Journal articles: 'Bodo Kirchhoff'

1

Zimmermann, Ulf. "Erinnerungen an meinen Porsche by Bodo Kirchhoff." World Literature Today 83, no. 4 (2009): 66. http://dx.doi.org/10.1353/wlt.2009.0053.

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Katinienė, Violeta. "Travel as the Answer: Bodo Kirchhoff “Widerfahrnis”." Literatūra 64, no. 4 (December 30, 2022): 72–81. http://dx.doi.org/10.15388/litera.2022.64.4.16.

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Travels and the longing for afar have been and still are the source of inspiration for many authors. This article analyses Bodo Kirchoff’s short story “Widerfahrnis” (“Encounter”), which belongs to the genre of travel literature and extends the literary tradition of German authors to choose the theme of travel to Italy in their work (Johann Wolfgang von Goethe, Heinrich Heine, Thomas Mann, etc.). The short story raises the existential questions of longing for love, loneliness, confrontation with refugees, and moral and social aspects of relations with them. The article aims to reveal how the structures of experience described by the German phenomenologist Bernhard Waldenfels appear in the work of Bodo Kirchhoff. What happens to us does not happen without our involvement but goes beyond it. The experience begins not with the intentional gaze of the subject, but when someone (a stranger) touches us, encounters us, causes us to react and raises tension. Bernhard Waldenfels attributes the encounter to the realm of pathos, meaning to the realm of feelings. Response or the inevitable response to an encounter comes earlier than an understanding or an answer. Although the title of the short story is in the singular form, it reveals many encounters: a meeting of an older couple, a spontaneous trip to Italy, an encounter with a refugee girl and a refugee family, the birth of love and its loss.

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Badura, Bożena Anna. "Tell the Migration. gehen, ging, gegangen of Jenny Erpenbeck and Widerfahrnis of Bodo Kirchhoff." Transfer. Reception Studies 3 (2018): 43–74. http://dx.doi.org/10.16926/trs.2018.03.01.

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Zhao, Ping, Norm F. Uren, Friedemann Wenzel, P. J. Hatherly, and John A. McDonald. "Kirchhoff diffraction mapping in media with large velocity contrasts." GEOPHYSICS 63, no. 6 (November 1998): 2072–81. http://dx.doi.org/10.1190/1.1444500.

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Finite‐difference methods for calculating traveltimes are superior to ray‐tracing methods in inhomogeneous media. However, when these techniques are applied to Kirchhoff migration, a severe problem occurs in the presence of large velocity contrasts. If finite‐difference traveltime methods are used to calculate first arrivals, an incomplete image is created because substantial subsurface information is often carried by direct body waves. We propose a solution to this problem by developing a new method of calculating later arrival times and applying both first and later arrival times to a Kirchhoff diffraction mapping algorithm. A comparison shows that the implementation of both first arrivals and later arrivals in Kirchhoff migration can substantially improve the images in media with large velocity contrasts.

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Lyrintzis, Anastasios S. "Surface Integral Methods in Computational Aeroacoustics—From the (CFD) Near-Field to the (Acoustic) Far-Field." International Journal of Aeroacoustics 2, no. 2 (April 2003): 95–128. http://dx.doi.org/10.1260/147547203322775498.

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A review of recent advances in the use of surface integral methods in Computational AeroAcoustics (CAA) for the extension of near-field CFD results to the acoustic far-field is given. These integral formulations (i.e. Kirchhoff's method, permeable (porous) surface Ffowcs-Williams Hawkings (FW-H) equation) allow the radiating sound to be evaluated based on quantities on an arbitrary control surface if the wave equation is assumed outside. Thus only surface integrals are needed for the calculation of the far-field sound, instead of the volume integrals required by the traditional acoustic analogy method (i.e. Lighthill, rigid body FW-H equation). A numerical CFD method is used for the evaluation of the flow-field solution in the near field and thus on the control surface. Diffusion and dispersion errors associated with wave propagation in the far-field are avoided. The surface integrals and the first derivatives needed can be easily evaluated from the near-field CFD data. Both methods can be extended in order to include refraction effects outside the control surface. The methods have been applied to helicopter noise, jet noise, propeller noise, ducted fan noise, etc. A simple set of portable Kirchhoff/FW-H subroutines can be developed to calculate the far-field noise from inputs supplied by any aerodynamic near/mid-field CFD code.

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Sychev, Vikt V. "TO THE THEORY OF KIRCHHOFF-TYPE POTENTIAL FLOWAROUND A BODY." TsAGI Science Journal 41, no. 5 (2010): 531–33. http://dx.doi.org/10.1615/tsagiscij.v41.i5.30.

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Rousseau, Jérôme H. Le, Henry Calandra, and Maarten V. de Hoop. "Three‐dimensional depth imaging with generalized screens: A salt body case study." GEOPHYSICS 68, no. 4 (July 2003): 1132–39. http://dx.doi.org/10.1190/1.1598105.

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We illustrate the performance of the generalized screen propagator on real seismic data for 3D zero‐offset and prestack depth imaging. We use TotalFinaElf's L7D data set from the North Sea, a 3D marine seismic survey that contained limited azimuthal coverage. The subsurface shows significant tectonic deformation, including an intrusive salt body in sedimentary sequences. A transformation to common azimuth is applied prior to the 3D prestack depth imaging procedure. We compare the performance of the generalized screen propagator with that of a hybrid phase shift plus interpolation (PSPI)/split‐step Fourier method. Three‐dimensional prestack results confirm the generalized screen method handles multipathing more accurately. Comparisons are also made with Kirchhoff migration results. The results differ mainly in the fine‐scale irregularities of the image and not in the wavefront set of the image. Using synthetic models of similar structure (the SEG/EAGE salt model), we further illustrate the importance of multipathing and multiple scattering. Overall, our results show that our wave‐equation approach produces better images than the Kirchhoff approach to prestack depth migration; we attribute this mainly to a more complete handling of wave diffraction in the generalized screen expansion, which becomes important in strongly heterogeneous and irregular velocity models such as the ones containing salt bodies.

