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Автор: Grafiati

Опубліковано: 18 травня 2024

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1

Zhang, WX. "Thermal Effect of Thin Elastic Plates." E3S Web of Conferences 236 (2021): 02040. http://dx.doi.org/10.1051/e3sconf/202123602040.

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Анотація:

Thermal effect refers to the heat released or absorbed by the object in the changing process at a certain temperature. In this process, the stress inside the material will change. Thermal stress refers to the stress produced when the temperature changes, because of the external constraints and the internal constraints between the various parts, so that it can not completely free expansion and contraction.

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2

Vallabhan, C. V. Girija, Bob Yao‐Ting Wang, Gee David Chou, and Joseph E. Minor. "Thin Glass Plates on Elastic Supports." Journal of Structural Engineering 111, no. 11 (November 1985): 2416–26. http://dx.doi.org/10.1061/(asce)0733-9445(1985)111:11(2416).

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3

Dauge, M., I. Djurdjevic, E. Faou, and A. Rössle. "Eigenmode Asymptotics in Thin Elastic Plates." Journal de Mathématiques Pures et Appliquées 78, no. 9 (November 1999): 925–64. http://dx.doi.org/10.1016/s0021-7824(99)00138-5.

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4

Porter, R. "Trapped waves in thin elastic plates." Wave Motion 45, no. 1-2 (November 2007): 3–15. http://dx.doi.org/10.1016/j.wavemoti.2007.04.001.

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5

Dauge, Monique, and Isabelle Gruais. "Edge layers in thin elastic plates." Computer Methods in Applied Mechanics and Engineering 157, no. 3-4 (May 1998): 335–47. http://dx.doi.org/10.1016/s0045-7825(97)00244-2.

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6

Zhang, R. J. "Size Effects in Elastic Thin Plates." Journal of Physics: Conference Series 633 (September 21, 2015): 012139. http://dx.doi.org/10.1088/1742-6596/633/1/012139.

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7

Radhakrishnan, G., M. K. Sundaresan, and B. Nageswara Rao. "FUNDAMENTAL FREQUENCY OF THIN ELASTIC PLATES." Journal of Sound and Vibration 209, no. 2 (January 1998): 373–76. http://dx.doi.org/10.1006/jsvi.1997.1242.

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8

Hayrapetyan, G. S., and S. H. Sargsyan. "Theory of micropolar orthotropic elastic thin plates." Mechanics - Proceedings of National Academy of Sciences of Armenia 65, no. 3 (2012): 22–33. http://dx.doi.org/10.33018/65.3.3.

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9

Meylan, Michael H., and Michael J. A. Smith. "Perforated grating stacks in thin elastic plates." Wave Motion 70 (April 2017): 15–28. http://dx.doi.org/10.1016/j.wavemoti.2016.07.013.

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10

Tweet, K. D., M. J. Forrestal, and W. E. Baker. "Diverging elastic waves in thin tapered plates." International Journal of Solids and Structures 34, no. 3 (January 1997): 289–96. http://dx.doi.org/10.1016/s0020-7683(96)00009-1.

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11

Atoyan,, A. A., and S. H. Sargsyan,. "Dynamic Theory of Micropolar Elastic Thin Plates." Journal of the Mechanical Behavior of Materials 18, no. 2 (April 2007): 81–88. http://dx.doi.org/10.1515/jmbm.2007.18.2.81.

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12

Weller, Thibaut, and Christian Licht. "Modeling of linearly electromagneto-elastic thin plates." Comptes Rendus Mécanique 335, no. 4 (April 2007): 201–6. http://dx.doi.org/10.1016/j.crme.2007.03.009.

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13

Morimoto, Takuya, and Yoshinobu Tanigawa. "Elastic stability of inhomogeneous thin plates on an elastic foundation." Archive of Applied Mechanics 77, no. 9 (February 24, 2007): 653–74. http://dx.doi.org/10.1007/s00419-007-0117-1.

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14

Sargsyan, S. H. "General mathematical models of micropolar thin elastic plates." Mechanics - Proceedings of National Academy of Sciences of Armenia 64, no. 1 (2011): 58–67. http://dx.doi.org/10.33018/64.1.7.

