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Rotordynamics
Rotordynamics, also known as rotor dynamics, is a specialized branch of applied mechanics concerned with the behavior and diagnosis of rotating structures. It is commonly used to analyze the behavior of structures ranging from jet engines and steam turbines to auto engines and computer disk storage. At its most basic level, rotor dynamics is concerned with one or more mechanical structures (rotors) supported by bearings and influenced by internal phenomena that rotate around a single axis. The supporting structure is called a stator. As the speed of rotation increases the amplitude of vibration often passes through a maximum that is called a critical speed. This amplitude is commonly excited by imbalance of the rotating structure; everyday examples include engine balance and tire balance. If the amplitude of vibration at these critical speeds is excessive, then catastrophic failure occurs. In addition to this, turbomachinery often develop instabilities which are related to the i ...
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Nils Otto Myklestad
Nils Otto Myklestad (March 24, 1909 – September 23, 1972) was an American mechanical engineer and engineering professor. An authority on mechanical vibration, he was employed by a number of important US engineering firms and served on the faculty of several major engineering universities. Myklestad made significant contributions to both engineering practice and engineering education, publishing a number of widely influential technical journal papers and textbooks. He also was granted five US patents during his career. Myklestad was employed in various technical capacities by AiResearch, North American Aviation, Westinghouse Electric, Fairbanks Morse, and Bell Helicopter Company. He served on the faculties of California Institute of Technology, University of California, Cornell University, Illinois Institute of Technology, University of Illinois, Arizona State University and the University of Texas at Arlington. He was elected fellow of the American Society of Mechanical Engineer ...
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August Föppl
August Otto Föppl (25 January 1854 – 12 August 1924) was a professor of Technical Mechanics and Graphical Statics at the Technical University of Munich, Germany. He is credited with introducing the Föppl–Klammer theory and the Föppl–von Kármán equations (large deflection of elastic plates). Life His doctoral advisor was Gustav Heinrich Wiedemann and one of Föppl's first doctoral students was Ludwig Prandtl, his future son-in-law. He had two sons Ludwig Föppl and Otto Föppl. Ludwig Föppl who was a mechanical engineer and Professor of Technical Mechanics at the Technical University of Munich. Otto Föppl who was an engineer and Professor of Applied Mechanics at the Technical University of Braunschweig for 30 years. Career In 1894, Föppl wrote a widely read introductory book on Maxwell's theory of electricity, titled ''Einführung in die Maxwellsche Theorie der Elektrizität''. (This was the first German-language textbook on Maxwell's theory of electrodynamics an ...
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Rotor (electric)
The rotor is a moving component of an electromagnetic system in the electric motor, electric generator, or alternator. Its rotation is due to the interaction between the windings and magnetic fields which produces a torque around the rotor's axis.Staff. "Understanding Alternators. What Is an Alternator and How Does It Work." N.p., n.d. Web. 24 November 2014 . Early development An early example of electromagnetic rotation was the first rotary machine built by Ányos Jedlik with electromagnets and a commutator, in 1826-27. Other pioneers in the field of electricity include Hippolyte Pixii who built an alternating current generator in 1832, and William Ritchie's construction of an electromagnetic generator with four rotor coils, a commutator and brushes, also in 1832. Development quickly included more useful applications such as Moritz Hermann Jacobi's motor that could lift 10 to 12 pounds with a speed of one foot per second, about 15 watts of mechanical power in ...
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Tire Balance
Tire balance, also called tire unbalance or tire imbalance, describes the distribution of mass within an automobile tire or the entire wheel (including the rim) on which it is mounted. When the wheel rotates, asymmetries in its mass distribution may cause it to apply periodic forces and torques to the axle, which can cause ride disturbances, usually as vertical and lateral vibrations, and this may also cause the steering wheel to oscillate. The frequency and magnitude of this ride disturbance usually increases with speed, and vehicle suspensions may become excited when the rotating frequency of the wheel equals the resonant frequency of the suspension. Tire balance is measured in factories and repair shops by two methods: with static balancers and with dynamic balancers. Tires with large unbalances are downgraded or rejected. When tires are fitted to wheels at the point of sale, they are measured again on a balancing machine, and correction weights are applied to counteract the ...