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Ershkov, Sergey V., Dmytro Leshchenko, and Ayrat R. Giniyatullin. "A New Solving Procedure for the Kelvin–Kirchhoff Equations in Case of a Falling Rotating Torus." International Journal of Bifurcation and Chaos 31, no. 01 (January 2021): 2150010. http://dx.doi.org/10.1142/s0218127421500103.

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We present a new solving procedure in this paper for Kelvin–Kirchhoff equations, considering the dynamics of a falling rigid rotating torus in an ideal incompressible fluid, assuming additionally the dynamical symmetry of rotation for the rotating body, [Formula: see text]. The fundamental law of angular momentum conservation is used for the aforementioned solving procedure. The system of Euler equations for the dynamics of torus rotation is explored for an analytic way of presentation of the approximated solution (where we consider the case of laminar flow at slow regime of torus rotation). The second finding is that the Stokes boundary layer phenomenon on the boundaries of the torus also assumed additionally at the formulation of basic Kelvin–Kirchhoff equations (for which the analytical expressions for the components of fluid’s torque vector [Formula: see text] were obtained earlier). The results for calculating the components of angular velocity [Formula: see text] should then be used for full solving the momentum equation of Kelvin–Kirchhoff system. The trajectories of motion can be divided into, preferably, three classes: zigzagging, helical spiral motion, and the chaotic regime of oscillations.

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CIARLET, PHILIPPE G., and SORIN MARDARE. "ON KORN'S INEQUALITIES IN CURVILINEAR COORDINATES." Mathematical Models and Methods in Applied Sciences 11, no. 08 (November 2001): 1379–91. http://dx.doi.org/10.1142/s0218202501001379.

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We show how the inequality of Korn's type on a surface can be established as a corollary to the three-dimensional Korn inequality in curvilinear coordinates. The proof relies in particular on a careful study of the linearized Kirchhoff–Love displacement fields inside a "shell-like" body.

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Meyer, Kenneth R., and Dieter S. Schmidt. "Bifurcations of Relative Equilibria in the N-Body and Kirchhoff Problems." SIAM Journal on Mathematical Analysis 19, no. 6 (November 1988): 1295–313. http://dx.doi.org/10.1137/0519094.

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11

Rauchenbacher, Marina. "In die Irre geführt. Zum Prinzip ‚Täuschung‘ in Bodo Kirchhoffs ›Der Sandmann‹." Sprachkunst Beiträge zur Literaturwissenschaft 1, no. 36/2 (2006): 311–26. http://dx.doi.org/10.1553/spk36_2s311.

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12

Majkut, Leszek, and Ryszard Olszewski. "Theoretical calculation of transmission loss of noise panels." AUTOBUSY – Technika, Eksploatacja, Systemy Transportowe 19, no. 12 (December 31, 2018): 553–56. http://dx.doi.org/10.24136/atest.2018.450.

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In the paper basic theoretical models of transmission loss calculation are described. Here only single homogeneous isotropic panels are analysed. Three impedance values of one rigid and two flexible body models of panel are described and analysed. As flexible models the thin plate (Kirchhoff-Love plate model) i thick (Mindlin – Reissner model) are analysed.

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Giaquinta, Mariano, Paolo Maria Mariano, and Giuseppe Modica. "Stress constraints in simple bodies undergoing large strains: a variational approach." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 145, no. 6 (October 22, 2015): 1183–214. http://dx.doi.org/10.1017/s0308210515000384.

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We consider a simple body that is hyperelastic in the large-strain regime until the 3-covector defining the first Piola–Kirchhoff stress, once it has been projected on the appropriate second-rank tensor space, reaches a threshold indicating critical states. No information is given on the post-critical behaviour. We determine the existence of equilibrium configurations according to the constraint. Such configurations can have a concentration of strain in regions with vanishing volume. The related stress appears naturally as a measure over the deformation graph. Once it is restricted to the regular part of the deformation, such a measure determines the first Piola–Kirchhoff stress tensor and may also be concentrated over sets with vanishing volume projections on the reference and current placements. These configurations in space can be interpreted as dislocations or dislocation walls. We analyse explicitly specific cases.

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14

Zhu, T. "A ray-Kirchhoff method for body-wave calculations in inhomogeneous media: theory." Geophysical Journal International 92, no. 2 (February 1, 1988): 181–93. http://dx.doi.org/10.1111/j.1365-246x.1988.tb01133.x.

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15

Ozenda, Olivier, and Epifanio G. Virga. "On the Kirchhoff-Love Hypothesis (Revised and Vindicated)." Journal of Elasticity 143, no. 2 (February 11, 2021): 359–84. http://dx.doi.org/10.1007/s10659-021-09819-7.

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AbstractThe Kirchhoff-Love hypothesis expresses a kinematic constraint that is assumed to be valid for the deformations of a three-dimensional body when one of its dimensions is much smaller than the other two, as is the case for plates. This hypothesis has a long history checkered with the vicissitudes of life: even its paternity has been questioned, and recent rigorous dimension-reduction tools (based on standard$\varGamma $Γ-convergence) have proven to be incompatible with it. We find that an appropriately revised version of the Kirchhoff-Love hypothesis is a valuable means to derive a two-dimensional variational model for elastic plates from a three-dimensional nonlinear free-energy functional. The bending energies thus obtained for a number of materials also show to contain measures of stretching of the plate’s mid surface (alongside the expected measures of bending). The incompatibility with standard$\varGamma $Γ-convergence also appears to be removed in the cases where contact with that method and ours can be made.

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Bustamante, R. "Some Universal Solutions for a Class of Incompressible Elastic Body that is Not Green Elastic: The Case of Large Elastic Deformations." Quarterly Journal of Mechanics and Applied Mathematics 73, no. 2 (April 4, 2020): 177–99. http://dx.doi.org/10.1093/qjmam/hbaa006.

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Summary Some universal solutions are studied for a new class of elastic bodies, wherein the Hencky strain tensor is assumed to be a function of the Kirchhoff stress tensor, considering in particular the case of assuming the bodies to be isotropic and incompressible. It is shown that the families of universal solutions found in the classical theory of nonlinear elasticity, are also universal solutions for this new type of constitutive equation.