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15

Sargsyan, S. H., and A. J. Farmanyan. "Theory of micropolar orthotropic elastic multilayered thin plates." Mechanics - Proceedings of National Academy of Sciences of Armenia 65, no. 4 (2012): 70–80. http://dx.doi.org/10.33018/65.4.7.

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16

Andronov, Ivan V. "Stoneley Type Flexure Waves in Thin Elastic Plates." Journal of Low Frequency Noise, Vibration and Active Control 23, no. 4 (December 2004): 249–57. http://dx.doi.org/10.1260/0263-0923.23.4.249.

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17

Kovalev, A. S., and E. S. Sokolova. "Two-parameter dynamical solitons in thin elastic plates." Low Temperature Physics 36, no. 4 (April 2010): 338–43. http://dx.doi.org/10.1063/1.3421088.

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18

Andronov, Ivan V. "Stoneley Type Flexure Waves in Thin Elastic Plates." Journal of Low Frequency Noise, Vibration and Active Control 23, no. 4 (December 1, 2005): 249–58. http://dx.doi.org/10.1260/0263092053498964.

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19

Kolpakov, A. G. "Thin elastic periodic plates with unilateral internal contacts." Journal of Applied Mechanics and Technical Physics 32, no. 5 (1992): 784–90. http://dx.doi.org/10.1007/bf00851954.

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20

Khludnev, Alexander. "Thin rigid inclusions with delaminations in elastic plates." European Journal of Mechanics - A/Solids 32 (March 2012): 69–75. http://dx.doi.org/10.1016/j.euromechsol.2011.09.004.

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21

Hu, Caifeng, and Gilbert A. Hartley. "Elastic analysis of thin plates with beam supports." Engineering Analysis with Boundary Elements 13, no. 3 (January 1994): 229–38. http://dx.doi.org/10.1016/0955-7997(94)90049-3.

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22

Lagnese, J. E., and G. Leugering. "Modelling of dynamic networks of thin elastic plates." Mathematical Methods in the Applied Sciences 16, no. 6 (June 1993): 379–407. http://dx.doi.org/10.1002/mma.1670160602.

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23

Dimitriadis, E. K., C. R. Fuller, and C. A. Rogers. "Piezoelectric Actuators for Distributed Vibration Excitation of Thin Plates." Journal of Vibration and Acoustics 113, no. 1 (January 1, 1991): 100–107. http://dx.doi.org/10.1115/1.2930143.

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Анотація:

The behavior of two dimensional patches of piezoelectric material bonded to the surface of elastic distributed structures and used as vibration actuators is analytically investigated. A static analysis is used to estimate the loads induced by the piezoelectric actuator to the supporting elastic structure. The theory is then applied to develop an approximate dynamic model for the vibration response of a simply supported elastic rectangular plate excited by a piezoelectric patch of variable rectangular geometry. The results demonstrate that modes can be selectively excited and that the geometry of the actuator shape markedly affects the distribution of the response among modes. It thus appears possible to tailor the shape of the actuator to either excite or suppress particular modes leading to improved control behavior.

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24

Li, Rui, Yang Zhong, and Ming Li. "Analytic bending solutions of free rectangular thin plates resting on elastic foundations by a new symplectic superposition method." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 469, no. 2153 (May 8, 2013): 20120681. http://dx.doi.org/10.1098/rspa.2012.0681.

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Analytic bending solutions of free rectangular thin plates resting on elastic foundations, based on the Winkler model, are obtained by a new symplectic superposition method. The proposed method offers a rational elegant approach to solve the problem analytically, which was believed to be difficult to attain. By way of a rigorous but simple derivation, the governing differential equations for rectangular thin plates on elastic foundations are transferred into Hamilton canonical equations. The symplectic geometry method is then introduced to obtain analytic solutions of the plates with all edges slidingly supported, followed by the application of superposition, which yields the resultant solutions of the plates with all edges free on elastic foundations. The proposed method is capable of solving plates on elastic foundations with any other combinations of boundary conditions. Comprehensive numerical results validate the solutions by comparison with those obtained by the finite element method.

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25

Ayorinde, E. O., and Lin Yu. "On the Use of Diagonal Modes in the Elastic Identification of Thin Plates." Journal of Vibration and Acoustics 121, no. 1 (January 1, 1999): 33–40. http://dx.doi.org/10.1115/1.2893945.

