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Статті в журналах з теми "Transformation elastodynamics"

Автор: Grafiati

Опубліковано: 11 березня 2023

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Norris, Andrew. "Transformation acoustics and elastodynamics." Journal of the Acoustical Society of America 128, no. 4 (October 2010): 2427. http://dx.doi.org/10.1121/1.3508670.

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Lu, Xiang Yang, and Jin Hu. "Approximate Elastodynamic Directional-Cloak with Isotropous Homogeneous Material." Advanced Materials Research 634-638 (January 2013): 2787–90. http://dx.doi.org/10.4028/www.scientific.net/amr.634-638.2787.

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Recently, the transformation method has been extended to control solid elastic waves in case of high frequency or small material gradient. An important device in practice, the approximate elastodynamic directional-cloak with isotropic homogeneous materials, can be designed based on this method. In this paper, this device’s design method is discussed in detail and its effect on cloaking arbitrary shaped obstacles is explored. It is also shown that this useful device cannot be designed based on the conventional transformation elastodynamics. Examples are conceived and validated by numerical simulations.

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Colquitt, D. J., M. Brun, M. Gei, A. B. Movchan, N. V. Movchan, and I. S. Jones. "Transformation elastodynamics and cloaking for flexural waves." Journal of the Mechanics and Physics of Solids 72 (December 2014): 131–43. http://dx.doi.org/10.1016/j.jmps.2014.07.014.

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Hu, Jin, and Xiang Yang Lu. "Concentrating Elastic Waves by Isotropic Homogeneous and Reflectionless Materials." Advanced Materials Research 625 (December 2012): 210–13. http://dx.doi.org/10.4028/www.scientific.net/amr.625.210.

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In this paper, we show that compared with the conventional transformation elastodynamics, the method based on physical interpretation of form-invariance can provide more flexibility in material design. As a result of this flexibility, the impedance-matched condition for both S and P waves in perpendicularly incident cases exists, thus the isotropic homogeneous elastic wave concentrator can be designed. Samples are conceived and validated by numerical simulations.

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Xiang, Chao Chun, and Jin Hu. "Guiding Solid Elastic Waves to Arbitrary Paths by Isotropic Materials." Applied Mechanics and Materials 302 (February 2013): 406–9. http://dx.doi.org/10.4028/www.scientific.net/amm.302.406.

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As a result of the flexibility provided by the transformation elastodynamics, the impedance-matched condition exists for both S and P waves in perpendicularly incident cases in isotropic materials, thus the isotropic elastic wave beam bender can be designed. In this paper, we explore some characteristics of this bender and show that by assembling the bender units a solid elastic beam can be guided to an arbitrary path, which will provide convenience in engineering practices. Examples are conceived and validated by numerical simulations.

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Nassar, H., Y. Y. Chen, and G. L. Huang. "A degenerate polar lattice for cloaking in full two-dimensional elastodynamics and statics." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 474, no. 2219 (November 2018): 20180523. http://dx.doi.org/10.1098/rspa.2018.0523.

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A lattice design of a cloak for full two-dimensional elasticity is suggested when the background continuum is isotropic with Lamé parameters (λ, μ ) satisfying μ ≤ λ. The lattice is polar in the sense that it elastically resists rotations; and is degenerate meaning it admits a stressless collapse mechanism. These characteristics are attained through the use of appropriately distributed restoring torques in conjunction with hinge-like spring-mass contacts. Thus, the lattice is proven to exhibit a rank-3 elasticity tensor lacking the minor symmetries. Accordingly, it rigorously adheres to the form-invariance requirements of the transformation method under the Brun–Guenneau–Movchan gauge. The cloak is numerically tested in statics and in dynamics under pressure and shear incident waves and shows satisfactory performance. Finally, a theoretical generalization extends the design to three dimensions and to arbitrarily anisotropic backgrounds so as to enable cloaking as well as other transformation-based static and dynamic field manipulation techniques in these cases.

