function. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cartesian Coordinate
In geometry, a Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of real numbers called ''coordinates'', which are the signed distances to the point from two fixed perpendicular oriented lines, called '' coordinate lines'', ''coordinate axes'' or just ''axes'' (plural of ''axis'') of the system. The point where the axes meet is called the '' origin'' and has as coordinates. The axes directions represent an orthogonal basis. The combination of origin and basis forms a coordinate frame called the Cartesian frame. Similarly, the position of any point in three-dimensional space can be specified by three ''Cartesian coordinates'', which are the signed distances from the point to three mutually perpendicular planes. More generally, Cartesian coordinates specify the point in an -dimensional Euclidean space for any dimension . These coordinates are the signed distances from the point to mutually perpendicular fixed h ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be used: \rho = \frac, where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Frequency
In physics, angular frequency (symbol ''ω''), also called angular speed and angular rate, is a scalar measure of the angle rate (the angle per unit time) or the temporal rate of change of the phase argument of a sinusoidal waveform or sine function (for example, in oscillations and waves). Angular frequency (or angular speed) is the magnitude of the pseudovector quantity '' angular velocity''. (UP1) Angular frequency can be obtained multiplying '' rotational frequency'', ''ν'' (or ordinary ''frequency'', ''f'') by a full turn (2 radians): . It can also be formulated as , the instantaneous rate of change of the angular displacement, ''θ'', with respect to time, ''t''. (11 pages) Unit In SI[...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Displacement Vector
In geometry and mechanics, a displacement is a vector whose length is the shortest distance from the initial to the final position of a point P undergoing motion. It quantifies both the distance and direction of the net or total motion along a straight line from the initial position to the final position of the point trajectory. A displacement may be identified with the translation that maps the initial position to the final position. Displacement is the shift in location when an object in motion changes from one position to another. For motion over a given interval of time, the displacement divided by the length of the time interval defines the average velocity (a vector), whose magnitude is the average speed (a scalar quantity). Formulation A displacement may be formulated as a '' relative position'' (resulting from the motion), that is, as the final position of a point relative to its initial position . The corresponding displacement vector can be defined as the differen ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
RUS 1
Rus or RUS may refer to: People * East Slavic historical peoples (). See Names of Rus', Russia and Ruthenia ** Rus' people, the people of Rus' ** Rus, a legendary eponymous ancestor, see Lech, Czech and Rus * Rus (surname), a surname found in Romania and elsewhere Historical places * Kievan Rus', a medieval East Slavic state, centered in Kiev * Rus' Khaganate, a ninth-century Eastern European state * Ruthenia * Vladimirian Rus', or Vladimir-Suzdal, an East Slavic medieval state, centered in Vladimir * Halychian Rus', or Principality of Halych, an East Slavic medieval state, in region of Halych * Volhynian Rus', or Principality of Volhynia, an East Slavic medieval state, in regions of Volhynia * Halych-Volhynian Rus', or Kingdom of Galicia–Volhynia, an East Slavic medieval state, uniting Halych and Volhynia * Kingdom of Rus', or Galicia-Volhynia, an East Slavic medieval kingdom * Turovian Rus', or Principality of Turov, an East Slavic medieval state, in region of Turov * Polo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