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Анотація:

This paper relates a further development of an earlier work by the first author and others, in which they presented a method of deriving the elastic constants of composite materials from resonance data obtained from the modal analysis of freely-supported plates made out of orthotropic or isotropic materials. In the present work, the diagonal modes are included in the optimized Rayleigh three-term displacement representation for the square isotropic or almost isotropic composite plates. The use of sensitivity analysis of the frequencies including the diagonal modes to each elastic constant is also investigated in the procedure of the identification of elastic properties. Comparison of results obtained using diagonal-inclusive modes with those excluding the diagonal modes suggest that lower diagonal modes have relatively higher sensitivities to the elastic constants and can significantly improve accuracy when included in the elastic identification method applied here to square isotropic or almost isotropic plates.

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26

Coman, C. D., and A. P. Bassom. "An asymptotic description of the elastic instability of twisted thin elastic plates." Acta Mechanica 200, no. 1-2 (February 4, 2008): 59–68. http://dx.doi.org/10.1007/s00707-007-0572-3.

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27

Alashkar, Adnan, Mohamed Elkafrawy, Rami Hawileh, and Mohammad AlHamaydeh. "Elastic Buckling Behavior of Functionally Graded Material Thin Skew Plates with Circular Openings." Buildings 14, no. 3 (February 21, 2024): 572. http://dx.doi.org/10.3390/buildings14030572.

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Анотація:

This study investigates the elastic buckling behavior of Functionally Graded Material (FGM) thin skew plates featuring a circular opening. FGMs, known for their unique property gradients, have gained prominence in structural engineering due to their mechanical performance and durability. Including a circular opening introduces a critical geometric consideration, influencing the structural stability and load-carrying capacity of FGM plates. The study examines the effects of the skew angle, plate’s aspect ratio, opening position, and size on the critical buckling load, normalized buckling load, and various buckling failure modes through computer modeling and finite element analysis. The results offer valuable insights into the interplay between material heterogeneity, geometric configuration, and structural stability. For instance, the critical buckling load increases by 29%, 82%, and 194% with an increment in skew angle from 0° to 30°, 45°, and 60°, respectively. Moreover, as the opening shifts from the plate’s edge closer to the center, the critical buckling load decreases by 26%. The critical buckling load is also dependent on the power index, as an increase in the power index from 0.2 to 5 reduced the buckling load by 1698 kN. This research contributes to the advancement of our understanding of FGM thin plates’ behavior under skew loading conditions, with implications for the design and optimization of innovative structures. The findings presented provide a foundation for further exploration of advanced composite materials and their applications in structural engineering.

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28

Banh, Thien-Thanh. "Topology Optimization for Thin Plates Embedded in Elastic Medium." Journal of Creative Sustainable Architecture & Built Environment 7, no. 1 (November 30, 2017): 57–62. http://dx.doi.org/10.21742/csabe.2017.7.1.09.

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29

Rokhlin, S. I., and W. Wang. "Measurements of elastic constants of very thin anisotropic plates." Journal of the Acoustical Society of America 94, no. 5 (November 1993): 2721–30. http://dx.doi.org/10.1121/1.407355.

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30

Manley, Martin G. "Higher‐order theory for fluid‐loaded thin elastic plates." Journal of the Acoustical Society of America 91, no. 4 (April 1992): 2416. http://dx.doi.org/10.1121/1.403231.

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31

Chebakov, R., J. Kaplunov, and G. A. Rogerson. "A non-local asymptotic theory for thin elastic plates." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 473, no. 2203 (July 2017): 20170249. http://dx.doi.org/10.1098/rspa.2017.0249.

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Анотація:

The three-dimensional dynamic non-local elasticity equations for a thin plate are subject to asymptotic analysis assuming the plate thickness to be much greater than a typical microscale size. The integral constitutive relations, incorporating the variation of an exponential non-local kernel across the thickness, are adopted. Long-wave low-frequency approximations are derived for both bending and extensional motions. Boundary layers specific for non-local behaviour are revealed near the plate faces. It is established that the effect of the boundary layers leads to the first-order corrections to the bending and extensional stiffness in the classical two-dimensional plate equations.

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32

Keltie, R. F., and H. Peng. "Acoustic power radiated from point-forced thin elastic plates." Journal of Sound and Vibration 112, no. 1 (January 1987): 45–52. http://dx.doi.org/10.1016/s0022-460x(87)80092-5.