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Peng, Yong, and Xiao Xu Bai. "KED Modeling of PLS Mechanism." Applied Mechanics and Materials 268-270 (December 2012): 1319–26. http://dx.doi.org/10.4028/www.scientific.net/amm.268-270.1319.

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For the super-size and large flexibility of Pipe Lay-down System, considering the influence on the mechanism from elastic deformation and mechanical vibration during the movements, the kineto-elastodynamics model is established by using the KED theory which is based on the analysis of kinematics. The PLS mechanism is divided into several finite elements. Dynamic equations of beam element are established in the local coordinate by using Lagrange’s equation. In the process of changing from local coordinate into global coordinate, no longer considering the instantaneous structure assumes. In consideration of the first and second derivative of the coordinate transformation matrix versus time are not zero. The mass matrix, damping matrix and stiffness matrix of the final system kinematic differential equation are the function of time. It realizes the continuity of variable in the time domain. Derivation of the results in this paper lays a foundation for the next more accurate and efficient methods being applied to solve the KED equation of PLS mechanism.

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Markenscoff, Xanthippi. "Properties of the self-similarly expanding Eshelby inclusions and application to the dynamic “Hill Jump Conditions”." Mathematics and Mechanics of Solids 22, no. 3 (August 5, 2016): 573–78. http://dx.doi.org/10.1177/1081286515607094.

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For a self-similarly subsonically dynamically expanding Eshelby inclusion, we show by an analytic argument (based on the analyticity of the coefficients of the ensuing elliptic system and the Cauchy–Kowalevska theorem) that the particle velocity vanishes in the whole interior domain of the expanding inclusion. Since the acceleration term is thus zero in the interior domain in the Navier equations of elastodynamics, this reduces to an Eshelby problem. The classical Hill jump conditions across the interface of a region with transformation strain are expanded here to dynamics when the interface is moving with inertia satisfying the Hadamard jump conditions. The validity of the Eshelby property and the determination of the constrained strain from the dynamic Eshelby tensor in the interior domain allow one to fully determine from the Hill jump conditions the stress across the moving phase boundary of a self-similarly expanding ellipsoidal Eshelby inhomogeneous inclusion. The driving force can then be obtained. Self-similar motion grasps the early response of the system.

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Al-Attar, David, and Ophelia Crawford. "Particle relabelling transformations in elastodynamics." Geophysical Journal International 205, no. 1 (February 29, 2016): 575–93. http://dx.doi.org/10.1093/gji/ggw032.

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Yavari, Arash, and Ashkan Golgoon. "Nonlinear and Linear Elastodynamic Transformation Cloaking." Archive for Rational Mechanics and Analysis 234, no. 1 (May 16, 2019): 211–316. http://dx.doi.org/10.1007/s00205-019-01389-2.

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Rogers, C., and W. K. Schief. "Bäcklund Transformations and Superposition Principles in Nonlinear Elastodynamics." Studies in Applied Mathematics 124, no. 2 (February 2010): 137–49. http://dx.doi.org/10.1111/j.1467-9590.2009.00465.x.

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Hu, Jin, and Xiang Yang Lu. "Bending Solid Elastic Waves with Arbitrary Angles by Bricks." Applied Mechanics and Materials 161 (March 2012): 26–29. http://dx.doi.org/10.4028/www.scientific.net/amm.161.26.

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Анотація:

Transformation method provides an efficient way to control wave propagation by materials. Recently, this method has been extended to control elastic waves in solids in case of high frequency or small material gradient. An important device in practice, elastodynamic beam bender with isotropic materials, can be designed by this method. In this paper, we will explore some characteristics of the isotropic elastodynamic beam bender and show that it can be used as bricks to guide the solid elastic beam to arbitrary angles, providing more flexibility in engineering practices. Examples are conceived and validated by numerical simulations.