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17

Caviglia, G., and A. Morro. "Kirchhoff’s equations for the rigid body motion revisited." Meccanica 52, no. 6 (June 29, 2016): 1485–89. http://dx.doi.org/10.1007/s11012-016-0476-1.

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18

Massa, Enrico, and Stefano Vignolo. "Newton–Euler, Lagrange and Kirchhoff formulations of rigid body dynamics: a unified approach." Meccanica 51, no. 8 (November 23, 2015): 2019–23. http://dx.doi.org/10.1007/s11012-015-0333-7.

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Maggiani, Giovanni Battista, and Maria Giovanna Mora. "A dynamic evolution model for perfectly plastic plates." Mathematical Models and Methods in Applied Sciences 26, no. 10 (August 25, 2016): 1825–64. http://dx.doi.org/10.1142/s0218202516500469.

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We consider the dynamic evolution of a linearly elastic-perfectly plastic thin plate subject to a purely vertical body load. As the thickness of the plate goes to zero, we prove that the three-dimensional evolutions converge to a solution of a certain reduced model. In the limiting model admissible displacements are of Kirchhoff–Love type. Moreover, the motion of the body is governed by an equilibrium equation for the stretching stress, a hyperbolic equation involving the vertical displacement and the bending stress, and a rate-independent plastic flow rule. Some further properties of the reduced model are also discussed.

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McMahon, Joseph, Alain Goriely, and Michael Tabor. "Nonlinear morphoelastic plates I: Genesis of residual stress." Mathematics and Mechanics of Solids 16, no. 8 (April 28, 2011): 812–32. http://dx.doi.org/10.1177/1081286510387233.

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Volumetric growth of an elastic body may give rise to residual stress. Here a rigorous analysis is given of the residual strains and stresses generated by growth in the axisymmetric Kirchhoff plate. Balance equations are derived via the Global Constraint Principle, growth is incorporated via a multiplicative decomposition of the deformation gradient, and the system is closed by a response function. The particular case of a compressible neo-Hookean material is analyzed, and the existence of residually stressed states is established.

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Dragović, Vladimir, and Fariba Khoshnasib-Zeinabad. "Topology of the isoenergy manifolds of the Kirchhoff rigid body case on e(3)." Topology and its Applications 311 (April 2022): 107955. http://dx.doi.org/10.1016/j.topol.2021.107955.

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NAIR, SUJIT, and EVA KANSO. "Hydrodynamically coupled rigid bodies." Journal of Fluid Mechanics 592 (November 14, 2007): 393–411. http://dx.doi.org/10.1017/s002211200700849x.

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This paper considers a finite number of rigid bodies moving in potential flow. The dynamics of the solid--fluid system is described in terms of the solid variables only using Kirchhoff potentials. The equations of motion are first derived for the problem of two submerged bodies where one is forced into periodic oscillations. The hydrodynamic coupling causes the free body to drift away from or towards the oscillating body. The method of multiple scales is used to separate the slow drift from the fast response. Interestingly, the free body, when attracted towards the forced one, starts to drift away after it reaches certain separation distance. This suggests that the hydrodynamic coupling helps in preventing collisions. The fluid's role in collision avoidance and motion coordination is examined further through examples. In particular, we show that a free body can coordinate its motion with that of its neighbours, which may be relevant to understanding the coordinated motion in fish schooling.

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Gai, S. L. "Some features of steady separated flow from low speed to hypersonic." Aeronautical Journal 112, no. 1128 (February 2008): 109–13. http://dx.doi.org/10.1017/s0001924000002049.

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Steady non-vortex shedding base flow behind a bluff body is considered. Such a flow is characterised by the flow separation at the trailing edge of the body with an emerging shear layer which reattaches on the axis with strong recompression and recirculating flow bounded by the base, the shear layer, and the axis. Steady wake flows behind a bluff body at low speeds have been studied for more than a century (for example, Kirchhoff; Riabouchinsky). Recently, research on steady bluff body wake flow at low speeds has been reviewed and reinterpreted by Roshko. Roshko has also commented on some basic aspects of steady supersonic base flow following on from Chapman and Korst analyses. In the present paper, we examine the steady base flow features both at low speeds and supersonic speeds in the light of Roshko’s model and expand on some further aspects of base flows at supersonic and hypersonic speeds, not covered by Roshko.

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Jesus, L. J. M., C. A. Cimini, and E. L. Albuquerque. "Application of the Radial Integration Method into Dynamic Formulation of Anisotropic Shallow Shells Using Boundary Element Method." Key Engineering Materials 627 (September 2014): 465–68. http://dx.doi.org/10.4028/www.scientific.net/kem.627.465.

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The formulation developed in this work is based on the coupling of plane elasticity formulation and thin plate formulation for plates (Kirchhoff plates). Both formulations use elastostatic fundamental solutions. Curvature effects are considered as body forces, which generates domain integrals. Domain integrals are transformed into boundary integrals using the radial integration method. Thus, only the boundary is discretized. A radial basis function is used as approximation function in domain integrals. The developed formulation is applied to the dynamic analysis of anisotropic and composite laminate shallow shells under time dependent loads. A computational implementation was performed for the formulation developed and results were compared with results from literature.

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Pius, Reet. "Familienkapellen auf dem Kirchhof und dem Gutshoffriedhof." Baltic Journal of Art History 13 (October 9, 2017): 131. http://dx.doi.org/10.12697/bjah.2017.13.07.