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33

Mora, T., and A. Boudaoud. "Thin elastic plates: On the core of developable cones." Europhysics Letters (EPL) 59, no. 1 (July 2002): 41–47. http://dx.doi.org/10.1209/epl/i2002-00157-x.

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34

Licht, Christian. "Asymptotic modeling of assemblies of thin linearly elastic plates." Comptes Rendus Mécanique 335, no. 12 (December 2007): 775–80. http://dx.doi.org/10.1016/j.crme.2007.10.008.

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35

Gousias, N., and A. K. Lazopoulos. "Axisymmetric bending of strain gradient elastic circular thin plates." Archive of Applied Mechanics 85, no. 11 (June 18, 2015): 1719–31. http://dx.doi.org/10.1007/s00419-015-1014-7.

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36

Dillard, D. A. "Bending of Plates on Thin Elastomeric Foundations." Journal of Applied Mechanics 56, no. 2 (June 1, 1989): 382–86. http://dx.doi.org/10.1115/1.3176093.

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Анотація:

Closed-form and series solutions are presented for the bending of plates bonded to a thin elastomeric foundation which is in turn bonded to a rigid substrate. The standard fourth-order governing differential equation of a classical Winkler elastic foundation becomes a sixth-order equation for the case of an incompressible foundation. Oscillation decay rates are shown to be significantly different from those of the Winkler solution due to the incompressibility of the elastomer.

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37

Kryshchuk, Mykola, Egor Ovcharenko, and Hanna Us. "Determination of elastic characteristics for a package of monolayers thin-walled plates from composite fibrous materials." Mechanics and Advanced Technologies 7, no. 2 (98) (September 19, 2023): 155–59. http://dx.doi.org/10.20535/2521-1943.2023.7.2.287711.

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Анотація:

An analytical method for calculating the equivalent elastic characteristics of anisotropic multilayer plates made of composite fibrous materials is laid out. The main assumptions taken into consideration when calculating elastic moduli and Pousson's coefficients are that fibers are elastic materials with orthotropic mechanical characteristics that deform together when multilayer plates are loaded. Analytical methods for calculating effective modulus of elasticity most common in practical applications of applied mechanics are laid out in the list of cited publications. These include the rules of the mixture, the model proposed by Hill and Khashin, the model of Kilchinsky, the methods of Vanin and L.P. Khoroshun. Numerical methods for determining the elastic mechanical properties of reinforced unidirectional and layered composite materials are based on information technologies of finite-element modeling of representative volumes of composite materials and solving a number of boundary value problems for them. For the constructions of thin-walled plates with composite fibrous materials, traditional calculation schemes are used, for which the plane stress state is typical. The stress-strain relationship for a monolayer of plates loaded at an arbitrary angle is presented in the form of Hooke's law for aniotropic materials. Deformations of a package of monolayers with composite fibrous materials in a plane elastic-deformed state are determined, as for a monolayer, by four independent elastic constants. With the use of a universal calculation model based on the equations of applied mechanics, the results of the calculations of elastic moduli and Poisson's coefficients were obtained for a package of monolayers of thin-walled plates with composite fibrous materials made of carbon fiber and carbon fiber. Research results are presented in an analytical and graphic form. The influence of the construction structure of composite fibrous materials of thin-walled plates on its mechanical properties and their dependence on the angle of the force load vector is presented. The research results can be used to determine the rational mechanical properties of multilayer composite plates, taking into account their structural and technological purpose in various industries.

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38

Zheng, Feng, and Ming Lu Wang. "The Levy Solution of Functionally Graded Materials Elastic Thin Plates." Advanced Materials Research 681 (April 2013): 329–32. http://dx.doi.org/10.4028/www.scientific.net/amr.681.329.

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The governing equation of elastic FGM thin plates was obtained by degenerating the governing equation of viscoelastic FGM thin plates. A Levy solution of a simply supported FGM rectangular plate was gotten. Based on the Levy solution, the influence of considering and ignoring mid-plane stain, due to the inhomogeneous property of the functionally graded materials, on the static responses of the functionally graded materials thin plate is investigated.

