Approximate formulation of the rigid body motions of an elastic rectangle under sliding boundary conditions

• Autorzy: Şahin Önur , Erbaş Barış , Wilson Brent

Identyfikatory

DOI

10.2478/ama-2021-0012

• Języki publikacji: EN

Abstrakty

EN

Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle. The derived explicit approximate formulae are tested for different kinds of end loadings together with numerical examples demonstrating the comparison against the exact solutions.

Słowa kluczowe

EN

elastic rectangle; low frequency; rigid body motion; perturbation schemes; sliding boundary conditions

• Wydawca: Oficyna Wydawnicza Politechniki Białostockiej
• Czasopismo: Acta Mechanica et Automatica
• Rocznik: 2021
• Tom: Vol. 15, no. 2
• Strony: 82--90
• Opis fizyczny: Bibliogr. 21 poz., rys., wykr.

Twórcy

autor

Şahin Önur

• Department of Mathematics, Giresun University, Gaziler, Prof. Ahmet Taner Kışlalı Cd., 28200 Giresun Turkey

autor

Erbaş Barış

• Department of Mathematics, Eskişehir Technical University, 2 Eylül Kampüsü, 26555 Eskişehir, Turkey

autor

Wilson Brent

• HUM Industrial Technology, INC, 911 Washington Ave, Suite 501 St. Louis, Missouri, USA

Bibliografia

• 1. Babenkova E., Kaplunov J. (2004), Low-frequency decay conditions for a semi-infinite elastic strip. Proc. R. Soc. A., 460(2048), 2153-2169.
• 2. Babenkova Y.V., Kaplunov Y.D., Ustinov Y.A. (2005), Saintvenant's principle in the case of the low-frequency oscillations of a half-strip, Appl. Math. Mech., 69(3), 405-416.
• 3. Gregory R.D., Wan F.Y.M. (1985), On plate theories and SaintVenant's principle, International journal of solids and structures, 21(10), 1005-1024.
• 4. Kaplunov J., Prikazchikov D.A., Prikazchikova L.A., Sergushova O. (2019), The lowest vibration spectra of multi-component structures with contrast material properties, J. Sound Vib., 445, 132-147.
• 5. Kaplunov J., Prikazchikov D.A., Rogerson G.A. (2005), On threedimensional edge waves in semi-infinite isotropic plates subject to mixed face boundary conditions, The Journal of the Acoustical Society of America, 118 (5), 2975-2983.
• 6. Kaplunov J., Prikazchikova L., Alkinidri M. (2021), Antiplane shear of an asymmetric sandwich plate, Continuum Mechanics and Thermodynamics, 1-16.
• 7. Kaplunov J., Şahin O. (2020), Perturbed rigid body motions of an elastic rectangle, Z Angew Math Phys., 71(5), 1-15.
• 8. Kaplunov J., Shestakova A., Aleynikov I., Hopkins B., Talonov A. (2015), Low-frequency perturbations of rigid body motions of a viscoelastic inhomogeneous bar, Mechanics of Time-Dependent Materials, 19(2), 135-151.
• 9. Kudaibergenov A., Nobili A., Prikazchikova L.A. (2016), On lowfrequency vibrations of a composite string with contrast properties for energy scavenging fabric devices, Journal of Mechanics of Materials and Structures, 11 (3), 231-243.
• 10. Martin T.P., Layman C.N., Moore K.M., Orris G.J. (2012), Elastic shells with high-contrast material properties as acoustic metamaterial components, Physical Review B, 85 (16), 161103.
• 11. Milton G.W. and Willis J.R. (2007), On modifications of Newton's second law and linear continuum elastodynamics, Proc. R. Soc. A., 463 (2079), 855-880.
• 12. Prikazchikova L., Aydın Y.E., Erbaş B., Kaplunov J. (2020), Asymptotic analysis of an anti-plane dynamic problem for a threelayered strongly inhomogeneous laminate, Math. Mech. Solids, 25 (1), 3-16.
• 13. Qin Y., Wang X., Wang Z.L. (2008), Microfibre--nanowire hybrid structure for energy scavenging, Nature, 451 (7180), 809—813.
• 14. Şahin O. (2019), The effect of boundary conditions on the lowest vibration modes of strongly inhomogeneous beams, J. Mech. Mater. Struct., 14(4), 569-585.
• 15. Şahin O., Erbaş B., Kaplunov J., Savsek T. (2020), The lowest vibration modes of an elastic beam composed of alternating stiff and soft components, Arch. Appl. Mech., 90 (2), 339-352.
• 16. Srivastava A., Nemat-Nasser S. (2012), Overall dynamic properties of three-dimensional periodic elastic composites, Proc. R. Soc. A., 468 (2137), 269-287.
• 17. Vigak V.M., Tokovyi Y.V. (2002), Construction of elementary solutions to a plane elastic problem for a rectangular domain. International applied mechanics, 38(7), 829-836.
• 18. Viverge K., Boutin C., Sallet F. (2016), Model of highly contrasted plates ver- sus experiments on laminated glass, International Journal of Solids and Structures, 102, 238-258.
• 19. Wang X. (2014), Dynamic behaviour of a metamaterial system with negative mass and modulus, Int. J. Solids Struct., 51(7-8), 1534-1541.
• 20. Willis J.R. (1981), Variational and related methods for the overall properties of composites, In Advances in applied mechanics, (21), pp. 1-78, Elsevier.
• 21. Willis J.R. (1981), Variational principles for dynamic problems for inhomogeneous elastic media, Wave Motion, 3(1) 1-11.