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The 1772 cemetery reform of Catherine the Great, Empress of Russia, resulted in great changes in the cemetery culture of Russia’s Baltic provinces. The ban on burials in churches and the vicinity of churches resulted in the rapid development of cemetery parks outside of settlements. The strong political relations of Estonia’s manor owners with the Russian central government resulted in the nobles being given the privilege to establish burial plots in the churchyards, but in Livonia, this was strictly prohibited. Simultaneously with the parish cemeteries, the owners of private manors established family cemeteries on their manors. The new cemeteries were not only places to bury the dead, but, inspired by contemporary poets, they were seen as family altars, which were visited regularly and which was accessed by path that was attuned to contemplation.The cemetery is complex, which includes a garden, chapel and allée, and if possible, a body of water. Noble trees were planted along the path leading to the cemetery. Oaks were preferred, which due their mighty shape were considered to be the symbol of family and nobility. Influenced by the poetry of the Enlightenment, evergreens – silver firs, thuja trees, and spruces – were called “sad trees”. The French poet Jacques Delille, whose works were popular among the Baltic Germans, sees women as mourners. And many family cemeteries were established at the initiative of women. Examples of Ancient Greek architecture, in the form of temples with porticos or antas, or the small-scale copies of the Pantheon from Ancient Rome, dominated in cemetery architecture. The chapel was comprised of underground burial chambers and above-ground memorials. A so-called memorial altar was located in the end wall of the chapel, which have survived until the present day in a few places. The Barclay de Tolly monument is the most majestic in Estonia.Already in the 1830s, the family chapels became memorials and burials no longer took place there. However, chapels continued to be built until in Estonia until the early 20th century.

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Wu, Xiao-Feng, and Allan D. Pierce. "Uniqueness of Solutions to Variationally Formulated Acoustic Radiation Problems." Journal of Vibration and Acoustics 112, no. 2 (April 1, 1990): 263–67. http://dx.doi.org/10.1115/1.2930121.

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Determination of the surface acoustic pressure given the surface velocity of a vibrating body can be formulated in various ways. However, for some such formulations such as the surface Helmholtz integral equation, solutions are not unique at certain discrete frequencies. Such uniqueness problems can also be present for variational formulations of the problem, but the variational formulation based on the normal derivative of the Kirchhoff integral theorem has unique solutions for vibrating disks and plate-like bodies. For bodies of finite volume, but for which each surface point is vibrating in phase, the total radiated acoustic power is always unique, even though the pressure may not be. The latter conclusion is supported by numerical calculations based on the Rayleigh-Ritz technique for the case of a finite cylinder vibrating as a rigid body in the axial direction.

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Abderrahmani, Sifeddine, Toufik Maalem, and Djamal Hamadi. "On Improved Thin Plate Bending Rectangular Finite Element Based on the Strain Approach." International Journal of Engineering Research in Africa 27 (December 2016): 76–86. http://dx.doi.org/10.4028/www.scientific.net/jera.27.76.

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We propose in this paper the development of a new rectangular finite element for thin plate bending based on the strain approach with linear elastic behavior. An analytical integration is used to evaluate the element stiffness matrix. The present element possesses the three main degrees of freedom (d.o.f) per node, namely, one transverse displacement (w) and two normal rotations about x and y axis respectively (Ɵx, Ɵy). The proposed displacement field represents exactly the rigid body motion and satisfies the compatibility equations. The numerical results converges rapidly to the Kirchhoff solution for thin plates, this makes the present element robust, better suitable for computations, and particularly interesting in modeling this type of structures.

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Candelier, Fabien, Mathieu Porez, and Frederic Boyer. "Note on the swimming of an elongated body in a non-uniform flow." Journal of Fluid Mechanics 716 (January 28, 2013): 616–37. http://dx.doi.org/10.1017/jfm.2012.560.

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AbstractThis paper presents an extension of Lighthill’s large-amplitude elongated-body theory of fish locomotion which enables the effects of an external weakly non-uniform potential flow to be taken into account. To do so, the body is modelled as a Kirchhoff beam, made up of elliptical cross-sections whose size may vary along the body, undergoing prescribed deformations consisting of yaw and pitch bending. The fluid velocity potential is decomposed into two parts corresponding to the unperturbed potential flow, which is assumed to be known, and to the perturbation flow. The Laplace equation and the corresponding Neumann’s boundary conditions governing the perturbation velocity potential are expressed in terms of curvilinear coordinates which follow the body during its motion, thus allowing the boundary of the body to be considered as a fixed surface. Equations are simplified according to the slenderness of the body and the weakness of the non-uniformity of the unperturbed flow. These simplifications allow the pressure acting on the body to be determined analytically using the classical Bernoulli equation, which is then integrated over the body. The model is finally used to investigate the passive and the active swimming of a fish in a Kármán vortex street.

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Scott, Patricia, and Donald V. Helmberger. "Applications of the transmitted Kirchhoff-Holmholtz method to transmitted body waves and possible structural effects at NTS." Bulletin of the Seismological Society of America 75, no. 1 (February 1, 1985): 131–56. http://dx.doi.org/10.1785/bssa0750010131.

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Abstract We extend the Kirchhoff-Helmholtz integral method to calculate acoustic potentials which transmit through three-dimensional warped boundaries. We specify the potentials on an arbitrary surface with Snell's law and plane-wave transmission coefficients and numerically integrate their contributions at a receiver via the scalar integral representation theorem. The method is appropriate for modeling precritical transmitted potentials. Results from test models compare well with optical solutions for transmissions through a flat interface. We model the effect of several idealized crust-mantle boundary structures on teleseismic P wave generated by explosion sources. The structures are all upwarps and are designed to produce travel-time residuals as a function of delta and azimuth which have the same magnitude as residuals observed for NTS tests within Pahute Mesa. These structures consistently cause complicated low amplitude waveforms which arrive early and simple high amplitude waveforms which arrive late. Thus, they cause systematic amplitude variations with azimuth, delta, and source location. The magnitude of this variation is less than or equal to 212. This factor is somewhat less than the observed ab amplitude variation with azimuth of Pahute Mesa tests; however, it is approximately the same magnitude as the observed ab variation at a given station as a function of test location within the mesa.

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Mielke, Alexander. "On Saint-Venant's problem for an elastic strip." Proceedings of the Royal Society of Edinburgh: Section A Mathematics 110, no. 1-2 (1988): 161–81. http://dx.doi.org/10.1017/s0308210500024938.