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Ladopoulos, E. G. "Nonlinear singular integral equations in elastodynamics by using Hilbert transformations." Nonlinear Analysis: Real World Applications 6, no. 3 (July 2005): 531–36. http://dx.doi.org/10.1016/j.nonrwa.2004.10.002.

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Roberts, Ronald A. "High‐frequency elastodynamic boundary integral inversion using asymptotic phase transformation." Journal of the Acoustical Society of America 92, no. 4 (October 1992): 2432. http://dx.doi.org/10.1121/1.404606.

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Kadic, Muamer, Martin Wegener, André Nicolet, Frédéric Zolla, Sébastien Guenneau, and André Diatta. "Elastodynamic behavior of mechanical cloaks designed by direct lattice transformations." Wave Motion 92 (January 2020): 102419. http://dx.doi.org/10.1016/j.wavemoti.2019.102419.

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Câmara, M. C., A. B. Lebre, and F. O. Speck. "Generalised factorisation for a class of Jones form matrix functions." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 123, no. 3 (1993): 401–22. http://dx.doi.org/10.1017/s0308210500025804.

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SynopsisA systematic approach is proposed for the generalised factorisation of certain non-rational n × n matrix functions. The first main result consists in a transformation of a meromorphic into a generalised factorisation by algebraic means. It closes a gap between the classical Wiener-Hopf procedure and the operator theoretic method of generalised factorisation. Secondly, as examples we consider certain matrix functions of Jones form or of N-part form, which are equivalent to each other, in a sense. The factorisation procedure is complete and explicit, based only on the factorisation of scalar functions, of rational matrix functions and upon linear algebra. Applications in elastodynamic diffraction theory are treated in detail and in a most effective way.

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Zhang, Shiping, and Zhan Xu. "Elastodynamic Solutions of a Finite Soil Layer under Interior Distributed Actions." Shock and Vibration 2021 (June 30, 2021): 1–18. http://dx.doi.org/10.1155/2021/5538319.

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Through a method of displacement potentials, Fourier series, and Hankel integral transformation, the generalized solutions of an elastic layer resting on a rigid base under arbitrary, distributed, buried, and time-harmonic loads are developed in this study. With the proposed solution, the specific results for two kinds of uniform distributions as a kind of fundamental solutions in the interaction analysis of media and inclusions by the method of boundary integral equations are included as illustrations. Finally, numerical examples involving surface and buried patch loads are presented to validate the solutions and examine the effects of the thickness of the elastic layer. The results show that the proposed solution can cover the classical half-space solution by taking enough large thickness of the elastic layer (e.g., the ratio of the layer thickness beneath the load to the load radius ≥ 50 ) and the surface load solution by setting the load depth to zero; the underlying rigid base has significant and complex influence on the dynamic response of the thin layer due to wave reflections, which needs to be considered in the design and practice of related engineering.

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Vives, Eduard, Daniel Enrique Soto Parra, Antoni Planes, Lluís Mañosa, Ricardo Romero, Rachel S. Edwards, and Steve Dixon. "Acoustic Emission Avalanches in Martensitic Transitions: New Perspectives for the Problem of Source Location." Solid State Phenomena 172-174 (June 2011): 144–49. http://dx.doi.org/10.4028/www.scientific.net/ssp.172-174.144.

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Different experimental procedures for the location of sources of Acoustic Emission (AE) avalanches during Martensitic Transformations are discussed. A first example corresponds to the 1D location of AE events during stress-induced martensitic transitions in a Cu-Zn-Al shape memory alloy (3.5 cm length). The obtained data allows monitoring of the interface advancement with a spatial resolution of less than 1 mm. Secondly, we discuss two different ideas that have significant potential for improving this resolution in the case of thermally induced transitions in small single crystalline samples (~1 cm): the use of elastodynamic simulations based on finite element methods and the simultaneous detection of AE and Barkhausen noise in ferromagnetic samples.

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Mahmoud, A., A. H. Shah, and S. B. Dong. "Transient Response of Transversely Isotropic Composite Plates to a Point Source." Journal of Applied Mechanics 73, no. 2 (June 13, 2005): 338–41. http://dx.doi.org/10.1115/1.2070007.