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39

Lindsay, A. E., W. Hao, and A. J. Sommese. "Vibrations of thin plates with small clamped patches." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 471, no. 2184 (December 2015): 20150474. http://dx.doi.org/10.1098/rspa.2015.0474.

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Анотація:

Eigenvalues of fourth-order elliptic operators feature prominently in stability analysis of elastic structures. This paper considers out-of-plane modes of vibration of a thin elastic plate perforated by a collection of small clamped patches. As the radius of each patch shrinks to zero, a point constraint eigenvalue problem is derived in which each patch is replaced by a homogeneous Dirichlet condition at its centre. The limiting problem is consequently not the eigenvalue problem with no patches, but a new type of spectral problem. The discrepancy between the eigenvalues of the patch-free and point constraint problems is calculated. The dependence of the point constraint eigenvalues on the location(s) of clamping is studied numerically using techniques from numerical algebraic geometry. The vibrational frequencies are found to depend very sensitively on the number and centre(s) of the clamped patches. For a range of number of punctures, we find spatial clamping patterns that correspond to local maxima of the base vibrational frequency of the plate.

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40

Fu, Yue Sheng, and Qing Ming Zhang. "Calculation of Dynamic Parameters of Elastic Thin Plates under Blast Loading." Key Engineering Materials 353-358 (September 2007): 2749–52. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.2749.

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Анотація:

With elastic theory and approximate calculation, the dynamic responses of elastic thin plates with four edges simply supported under blast loading is analyzed in this paper , with dimensional analysis , 30 cases are calculated, and a reasonable model of engineering calculation is built up in the end.

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41

Verdiere, Kevin, Simon Campeau, and Julien Biboud. "Characterizing elastic parameters of isotropic thin plates using impedance tube and transmission loss measurements: a numerical inverse method." INTER-NOISE and NOISE-CON Congress and Conference Proceedings 266, no. 1 (May 25, 2023): 1020–35. http://dx.doi.org/10.3397/nc_2023_0123.

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Анотація:

Thin plates are widely used in various engineering applications, including aerospace, automotive, and construction industries. The mechanical properties of these plates, such as Young's modulus, Poisson's ratio, and structural damping, are essential in determining their acoustic performance. While there are various methods for measuring these properties individually or simultaneously, accurately obtaining them can be difficult due to the thin plate's delicate structure and the need for high precision and sensitive equipment. In this paper, we present a numerical inverse method for characterizing the elastic parameters of isotropic thin plates using transmission loss measurements obtained from an impedance tube and clamped circular specimen. The proposed method is compared to the Oberst beam technique (ASTM E756-05), and demonstrated through several examples ultimately allowing for the prediction of diffused field transmission loss obtained through intensity measurements in a small reverberant room.

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42

Ru, C. Q. "Surface Instability of an Elastic Thin Film Interacting With a Suspended Elastic Plate." Journal of Applied Mechanics 69, no. 2 (October 5, 2001): 97–103. http://dx.doi.org/10.1115/1.1445146.

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Анотація:

This paper studies surface instability of a compliant elastic thin film on a rigid substrate interacting with a suspended elastic plate through van der Waals forces. The analysis is based on a novel method which permits a simple rational expression for the interaction coefficient as a function of the wave number of instability mode. The critical value of the interaction coefficient and the instability mode of the film-plate system can be determined easily by identifying the minimum of the interaction coefficient within an admissible range. When the stability strength of the plate is lower than the film even for the shortest plate-lengths, the interaction coefficient is found to be an increasing function of the wave number, and thus the film-plate system exhibits a long-wave instability mode determined by the suspended plate. In all other cases, the interaction coefficient admits an internal local minimum representing the short-wave mode of the film, and the critical value and instability mode of the film-plate system are determined by the internal local minimum for shorter plates, or by the long-wave mode of the plate for longer plates. Some numerical examples are given to illustrate the results.

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43

Licht, Christian, and Thibaut Weller. "Mathematical Modeling of Thin Multiphysical Structures." Advanced Materials Research 47-50 (June 2008): 483–85. http://dx.doi.org/10.4028/www.scientific.net/amr.47-50.483.

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Анотація:

Smart materials, which present significant multiphysical couplings, are now widely used for the conception of smart structures whose mathematical modelings are here presented in the case of thin plates or slender rods made of piezoelectric or electromagneto-elastic materials.