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SynopsisThe equilibrium equations for elastic deformations of an infinite strip are considered. Under the assumption of sufficiently small strains along the whole body, it is shown that all solutions lie on a six-dimensional manifold. This is achieved by rewriting the field equations as a differential equation in a function spaceover the cross-section, the axial variable taken as time. Then the theory of centre manifolds for elliptic systems applies. Thus the local Saint-Venant's problem is solved. Moreover, the structure of the finite-dimensional solution space is analysed to reveal exactly the two-dimensional rod equations of Kirchhoff. The constitutive relations for this rod model are calculated in a mathematically rigorous way out of the constitutive law of the material forming the strip.

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Pasternak, Yuri G., Aleksander V. Ashikhmin, Yuri A. Rembovsky, Sergey M. Fedorov, and Dmitry V. Zhuravlev. "Virtual Antenna Array for Minimization of DOA Estimation Systematic Error Caused by Scattering of Incident Waves on Antenna Carrier Body." Electronics 9, no. 2 (February 10, 2020): 308. http://dx.doi.org/10.3390/electronics9020308.

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The Direction of Arrival (DOA) estimations of systematic errors are caused by diffraction distortions of the measured spatial structure of a electromagnetic field. These distortions result from scattering of incident waves on the antenna system and nearby scatterers (mobile carrier body, antenna mast, underlying surface, etc.) in wide frequency band, including the resonant frequencies of nearby objects. This article proposes a method for minimizing the DOA estimation systematic error by forming an additional virtual receiving channel—a Virtual Antenna Array (VAA). The VAAs were formed by use of classical apparatus of electrodynamics—the Huygens-Kirchhoff principle, the method of equivalent fields and sources, and the quasistatic approximation of the field based on the theory of analytical functions of the complex variable (Cauchy integral, Laurent series). The proposed method does not require calibration of the antenna system or a priori information about the geometry and material properties of the scatterers (dry or wet soil, opened or closed vehicle doors, etc.). Therefore, it gives good results in cases of mobile and stationary arrays, or changing carrier body geometry.

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Bitkina, Olga, Jang-Ho Lee, Ki-Weon Kang, and Elena Darlington. "Analytical model of the stress–strain state of multilayer composite plates under the influence of different load types with asymmetrical boundary conditions." Journal of Composite Materials 54, no. 12 (March 9, 2016): 1535–48. http://dx.doi.org/10.1177/0021998316636463.

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Composite structure design experience has demonstrated that use of the finite element method during the first stage of the design process is unfounded and that analytical methods to determine the stress–strain state are needed for more accurate calculations. Therefore, an analytical model of the stress–strain state of multilayer composite plates under the influence of temperature, technological, and power loads with different boundary conditions around four boundaries of a rectangular plate was developed. This model enables the solution of more than 240 different boundary value problems with a combination of the following boundary conditions: fixed, moving, hinged, and free edge. In the derivation of this mathematical analytic model, the Kirchhoff hypothesis was applied to the entire body of the anisotropic medium for the interconnected deflection and bending in the plate plane. The resulting equation is an octic linear partial differential equation to express the generalized function of movements.

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Mirparizi, Mina, Chunwei Zhang, and Mohammad Javad Amiri. "One-dimensional electro- magneto-poro-thermoelastic wave propagation in a functionally graded medium with energy dissipation." Physica Scripta 97, no. 4 (March 4, 2022): 045203. http://dx.doi.org/10.1088/1402-4896/ac576f.

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Abstract Laser-induced wave propagation and reflection phenomenon in a functionally graded porous medium subjected to electro- magnetic field is studied in the present research. Firstly, a modified generalized thermoelastic theory named Modified Green Lindsay (MGL) for wave propagation in a porous medium is developed. The properties of the medium are considered as a temperature-dependent nonlinear function. Furthermore, the influence of thermal and mechanical rates in the modified generalized equations are considered. An updated FEM and Newmark’s technique are applied to solve the time-dependent and nonlinear equations. The second Piola-Kirchhoff stress, temperature and displacement distributions in the body subjected to laser shock are presented graphically. Based on the results, the wave propagation amplitude in the body subjected to heat flux reduces over time because of the backplane influenced by convection heat transfer. Wave propagation is more obvious in MGL simulation outcomes compared to the classical ones. In addition, it is observed that the MGL simulation is superior in presenting more exact wave propagation in comparison to the simple GL theory. As the boundary condition receives the most energy due to the laser pulse, the maximum variations of the volume fraction are experienced in this boundary.

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Cheng, J. T., W. L. Zhao, C. Zhao, and W. H. Wu. "Design of Sinusoidal Grating Projection Depicts Transmission." Key Engineering Materials 567 (July 2013): 149–54. http://dx.doi.org/10.4028/www.scientific.net/kem.567.149.

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The measurement of body contours grating fringe projection technology is the three-dimensional measurement of a hotspot. Basic principle is to be tested based on grating projection three-dimensional object shape; key technology is to enable the generation of sinusoidal grating projection stripes projected onto the measured object. Theoretical sinusoidal intensity stripes should be a phase grating, but such grating is difficult and costly. Therefore, this paper structure of smooth three-dimensional measurement system, the core scanning devices-grating, through the characterization method to design a production, and enable it to project a stripe of light intensity by the sine distribution is given the experimental results. From the start of the study to refine and perfect the final three stages, each stage is accompanied by a large number of experiments. Using Fresnel-Kirchhoff formula. The overall structure of the grating design and the gradual improvement，Achieved good results, And proposed future research ideas and program，Also gives the experimental data and results.

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35

Sab, Karam. "Homogenization of Out-of-Plane Loaded Random Plates." Materials Science Forum 638-642 (January 2010): 2766–71. http://dx.doi.org/10.4028/www.scientific.net/msf.638-642.2766.

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The homogenization of elastic periodic plates is as follows: The 3D heterogeneous body is replaced by a homogeneous Love-Kirchhoff plate whose stiffness constants are computed by solving an auxiliary boundary problem on a 3D unit cell that generates the plate by periodicity in the in-plane directions. In the present study, a generalization of the above mentioned approach is presented for the random case. The homogenized bending stiffness and the moduli for in-plane deformation of a plate cut from a block of composite material, considered to be a statistically uniform random material in the in-plane directions, are defined in three equivalent manners: a) the first definition considers statistically invariant stress and strain fields in the infinite plate. In the second and third definitions, a finite representative volume element of the plate is submitted to suitable b) kinematically uniform boundary conditions and c) statically uniform boundary conditions. The relationships between these three definitions are studied and bounds are derived.

