Asymptotic behavior of the eigenfrequencies of a thin elastic rod with non-uniform cross-section of extremely oblate shape

[1]  S. Nazarov,et al.  Asymptotic analysis of an elastic rod with rounded ends , 2020, Mathematical Methods in the Applied Sciences.

[2]  Albert Y. Zomaya,et al.  Partial Differential Equations , 2007, Explorations in Numerical Analysis.

[3]  S. Nazarov,et al.  Korn inequality for a thin rod with rounded ends , 2014 .

[4]  Georges Griso,et al.  ASYMPTOTIC BEHAVIOR OF STRUCTURES MADE OF CURVED RODS , 2011, 1109.1907.

[5]  S. Nazarov.  Uniform Estimates of Remainders in Asymptotic Expansions of Solutions to the Problem on Eigenoscillations of a Piezoelectric Plate , 2003 .

[6]  J. Tambača.  One‐dimensional approximations of the eigenvalue problem of curved rods , 2001 .

[7]  J. M. Viaño,et al.  Asymptotic modelling of a nonsymmetric beam , 2000 .

[8]  J. M. Viaño,et al.  Mathematical justification of stretching and torsional vibration models for elastic rods , 2000 .

[9]  V. Maz'ya,et al.  Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains: Volume I , 2000 .

[10]  J. M. Viaño,et al.  Asymptotic analysis of torsional and stretching modes of thin rods , 2000 .

[11]  S. Nazarov,et al.  One-dimensional equations of deformation of thin slightly curved rods. Asymptotical analysis and justification , 2000 .

[12]  S. Nazarov.  Justification of the asymptotic theory of thin rods. Integral and pointwise estimates , 1999 .

[13]  J. M. Viaño,et al.  SECOND-ORDER ASYMPTOTIC APPROXIMATION OF FLEXURAL VIBRATIONS IN ELASTIC RODS , 1998 .

[14]  N. Kerdid,et al.  Analyse asymptotique des modes de hautes fréquences dans les poutres minces , 1998 .

[15]  Philippe G. Ciarlet,et al.  Two-dimensional approximations of three-dimensional eigenvalue problems in plate theory , 1981 .

[16]  S. Jimbo,et al.  Asymptotic behavior of eigenfrequencies of a thin elastic rod with non-uniform cross-section , 2020 .

[17]  S. Nazarov.  Estimating the convergence rate for eigenfrequencies of anisotropic plates with variable thickness , 2002 .

[18]  J. M. Viaño,et al.  Mathematical model for elastic beams with longitudinally variable depth , 2001 .

[19]  N. Kerdid.  Modélisation des vibrations d'une multi-structure formée de deux poutres , 1995 .

[20]  N. Kerdid.  Comportement asymptotique quand l'épaisseur tend vers zéro du problème de valeurs propres pour une poutre mince encastrée en élasticité linéaire , 1993 .

[21]  C. DeWitt-Morette,et al.  Mathematical Analysis and Numerical Methods for Science and Technology , 1990 .

[22]  B. A. Shoikhet.  On asymptotically exact equations of thin plates of complex structure: PMM vol. 37, n≗5, 1973, pp. 914–924 , 1973 .

[23]  Dietrich Morgenstern,et al.  Herleitung der plattentbeorie aus der dreidimensionalen elastizitätstheorie , 1959 .