Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/inverse-problem-of-determining-an-unknown-coefficient-in-the-beam-hOMj8BiMKg
References (26)
-
D. Durdiev (1994)
A multidimensional inverse problem for an equation with memorySiberian Mathematical Journal, 35
-
(2015)
Initial-boundary value problem for the beam vibration equation, in Matematicheskie metody i modeli v stroitel'stve, arkhitekture i dizaine (Mathematical Methods and Models in Construction -
(1984)
Obratnye zadachi matematicheskoi fiziki (Inverse Problems of Mathematical Physics) -
Yi-Ren Wang, Zhi-Wei Fang (2015)
Vibrations in an elastic beam with nonlinear supports at both endsJournal of Applied Mechanics and Technical Physics, 56
-
K. Sabitov, A. Akimov (2020)
Initial–Boundary Value Problem for a Nonlinear Beam Vibration EquationDifferential Equations, 56
-
Suzhen Li, E. Reynders, K. Maes, G. Roeck (2013)
Vibration-based estimation of axial force for a beam member with uncertain boundary conditionsJournal of Sound and Vibration, 332
-
K. Sabitov (2020)
Inverse Problems of Determining the Right-Hand Side and the Initial Conditions for the Beam Vibration EquationDifferential Equations, 56
-
A. Karchevsky (2017)
Determination of the possibility of rock burst in a coal seamJournal of Applied and Industrial Mathematics, 11
-
(2012)
Vibratsiya sudov (Vibration of Ships) -
K. Sabitov (2020)
Inverse Problems of Determining the Right-Hand Side and the Initial Conditions for the Beam Vibration EquationDifferential Equations, 56
-
D. Durdiev, Z. Totieva (2017)
The problem of determining the one-dimensional kernel of the electroviscoelasticity equationSiberian Mathematical Journal, 58
-
(2014)
Obratnye zadachi dlya sred s posledeistviem (Inverse Problems for Media with Aftereffect), Tashkent: Turon-Ikbol -
A. Karchevsky (2020)
Analytical Solutions to the Differential Equation of Transverse Vibrations of a Piecewise Homogeneous Beam in the Frequency Domain for the Boundary Conditions of Various TypesJournal of Applied and Industrial Mathematics, 14
-
U. Durdiev (2019)
A PROBLEM OF IDENTIFICATION OF A SPECIAL 2D MEMORY KERNEL IN AN INTEGRO–DIFFERENTIAL HYPERBOLIC EQUATIONEurasian Journal of Mathematical and Computer Applications
-
K. Sabitov (2017)
A remark on the theory of initial-boundary value problems for the equation of rods and beamsDifferential Equations, 53
-
K.B. Sabitov, O.V. Fadeeva (2021)
Initial–boundary value problem for the equation of forced vibrations of a cantilevered beamVestn. Samarsk. Gos. Tekh. Univ. Ser. Fiz.-Mat. Nauki, 25
-
Numerical determination of the dependence of the permittivity of a layered medium on the time frequency -
Shakirbai Kasimov, U. Madrakhimov (2019)
Initial-Boundary Value Problem for the Beam Vibration Equation in the Multidimensional CaseDifferential Equations, 55
-
U. Durdiev, Z. Totieva (2019)
A problem of determining a special spatial part of 3D memory kernel in an integro‐differential hyperbolic equationMathematical Methods in the Applied Sciences, 42
-
K.B. Sabitov (2015)
Initial–boundary value problem for the beam vibration equationMatematicheskie metody i modeli v stroitel’stve, arkhitekture i dizaine (Mathematical Methods and Models in Construction, Architecture, and Design)
-
(2001)
Numerical solution of the inverse problem for an elasticity system with aftereffect for a vertically inhomogeneous medium -
(1975)
Integral’nye uravneniya. Vvedenie v teoriyu (Integral Equations. Introduction to the Theory) -
D. Durdiev, A. Rakhmonov (2020)
The Problem of Determining the 2D Kernel in a System of Integro-Differential Equations of a Viscoelastic Porous MediumJournal of Applied and Industrial Mathematics, 14
-
U. Durdiev (2019)
An Inverse Problem for the System of Viscoelasticity Equations in Homogeneous Anisotropic MediaJournal of Applied and Industrial Mathematics, 13
-
K. Sabitov (2017)
Cauchy problem for the beam vibration equationDifferential Equations, 53
-
(2002)
Funktsional’nyi analiz (Functional Analysis), Moscow: Izd
- Publisher
- Springer Journals
- Copyright
- Copyright © Pleiades Publishing, Ltd. 2022
- ISSN
- 0012-2661
- eISSN
- 1608-3083
- DOI
- 10.1134/s0012266122010050
- Publisher site
- See Article on Publisher Site
Abstract
We consider the direct initial–boundary value problem for the equation of transversevibrations of a homogeneous beam freely supported at the ends and study the inverse problem ofdetermining the time-dependent beam stiffness coefficient. With the help of the eigenvalues andeigenfunctions of the beam vibration operator, the problems are reduced to integral equations.The Schauder contraction principle is applied to these equations, and theorems on the existenceand uniqueness of solutions are proved.
Journal
Differential Equations – Springer Journals
Published: Jan 1, 2022