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S. Agrawal, Nikhil, P. B. Kulkarni, P. D. Pachpor, R. N. Khapre, and Dipak Nakhate. "A parametric study of residual stress in plate." International Journal of Engineering & Technology 7, no. 2.31 (May 29, 2018): 127. http://dx.doi.org/10.14419/ijet.v7i2.31.13424.

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Residual stress is a process-induced stress in a molded part that exists in the body in the absence of external loading or it exists in steel section of the unloaded state. Residual stress is also termed as ‘Locked Stress’. This paper presents to find out this lock stress analytically. The theoretical and analytical inputs are considered in terms of aspect ratio and these results are compared by percentage error. The previous study mentioned many experimental methods by which residual stresses were sorted out. A Plate is a flat surface having thickness small as compared to other two dimensions. Researchers are mainly focused on the treatment of the different plate theories related to Kirchhoff or Reissner/Mindlin. The developed ANSYS finite element model analyzed square and rectangular plate and compared the analytical results in terms of deflection and stress with theoretical results which are obtained from classical theory. Different boundary conditions for different plate size are considered and solved.

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Qian, Z., and J. G. Simmonds. "Constructing Exact Dynamic Elasticity Solutions for Axisymmetrically Deformed Plates From Classical Plate Theory Solutions." Journal of Applied Mechanics 65, no. 1 (March 1, 1998): 1–6. http://dx.doi.org/10.1115/1.2789026.

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This paper addresses the question of how to assess the errors made when the exact three-dimensional linear elasticity solution for the axisymmetric dynamic deformation of an elastic plate is approximated by a solution inferred from the classical plate theory of Kirchhoff. Following the strategy used by Ladeve`ze and Simmonds for beams, the exact solution of a “nearby” three-dimensional problem, which differs from the original problem by the addition of incremental, computable body forces, face shears, and initial conditions—error increments, for short—is expressed in terms of the solution of a wave equation in which distance normal to the plate’s midplane plays the role of a time-like variable while the physical time itself enters only as a parameter. The error increments which, ultimately, can be computed in terms of the solution delivered by plate theory, can be regarded as an “engineering norm” because with them an engineer can decide if such a shift in the external data lies within acceptable bounds.

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38

Gray, Samuel H. "Gaussian beam migration of common-shot records." GEOPHYSICS 70, no. 4 (July 2005): S71—S77. http://dx.doi.org/10.1190/1.1988186.

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Gaussian beam migration is a depth migration method whose accuracy rivals that of migration by wavefield extrapolation — so-called “wave-equation migration” — and whose efficiency rivals that of Kirchhoff migration. This migration method can image complicated geologic structures, including very steep dips, in areas where the seismic velocity varies rapidly. However, applications of prestack Gaussian beam migration either have been limited to common-offset common-azimuth data volumes, and thus are inflexible, or suffer from multiarrival inaccuracies in a common-shot implementation. In order to optimize both the flexibility and accuracy of Gaussian beam migration, I present a common-shot implementation that handles multipathing in a natural way. This allows the migration of data sets that can include a variety of azimuths, and it allows a simplified treatment of near-surface issues. Application of this method to model data typical of Canadian Foothills structures and to model data that includes a complicated salt body demonstrates the accuracy and versatility of the migration.

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CANDELIER, FABIEN, FREDERIC BOYER, and ALBAN LEROYER. "Three-dimensional extension of Lighthill's large-amplitude elongated-body theory of fish locomotion." Journal of Fluid Mechanics 674 (March 11, 2011): 196–226. http://dx.doi.org/10.1017/s002211201000649x.

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The goal of this paper is to derive expressions for the pressure forces and moments acting on an elongated body swimming in a quiescent fluid. The body is modelled as an inextensible and unshearable (Kirchhoff) beam, whose cross-sections are elliptic, undergoing prescribed deformations, consisting of yaw and pitch bending. The surrounding fluid is assumed to be inviscid, and irrotational everywhere, except in a thin vortical wake. The Laplace equation and the corresponding Neumann boundary conditions are first written in terms of the body coordinates of a beam treating the body as a fixed surface. They are then simplified according to the slenderness of the body and its kinematics. Because the equations are linear, the velocity potential is sought as a sum of two terms which are linked respectively to the axial movements of the beam and to its lateral movements. The lateral component of the velocity potential is decomposed further into two sub-components, in order to exhibit explicitly the role of the two-dimensional potential flow produced by the lateral motion of the cross-section, and the role played by the curvature effects of the beam on the cross-sectional flow. The pressure, which is given by Bernoulli's equation, is integrated along the body surface, and the expressions for the resultant and the moment are derived analytically. Thereafter, the validity of the force and moment obtained analytically is checked by comparisons with Navier–Stokes simulations (using Reynolds-averaged Navier–Stokes equations), and relatively good agreements are observed.

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PALIERNE, J. F. "On the motion of rigid bodies in incompressible inviscid fluids of inhomogeneous density." Journal of Fluid Mechanics 393 (August 25, 1999): 89–98. http://dx.doi.org/10.1017/s0022112099005509.

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The motion of a rigid body in an inviscid incompressible fluid of inhomogeneous density is considered. The size of the body is taken small with respect to the length scale of the density variations; its shape is otherwise arbitrary. The force and the torque acting on the body in an arbitrary motion are derived from Hamilton's principle of least action, thus offering a variational derivation of Kirchhoff's equations, supplemented by the terms due to the density gradient. The force and the torque due to a density gradient are proportional to the gradient and quadratic in the velocity and the angular velocity. The same coefficients are shown to govern both the inertial behaviour of the body, i.e. the response to accelerations, and the effects of density gradients. The free motion of spheres and two-dimensional circular cylinders is shown to obey a condition akin to the Fermat principle in optics.