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44

Faraci, David, and Claudia Comi. "Asymptotic homogenization of metamaterials elastic plates." Journal of Physics: Conference Series 2015, no. 1 (November 1, 2021): 012038. http://dx.doi.org/10.1088/1742-6596/2015/1/012038.

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Анотація:

Abstract The asymptotic homogenization technique is applied to evaluate the effective properties of thin plates with periodic heterogeneity. The effect of shear deformation in the homogenization process is evidenced and the role of cell slenderness, besides that of the plate, is clarified by several numerical analyses.

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45

Mehrara, M., and Mohammad Javad Nategh. "Analytical-Numerical Solution of Bending Problem of Thin Plates in Rubber Pad Bending." Key Engineering Materials 473 (March 2011): 190–97. http://dx.doi.org/10.4028/www.scientific.net/kem.473.190.

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Анотація:

The bending of plates on rubber pad is a relatively new method used for roll bending of thin plates in recent years. In the present work the problem of plastic deformation of thin plates was analyzed. The governing differential equations for the plate’s elastic and plastic zones were derived. An analytical-numerical solution to these equations was subsequently presented. In addition, the equations were solved for a given problem and the effect of indentation depth of plate on its bending radius was investigated. A relationship has been proposed to correlate these parameters. This relationship is a powerful tool in controlling the process and process planning. This tool helps the operator set the indentation depth to a predefined amount in order that the plate to be bent by a given radius, without any try and error effort. The results were verified by experiment.

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46

Yanyutin, Yevgeniy Grigor'yevich, and Andrey Sergeevich Sharapata. "Impulse deformation of triangular plates based on the classical theory." Bulletin of Kharkov National Automobile and Highway University, no. 95 (December 16, 2021): 165. http://dx.doi.org/10.30977/bul.2219-5548.2021.95.0.165.

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Анотація:

This article discusses the impulse effects of various loads on triangular, isosceles, elastic, isotropic plates. Analytical solutions of the direct problem of determining the internal moments and deflections of the plate, as well as the numerical results of calculations of specific loading case are presented. Goal. The goal is to develop a method for solving direct problems of determining internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates. Methodology. To solve the direct problem, the Navier method, the classical theory of modeling vibrations of thin plates and the Laplace transform are used. Results. A technique has been obtained that allows one to obtain numerical and analytical dependences for calculating the internal moments and deflections in a triangular plate. Originality. For the first time, a technique was developed for solving direct non-stationary problems to determine the internal moments and deflections in rectangular triangular, isosceles, elastic, thin, isotropic plates based on the classical theory. Practical value. The obtained analytical dependences can be used to simulate impulse vibrations of square and isosceles rectangular triangular thin isotropic elastic plates, which can be critical structural elements.

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Aslanyan, N. S., and S. H. Sargsyan. "Mathematical model of thermoelasticity of micropolar orthotropic elastic thin plates." Mechanics - Proceedings of National Academy of Sciences of Armenia 66, no. 1 (2013): 34–47. http://dx.doi.org/10.33018/66.1.4.

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48

Sator, Ladislav, Vladimir Sladek, and Jan Sladek. "Vibration of thin elastic FGM plates with multi-gradation effects." Vibroengineering PROCEDIA 23 (April 25, 2019): 24–29. http://dx.doi.org/10.21595/vp.2019.20707.

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49

Felsen, L. B., and I. T. Lu. "Wave propagation on thin‐walled curved elastic plates with truncations." Journal of the Acoustical Society of America 84, S1 (November 1988): S147. http://dx.doi.org/10.1121/1.2025850.

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50

Jillella, Nagarjuna, and John Peddieson. "Elastic Stability of Annular Thin Plates with One Free Edge." Journal of Structures 2013 (September 26, 2013): 1–9. http://dx.doi.org/10.1155/2013/389148.

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Анотація:

The elastic stability of annular thin plates having one free edge and subjected to axisymmetric radial edge loads at the other edge is investigated. The supported edge is allowed to be either simply supported or clamped against axial (transverse) deflection. Both compression buckling and tension buckling (wrinkling) are investigated. To insure accuracy, two methods of solving the appropriate eigenvalue problems are used and found to yield essentially identical results. A selection of these results for both compression and tension buckling is presented graphically and used to illustrate interesting aspects of the solutions.

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