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In this paper, transient three-dimensional response of a transversely isotropic composite plate to a time varying point load is efficiently computed by reducing the elastodynamic equation through integral and coordinate transformations to a series of two-dimensional problems, each associated with a plane wave along a given direction in the plate. Discrete equations of a semi-analytical finite element model are solved for the thickness profile eigendata at a given frequency. Three-dimensional steady state responses in the wave number domain are formed by summing contributions from eigenmodes over propagation directions. The transient response is obtained by a numerical integration of inverse Fourier time transform of these steady state responses. Present results showed good agreement with data reported in the literature and confirmed previously observed phenomena.

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Teymouri, Hamid, Ali Khojasteh, Mohammad Rahimian, and Ronald Y. S. Pak. "Wave motion in multi-layered transversely isotropic porous media by the method of potential functions." Mathematics and Mechanics of Solids 25, no. 3 (October 24, 2019): 547–72. http://dx.doi.org/10.1177/1081286519883925.

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Wave propagation in a multi-layered transversely isotropic porous medium has been considered in this paper, which consists of n parallel layers overlying on a half-space. Potential functions are used to solve elastodynamic differential equations of the poroelastic medium. Time-harmonic excitation is assumed and the procedure of solution is performed in the frequency domain. Generalized reflection and transmission matrices are generated for compressional and shear waves separately. By means of the Hankel transformation method, coupled differential equations are altered to ordinary ones and Riemann surfaces are used to establish the path of integrations. A closed-form solution is described to reach Green’s functions of displacements and stresses. Some special cases of excitations are discussed and verification of the solution is presented. The numerical results of a three-layered medium on a porous half-space are determined and discussed.

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Dempsey, J. P., and E. B. Smith. "The Rapid Tearing of a Half Plane." Journal of Applied Mechanics 52, no. 1 (March 1, 1985): 51–56. http://dx.doi.org/10.1115/1.3169025.

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The surface of an elastic half space is subjected to sudden antiplane mechanical disturbances. Crack initiation and subsequent crack instability are examined via two idealized problems; the first is concerned with instantaneous crack bifurcation and the second with instantaneous skew crack propagation. In either problem, crack propagation occurs at a constant subsonic velocity under an angle κπ with the normal to the surface. For the externally applied disturbances that are considered here, and for contstant crack-tip velocities, the particle velocity and τθz are functions of r/t and θ only, which allows Chaplygin’s transformation and conformal mapping to be used. The problems can then be solved using analytic function theory. For various values of the angle of crack propagation, the dependence of the elastodynamic stress intensity factors on the crack propagation velocity is investigated. For certain specific geometries, fully analytical solutions are derived to provide check cases.

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Ing, Yi-Shyong, and Chien-Ching Ma. "Exact transient full–field analysis of a finite crack subjected to dynamic anti–plane concentrated loadings in anisotropic materials." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 461, no. 2054 (February 8, 2005): 509–39. http://dx.doi.org/10.1098/rspa.2004.1382.

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In this study, the elastodynamic full–field response of a finite crack in an anisotropic material subjected to a dynamic anti–plane concentrated loading with Heaviside–function time dependence is investigated. A linear coordinate transformation is introduced to simplify the problem. The linear coordinate transformation reduces the anisotropic finite–crack problem to an equivalent isotropic problem. An alternative methodology, different from the conventional superposition method, is developed to construct the reflected and diffracted wave fields. The transient solutions are determined by superposition of two proposed fundamental solutions in the Laplace transform domain. The fundamental solutions to be used are the problems for applying exponentially distributed traction and displacement on the crack faces and along the crack–tip line in the Laplace transform domain, respectively. Exact analytical transient solutions for dynamic shear stresses, displacement and stress–intensity factor are obtained by using the Cagniard–de Hoop method of Laplace inversion and are expressed in explicitly compact formulations. The solutions have accounted for the contributions of all diffracted waves generated from two crack tips. Numerical results for the time history of shear stresses and stress–intensity factors during the transient process are calculated based on analytical solutions and are discussed in detail. The transient solutions of stresses have been shown to approach the corresponding static values after the first eight waves have passed the field point. The dynamic stress–intensity factor will reach a maximum value when the incident wave arrives at the crack tip, and remain constant before the first diffracted wave generated from the other crack tip arrives, and then will oscillate near the static value. A simple explicit expression of the dynamic overshoot for stress–intensity factors is derived as a function of the location for applied loadings, the crack length and material constants.

