Equation of motion

In this paper, the free vibration of a bi-directional functionally graded (2D-FG) nanobeams is investigated by the finite element method. Nanobeams are made of two kinds of porous materials. The material properties of 2D-FG nanobeams are assumed to vary in both axial and thickness directions according to a power law . Based on Eringen's nonlocal elasticity theory, the governing equations of motion are derived.

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In this paper, geometrical nonlinear flutter analysis of functionally graded carbon nanotubes reinforced composite plates is presented. The governing equations of the system are obtained using the Mindlin plate theory and von Karman geometric nonlinearity. The linear piston theory is utilized to determine the aerodynamic pressure. Applying the Hamilton principle, equations of motion of a system are derived in the matrix form, and then the finite element method is used to obtain the discretized equations.

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The paper "Dynamic analysis of stiffened functionally graded composite plates reinforced by carbon nanotubes under blast loading" presents a study of the geometrical nonlinear dynamic of stiffened functionally graded composite plates reinforced by carbon nanotubes (SFG-CNTRC) subjected to blast loading. The governing equations of the system are obtained using the Mindlin plate theory and von Karman geometric nonlinearity.

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The paper "Nonlinear vibration of functionally graded porous micro-beams resting on elastic foundation" presents the analysis of nonlinear vibration of functionally graded porous (FGP) micro-beams resting on an elastic foundation. The Euler-Bernoulli beam theory (EBT) and the nonlocal strain gradient theory (NSGT) are considered to establish the equations of motion of the micro-beam. The material properties of the micro-beam are assumed to be changed continuously along thickness direction according to simple power-law distribution.

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This paper presents the time history response of a sandwich beam with a porous core subjected to two moving harmonic loads with opposite directions. In the modelling, the beam is combined of two isotropic face sheets and a porous core with symmetric porosity distribution. The quasi-3D shear deformation beam theory in conjunction with Hamilton’s variational principle is utilized to set up the governing equations of motion. The Navier solution is used to obtain the displacement field.

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Part 2 book "Thomas’ calculus - Early transcendentals" includes content: Infinite sequences and series, parametric equations and polar coordinates, vectors and the geometry of space, vector valued functions and motion in space, partial derivatives, multiple integrals, integrals and vector fields.

620p dianmotminh00 22-04-2024 3 3   Download

Ebook "Dynamic studies through control of relaxation in NMR spectroscopy" offers a remarkably cogent view of highly sophisticated NMR methods. Salvi developed these methods in order to characterize the amplitudes and frequency ranges of local motions in biomolecules such as proteins. These local motions play an essential role since they can explain many of the remarkable properties of proteins and enable them to carry out all sorts of vital functions, from enzymatic catalysis to intermolecular recognition and signalling in cells.

118p tudohanhtau1006 29-03-2024 4 1   Download

Part 2 book "Quantum optics for beginners" by author Zbigniew Ficek includes contents: Heisenberg equations of motion; dressed atom model; fokker– planck equation; quantum trajectory theory; interaction - free measurements; classical and quantum interference; atom– atom entanglement; classical and quantum lithography; laser model in the high; input– output theory; motion of atoms in a laser field.

171p muasambanhan09 16-03-2024 6 0   Download

Part 1 book "Introduction to engineering fluid mechanics" includes content: Introduction to engineering fluid mechanics introduction, fluids and fluid properties, units of measurement, dimensions and dimensional analysis, pressure variation in a fluid at rest (hydrostatics), hydrostatic force exerted on a submerged surface, kinematic description of fluids in motion and approximations, Bernoulli's equation, engineering applications of Bernoulli's equation, linear momentum equation and hydrodynamic forces.

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Part 1 book "Applied chemistry and chemical engineering (Vol 1: Mathematical and analytical techniques)" includes content: Digraphs, graphs, and thermodynamics equations; usefulness and limits of predictive relationships; computational model for byproduct of wastewater treatment; complex calculation of a critical path of motion of a corpuscle taking into account a regime and design of the apparatus; the modern approach to modeling and calculation of efficiency of process of a gas cleaning;... and other contents.

157p muasambanhan08 01-03-2024 2 1   Download

Ebook "Introduction to physical oceanography" begins with the basic equations of motion in integral form and covers such essential topics as geostropic flow, barotropic and baroclinic ocean circulations, vorticity, and the astronomical tides. Among the many appendices is one on the method of Matched Asymptotic Expansions as applied to the Gulf Stream the most modern and systematic way of looking at boundary layer problems. Problems are included at the end of each chapter.

354p duongthandue0501 28-02-2024 1 1   Download

Part 1 book "Hydraulics and fluid mechanics including hydraulic machines" includes content: Properties of fluids, fluid pressure and its measurement, hydrostatic forces on surfaces, buoyancy and floatation, liquids in relative equilibrium, fundamentals of fluid flow, equations of motion and energy equation, impulse momentum equation and its applications, flow through orifices and mouthpieces.

470p muasambanhan08 23-02-2024 7 3   Download

Part 1 book "Introduction to fluid mechanics" includes content: introduction, fundamental concepts, fluid statics, basic equations in integral form for a control volume, introduction to differential analysis of fluid motion, incompressible inviscid flow, dimensional analysis and similitude.

323p muasambanhan07 18-02-2024 1 0   Download

Part 1 book "An introduction to beam physics" includes content: Beams and beam physics; linear beam optics; fields, potentials and equations of motion; the linearization of the equations of motion; computation and properties of maps.

155p muasambanhan07 08-02-2024 0 0   Download

Part 1 book "Physics demystified" includes content: Equations, formulas, and vectors; scientific notation; graphing schemes; basics of geometry; logarithms, exponentials, and trigonometry; units and constants; mass, force, and motion; momentum, work, energy, and power; particles of matter; basic states of matter; temperature, pressure, and changes of state.

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Part 1 book "String theory demystified" includes content: Introduction, the classical string I - Equations of motion, the classical string II - Symmetries and worldsheet currents, string quantization, conformal field theory part I, BRST quantization, RNS superstrings.

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Part 1 book "Quantum statistical theory of superconductivity" includes content: Introduction; free electron model for a metal; lattice vibrations - phonons; liquid helium - bose–einstein condensation; bloch electrons - band structures; second quantization - equation of motion method; interparticle interaction - perturbation methods.

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Part 1 book "The picture book of quantum mechanics" includes content: Introduction, light waves, probability waves of matter; solution of the schrödinger equation in one dimension; one dimensional quantum mechanics - Scattering by a potential; one dimensional quantum mechanics - Motion within a potential, stationary bound states; quantile motion in one dimension; coupled harmonic oscillators - Distinguishable particles; coupled harmonic oscillators - Indistinguishable particles; wave packet in three dimensions.

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Part 1 book "Engineering mechanics - Statics and dynamics shames" includes content: Fundamentals of mechanics review I, elements of vector algebra review II, important vector quantities, equivalent force systems, equations of equilibrium, introduction to structural mechanics, friction forces, properties of surfaces, moments and products oflnertia, kinematics of a particle simple relative motion, methods of virtual work and stationary potential energy, particle dynamics.

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Ebook "Nonlinear hamiltonian mechanics applied to molecular dynamics: Theory and computational methods for understanding molecular spectroscopy and chemical reactions" presents numerical methods for describing and calculating invariant phase space structures, as well as solving the classical and quantum equations of motion for polyatomic molecules. Examples covered include simple model systems to realistic cases of molecules spectroscopically studied.

165p nhanphanguyet 28-01-2024 6 2   Download