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Matrix(mathematics)
In mathematics, a matrix (plural matrices) is a rectangular array or table of numbers, symbols, or expressions, arranged in rows and columns, which is used to represent a mathematical object or a property of such an object. For example, \begin1 & 9 & -13 \\20 & 5 & -6 \end is a matrix with two rows and three columns. This is often referred to as a "two by three matrix", a "-matrix", or a matrix of dimension . Without further specifications, matrices represent linear maps, and allow explicit computations in linear algebra. Therefore, the study of matrices is a large part of linear algebra, and most properties and operations of abstract linear algebra can be expressed in terms of matrices. For example, matrix multiplication represents composition of linear maps. Not all matrices are related to linear algebra. This is, in particular, the case in graph theory, of incidence matrices, and adjacency matrices. ''This article focuses on matrices related to linear algebra, and ...
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William John Macquorn Rankine
William John Macquorn Rankine (; 5 July 1820 – 24 December 1872) was a Scottish mechanical engineer who also contributed to civil engineering, physics and mathematics. He was a founding contributor, with Rudolf Clausius and William Thomson (Lord Kelvin), to the science of thermodynamics, particularly focusing on the first of the three thermodynamic laws. He developed the Rankine scale, an equivalent to the Kelvin scale of temperature, but in degrees Fahrenheit rather than Celsius. Rankine developed a complete theory of the steam engine and indeed of all heat engines. His manuals of engineering science and practice were used for many decades after their publication in the 1850s and 1860s. He published several hundred papers and notes on science and engineering topics, from 1840 onwards, and his interests were extremely varied, including, in his youth, botany, music theory and number theory, and, in his mature years, most major branches of science, mathematics and engineerin ...
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Idealization (science Philosophy)
In philosophy of science, idealization is the process by which scientific models assume facts about the phenomenon being modeled that are strictly false but make models easier to understand or solve. That is, it is determined whether the phenomenon approximates an "ideal case," then the model is applied to make a prediction based on that ideal case. If an approximation is accurate, the model will have high predictive power; for example, it is not usually necessary to account for air resistance when determining the acceleration of a falling bowling ball, and doing so would be more complicated. In this case, air resistance is idealized to be zero. Although this is not strictly true, it is a good approximation because its effect is negligible compared to that of gravity. Idealizations may allow predictions to be made when none otherwise could be. For example, the approximation of air resistance as zero was the only option before the formulation of Stokes' law allowed the calculation ...
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Gustaf De Laval
Karl Gustaf Patrik de Laval (; 9 May 1845 – 2 February 1913) was a Swedish engineer and inventor who made important contributions to the design of steam turbines and centrifugal separation machinery for dairy. Life Gustaf de Laval was born at Orsa in Dalarna in the Swedish de Laval Huguenot family (immigrated 1622 - Claude de Laval, soldier - knighted de Laval 1647). He enrolled at the Institute of Technology in Stockholm (later the Royal Institute of Technology, KTH) in 1863, receiving a degree in mechanical engineering in 1866, after which he matriculated at Uppsala University in 1867. He was then employed by the Swedish mining company, Stora Kopparberg. From there he returned to Uppsala University and completed his doctorate in 1872. He was further employed in Kloster Iron works in Husby parish, Sweden. de Laval was a member of the Royal Swedish Academy of Sciences from 1886. He was a successful engineer and businessman. He also held national office, being elected to ...
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Eigenvectors
In linear algebra, an eigenvector () or characteristic vector of a linear transformation is a nonzero vector that changes at most by a scalar factor when that linear transformation is applied to it. The corresponding eigenvalue, often denoted by \lambda, is the factor by which the eigenvector is scaled. Geometrically, an eigenvector, corresponding to a real nonzero eigenvalue, points in a direction in which it is stretched by the transformation and the eigenvalue is the factor by which it is stretched. If the eigenvalue is negative, the direction is reversed. Loosely speaking, in a multidimensional vector space, the eigenvector is not rotated. Formal definition If is a linear transformation from a vector space over a field into itself and is a nonzero vector in , then is an eigenvector of if is a scalar multiple of . This can be written as T(\mathbf) = \lambda \mathbf, where is a scalar in , known as the eigenvalue, characteristic value, or characteristic root a ...
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Complex Number
In mathematics, a complex number is an element of a number system that extends the real numbers with a specific element denoted , called the imaginary unit and satisfying the equation i^= -1; every complex number can be expressed in the form a + bi, where and are real numbers. Because no real number satisfies the above equation, was called an imaginary number by René Descartes. For the complex number a+bi, is called the , and is called the . The set of complex numbers is denoted by either of the symbols \mathbb C or . Despite the historical nomenclature "imaginary", complex numbers are regarded in the mathematical sciences as just as "real" as the real numbers and are fundamental in many aspects of the scientific description of the natural world. Complex numbers allow solutions to all polynomial equations, even those that have no solutions in real numbers. More precisely, the fundamental theorem of algebra asserts that every non-constant polynomial equation with re ...
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