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Xie, Jiawen, and Anthony M. Waas. "2D Elastodynamic Solution for the Impact Response of Laminated Composites." Journal of Applied Mechanics 81, no. 4 (October 16, 2013). http://dx.doi.org/10.1115/1.4025276.

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This paper presents a general, exact, two-dimensional (2D) elastodynamic analysis of the response of laminated composite panels subjected to transverse impact loading under conditions of planar deformation. The natural frequencies and mode shapes of free vibration are first extracted. Inspired by a transformation technique for solving a special class of partial differential equations, the forced vibration problem of an impacted laminated panel is solved using an eigenfunction expansion technique. Several examples are studied by varying the laminate lay-up and length-to-thickness ratio. The distributions of transverse stresses in the through-the-thickness direction are further compared with two one-dimensional theories, classical lamination theory (CLT) and first-order shear deformation theory (FSDT), showing the inadequacy of these theories and the necessity to establish a benchmark solution for 2D elastodynamics. The 2D elastodynamic theory that is formulated is also applicable for studying other multilayered structures subjected to arbitrary loading profiles.

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Mondal, Priti, and Jagabandhu De. "Hilbert transform approach to solve a problem of collinear Griffith crack in the mid-plane of an infinite orthotropic strip." Mathematics and Mechanics of Solids, November 17, 2020, 108128652096977. http://dx.doi.org/10.1177/1081286520969770.

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In this paper, an integral transformation of the displacement is employed to determine the solution of the elastodynamics problem of two collinear Griffith cracks with constant velocity situated in a mid-plane of an infinite orthotropic strip where the boundaries are assumed to be stress-free. By use of the integral transformation of the displacement, the problem is reduced to a solution of the triple integral equations and the finite Hilbert transformation technique is used to solve it. The expressions of stresses are obtained asymptotically for large values of strip depth. An analytical expression of the stress intensity factor at the crack tip is obtained and represented graphically for two different orthotropic materials.

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Rossi, Marco, Daniele Veber, and Massimiliano Gei. "Numerical Assessment of the Performance of Elastic Cloaks for Transient Flexural Waves." Frontiers in Materials 7 (November 27, 2020). http://dx.doi.org/10.3389/fmats.2020.603667.

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A relevant application of transformation elastodynamics has shown that flexural waves in a Kirchhoff-Love plate can be diverted and channeled to cloak a region of the ambient space. To achieve the goal, an orthotropic meta-structural plate should be employed. However, the corresponding mathematical transformation leads to the presence of an unwanted strong compressive prestress, likely beyond the buckling threshold of the structure, with a set of in-plane body forces to warrant equilibrium. In addition, the plate must possess, at the same time, high bending stiffnesses, but a null twisting rigidity. With the aim of estimating the performance of cloaks modelled with approximate parameters, an in-house finite element code, based on a subparametric technique, is implemented to deal with the cloaking of transient waves in orthotropic thin plates. The tool allows us to explore the sensitivity of specific stiffness parameters that may be difficult to match in a real cloak design. In addition, the finite element code is extended to investigate a meta-plate interacting with a Winkler foundation, to confirm how the subgrade modulus should transform in the cloak region.