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Park, Yunyoung, Yongsam Kim, and Sookkyung Lim. "Locomotion of a single-flagellated bacterium." Journal of Fluid Mechanics 859 (November 21, 2018): 586–612. http://dx.doi.org/10.1017/jfm.2018.799.

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Single-flagellated bacteria propel themselves by rotating a flagellar motor, translating rotation to the filament through a compliant hook and subsequently driving the rotation of the flagellum. The flagellar motor alternates the direction of rotation between counterclockwise and clockwise, and this leads to the forward and backward directed swimming. Such bacteria can change the course of swimming as the hook experiences its buckling caused by the change of bending rigidity. In this paper, we present a comprehensive model of a monotrichous bacterium as a free swimmer in a viscous fluid. We describe a cell body as a rigid body using the penalty method and a flagellum as an elastic rod using Kirchhoff rod theory. The hydrodynamic interaction of the bacterium is described by the regularized Stokes formulation. Our model of a single-flagellated micro-organism is able to mimic a swimming pattern that is well matched with the experimental observation. Furthermore, we find the critical thresholds of the rotational frequency of the motor and the bending modulus of the hook for the buckling instability, and investigate the dependence of the buckling angle and the reorientation of the swimming cell after buckling on the physical and geometrical parameters of the model.

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FERNANDES, PEDRO C., PATRICIA ERN, FRÉDÉRIC RISSO, and JACQUES MAGNAUDET. "Dynamics of axisymmetric bodies rising along a zigzag path." Journal of Fluid Mechanics 606 (July 10, 2008): 209–23. http://dx.doi.org/10.1017/s0022112008001663.

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The forces and torques governing the planar zigzag motion of thick, slightly buoyant disks rising freely in a liquid at rest are determined by applying the generalized Kirchhoff equations to experimental measurements of the body motion performed for a single body-to-fluid density ratio ρs/ρf ≈ 1. The evolution of the amplitude and phase of the various contributions is discussed as a function of the two control parameters, i.e. the body aspect ratio (the diameter-to-thickness ratio χ = d/h ranges from 2 to 10) and the Reynolds number (100 < Re < 330), Re being based on the rise velocity and diameter of the body. The body oscillatory behaviour is found to be governed by the force balance along the transverse direction and the torque balance. In the transverse direction, the wake-induced force is mainly balanced by two forces that depend on the body inclination, i.e. the inertia force generated by the body rotation and the transverse component of the buoyancy force. The torque balance is dominated by the wake-induced torque and the restoring added-mass torque generated by the transverse velocity component. The results show a major influence of the aspect ratio on the relative magnitude and phase of the various contributions to the hydrodynamic loads. The vortical transverse force scales as fo = (ρf − ρs)ghπd2 whereas the vortical torque involves two contributions, one scaling as fod and the other as f1d with f1 = χfo. Using this normalization, the amplitudes and phases of the vortical loads are made independent of the aspect ratio, the amplitudes evolving as (Re/Rec1 − 1)1/2, where Rec1 is the threshold of the first instability of the wake behind the corresponding body held fixed in a uniform stream.

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Mougin, G., and J. Magnaudet. "The generalized Kirchhoff equations and their application to the interaction between a rigid body and an arbitrary time-dependent viscous flow." International Journal of Multiphase Flow 28, no. 11 (November 2002): 1837–51. http://dx.doi.org/10.1016/s0301-9322(02)00078-2.

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LIERO, MATTHIAS, and ALEXANDER MIELKE. "AN EVOLUTIONARY ELASTOPLASTIC PLATE MODEL DERIVED VIA Γ-CONVERGENCE." Mathematical Models and Methods in Applied Sciences 21, no. 09 (September 2011): 1961–86. http://dx.doi.org/10.1142/s0218202511005611.

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This paper is devoted to dimension reduction for linearized elastoplasticity in the rate-independent case. The reference configuration of the three-dimensional elastoplastic body has a two-dimensional middle surface and a positive but small thickness. Under suitable scalings we derive a limiting model for the case in which the thickness of the plate tends to 0. This model contains membrane and plate deformations (linear Kirchhoff–Love plate), which are coupled via plastic strains. We establish strong convergence of the solutions in the natural energy space. The analysis uses an abstract Γ-convergence theory for rate-independent evolutionary systems that is based on the notion of energetic solutions. This concept is formulated via an energy-storage functional and a dissipation functional, such that energetic solutions are defined in terms of a stability condition and an energy balance. The Mosco convergence of the quadratic energy-storage functional follows the arguments of the elastic case. To handle the evolutionary situation the interplay with the dissipation functional is controlled by cancellation properties for Mosco-convergent quadratic energies.

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Rubin, Shimon, Arie Tulchinsky, Amir D. Gat, and Moran Bercovici. "Elastic deformations driven by non-uniform lubrication flows." Journal of Fluid Mechanics 812 (January 5, 2017): 841–65. http://dx.doi.org/10.1017/jfm.2016.830.

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The ability to create dynamic deformations of micron-sized structures is relevant to a wide variety of applications such as adaptable optics, soft robotics and reconfigurable microfluidic devices. In this work, we examine non-uniform lubrication flow as a mechanism to create complex deformation fields in an elastic plate. We consider a Kirchhoff–Love elasticity model for the plate and Hele-Shaw flow in a narrow gap between the plate and a parallel rigid surface. Based on linearization of the Reynolds equation, we obtain a governing equation which relates elastic deformations to gradients in non-homogeneous physical properties of the fluid (e.g. body forces, viscosity and slip velocity). We then focus on a specific case of non-uniform Helmholtz–Smoluchowski electro-osmotic slip velocity, and provide a method for determining the zeta-potential distribution necessary to generate arbitrary static and quasi-static deformations of the elastic plate. Extending the problem to time-dependent solutions, we analyse transient effects on asymptotically static solutions, and finally provide a closed form solution for a Green’s function for time periodic actuations.

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Destrade, Michel, Yibin Fu, and Andrea Nobili. "Edge wrinkling in elastically supported pre-stressed incompressible isotropic plates." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 472, no. 2193 (September 2016): 20160410. http://dx.doi.org/10.1098/rspa.2016.0410.

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The equations governing the appearance of flexural static perturbations at the edge of a semi-infinite thin elastic isotropic plate, subjected to a state of homogeneous bi-axial pre-stress, are derived and solved. The plate is incompressible and supported by a Winkler elastic foundation with, possibly, wavenumber dependence. Small perturbations superposed onto the homogeneous state of pre-stress, within the three-dimensional elasticity theory, are considered. A series expansion of the plate kinematics in the plate thickness provides a consistent expression for the second variation of the potential energy, whose minimization gives the plate governing equations. Consistency considerations supplement a constraint on the scaling of the pre-stress so that the classical Kirchhoff–Love linear theory of pre-stretched elastic plates is retrieved. Moreover, a scaling constraint for the foundation stiffness is also introduced. Edge wrinkling is investigated and compared with body wrinkling. We find that the former always precedes the latter in a state of uni-axial pre-stretch, regardless of the foundation stiffness. By contrast, a general bi-axial pre-stretch state may favour body wrinkling for moderate foundation stiffness. Wavenumber dependence significantly alters the predicted behaviour. The results may be especially relevant to modelling soft biological materials, such as skin or tissues, or stretchable organic thin-films, embedded in a compliant elastic matrix.

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Steckenbiller, Christiane. "Futurity, Aging, and Personal Crises: Writing about Refugees in Jenny Erpenbeck's Gehen, ging, gegangen (2015) and Bodo Kirchhoff's Widerfahrnis (2016)." German Quarterly 92, no. 1 (January 2019): 68–86. http://dx.doi.org/10.1111/gequ.12095.

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Kim, Dokyum, Yongsam Kim, and Sookkyung Lim. "Effects of swimming environment on bacterial motility." Physics of Fluids 34, no. 3 (March 2022): 031907. http://dx.doi.org/10.1063/5.0082768.

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Swimming trajectories of bacteria can be altered by environmental conditions, such as background flow and physical barriers, that limit the free swimming of bacteria. We present a comprehensive model of a bacterium that consists of a rod-shaped cell body and a flagellum which is composed of a motor, a hook, and a filament. The elastic flagellum is modeled based on the Kirchhoff rod theory, the cell body is considered to be a rigid body, and the hydrodynamic interaction of a bacterium near a wall is described by regularized Stokeslet formulation combined with the image system. We consider three environmental conditions: (1) a rigid surface is placed horizontally and there is no shear flow, (2) a shear fluid flow is present and the bacterium is near the rigid surface, and (3) while the bacterium is near the rigid surface and is under shear flow, an additional sidewall which is perpendicular to the rigid surface is placed. Each environmental state modifies the swimming behavior. For the first condition, there are two modes of motility, trap and escape, whether the bacterium stays near the surface or moves away from the surface as we vary the physical and geometrical properties of the model bacterium. For the second condition, there exists a threshold of shear rate that classifies the motion into two types of paths in which the bacterium takes either a periodic coil trajectory or a linear trajectory. For the last condition, the bacterium takes upstream motility along the sidewall for lower shear rates and downstream motility for larger shear flow rates.

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Gauthier, Stéphane, and John K. Horne. "Acoustic characteristics of forage fish species in the Gulf of Alaska and Bering Sea based on Kirchhoff-approximation models." Canadian Journal of Fisheries and Aquatic Sciences 61, no. 10 (October 1, 2004): 1839–50. http://dx.doi.org/10.1139/f04-117.

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Acoustic surveys are routinely used to assess fish abundance. To ensure accurate population estimates, the characteristics of echoes from constituent species must be quantified. Kirchhoff-ray mode (KRM) backscatter models were used to quantify acoustic characteristics of Bering Sea and Gulf of Alaska pelagic fish species: capelin (Mallotus villosus), Pacific herring (Clupea pallasii), walleye pollock (Theragra chalcogramma), Atka mackerel (Pleurogrammus monopterygius), and eulachon (Thaleichthys pacificus). Atka mackerel and eulachon do not have swimbladders. Acoustic backscatter was estimated as a function of insonifying frequency, fish length, and body orientation relative to the incident wave front. Backscatter intensity and variance estimates were compared to examine the potential to discriminate among species. Based on relative intensity differences, species could be separated in two major groups: fish with gas-filled swimbladders and fish without swimbladders. The effects of length and tilt angle on echo intensity depended on frequency. Variability in target strength (TS) resulting from morphometric differences was high for species without swimbladders. Based on our model predictions, a series of TS to length equations were developed for each species at the common frequencies used by fisheries acousticians.

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Gauthier, Stéphane, and John K. Horne. "Potential acoustic discrimination within boreal fish assemblages." ICES Journal of Marine Science 61, no. 5 (January 1, 2004): 836–45. http://dx.doi.org/10.1016/j.icesjms.2004.03.033.

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Abstract Differences in the acoustic characteristics of forage fish species in the Gulf of Alaska and the Bering Sea were examined using Kirchhoff ray-mode (KRM) backscatter models. Our goal was to identify species-specific characteristics and metrics that facilitate the discrimination of species using acoustic techniques. Five fish species were analyzed: capelin (Mallotus villosus), Pacific herring (Clupea pallasii), walleye pollock (Theragra chalcogramma), Atka mackerel (Pleurogrammus monopterygius), and eulachon (Thaleichthys pacificus). Backscatter amplitude differences exist among these species, especially between swimbladdered and non-swimbladdered fish. Echo intensities were variable within and among species. The effect of morphological variability was indexed using the ratio of the Reduced-scattering length (RSL) standard deviation over its mean. Morphological variability was low only at fish length to acoustic wavelength ratios less than eight. Target strength differences between pairs of carrier frequencies (ranging from 12 kHz to 200 kHz) differed among species, and were dependent on fish size and body orientation. Frequency differencing successfully discriminated between fish species but the choice of frequency to maximize target strength differences was not consistent among species pairs. Frequency-dependent, backscatter model predictions facilitate comparison of target strength differences prior to acoustic data collection.

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Journal articles on the topic 'Bodo Kirchhoff'

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