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Sozio, Fabio, Ashkan Golgoon, and Arash Yavari. "Elastodynamic transformation cloaking for non-centrosymmetric gradient solids." Zeitschrift für angewandte Mathematik und Physik 72, no. 3 (May 19, 2021). http://dx.doi.org/10.1007/s00033-021-01555-1.

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"Three-dimensional time-harmonic elastodynamic Green ’ s functions for anisotropic solids." Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences 449, no. 1937 (June 8, 1995): 441–58. http://dx.doi.org/10.1098/rspa.1995.0052.

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A method based on the Radon transform is presented to determine the displacement field in a general anisotropic solid due to the application of a time-harmonic point force. The Radon transform reduces the system of coupled partial differential equations for the displacement components to a system of coupled ordinary differential equations. This system is reduced to an uncoupled form by the use of properties of eigenvectors and eigenvalues. The resulting simplified system can be solved easily. A back transformation to the original coordinate system and a subsequent application of the inverse Radon transform yields the displacements as a summation of a regular elastodynamic term and a singular static term. Both terms are integrals over a unit sphere. For the regular dynamic term, the surface integration can be evaluated numerically without difficulty. For the singular static term, the surface integral has been reduced to a line integral over half a unit circle. Reductions to the cases of isotropy and transverse isotropy have been worked out in detail. Examples illustrate applications of the method.

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Toktaş, Selim E., and Serkan Dag. "Multi-layer model for moving contact problems of functionally graded coatings with general variations in physical properties." Proceedings of the Institution of Mechanical Engineers, Part L: Journal of Materials: Design and Applications, April 4, 2022, 146442072210921. http://dx.doi.org/10.1177/14644207221092119.

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This paper presents a multi-layer model for moving contact problems of functionally graded coatings whose physical properties have general spatial variations. The coating is assumed to be composed of an arbitrary number of layers and perfectly bonded to an elastic substrate. Wave equations for the layers and the substrate are derived in accordance with the plane theory of elastodynamics. The equations are solved by the application of Galilean and Fourier transformations. Flat and triangular punch profiles are considered, and the formulation is reduced to a singular integral equation of the second kind in both cases. The integral equations are solved by means of Jacobi expansion and collocation techniques. Proposed procedures are verified through comparisons to the results available for a special case in the literature. Parametric analyses are carried out for functionally graded coatings possessing ceramic-rich, metal-rich, and linear profiles. The results presented demonstrate the influences of factors such as punch speed, coefficient of friction, material property variation profile, and contact-length-to-thickness ratio on contact stresses, punch stress intensity factors, and required contact force. It is shown that the multi-layer model is required to account for general property distributions in a functionally graded coating subject to moving contact.

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Wang, Chensheng, Yanqin Zhao, Hongda Liu, Yonghao Guo, and Wentie Niu. "Evolution of lower-order vibration mode of the slender ball screw feed system." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture, February 26, 2022, 095440542210805. http://dx.doi.org/10.1177/09544054221080599.

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Dynamic performance characterized by lower-order natural frequency and lower-order vibration mode is vital for the dynamic positioning accuracy of the ball screw feed system. This paper focuses on the evolution between the lateral vibration mode and the axial vibration mode of the slender ball screw feed system (SBSFS). Firstly, it is proved the first-order vibration mode transformation of the SBSFS is subject to the position of the nut based on an elastodynamic model. This model is established using substructure synthesis method considering the axial, torsional, and lateral deformation of the screw simultaneously through dealing with the screw as Timoshenko Beam elements. By comparing with the experimental results, the validity and accuracy of the established dynamic model are verified. The effects of the stiffness of the kinematic joints on the dynamic performance of SBSFS are then analyzed. The results demonstrate that the dynamic behavior evolution of the SBSFS undergoes the coupling effects from the kinematics joints’ stiffness. Furthermore, a dynamic index ( RSP) is proposed considering the evolution of the first-order vibration mode. On the basis of RSP, three optimization schemes are illustrated. The results show that the RSP can be used to evaluate the dynamic performance of the SBSFS considering the vibration mode.

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