Simultaneous determination of an unknown bending moment and shear force in the Euler–Bernoulli cantilever beam from measured boundary deflection and slope
Year: 2026
Type: article
Abstract: It is known that the study of vibration characteristics at the tip of the micro-cantilever and its relationship to the sample plays a very important role in improving the resolution of atomic force microscopy (AFM). In this paper, within the Euler–Bernoulli beam structure, a mathematical model, defined as a model with two unknown inputs and two measured outputs , is considered for the simultaneous determination of the unknown bending moment and the shear force at the tip of the micro-cantilever from two feasible measured outputs at the same tip: the deflection and the slope. This model leads to the following inverse problem: find M ( t ) {M(t)} and g ( t ) {g(t)} in ρ A ( x ) u t t + μ ( x ) u t + ( r ( x ) u x x ) x x = 0 {\rho_{A}(x)u_{tt}+\mu(x)u_{t}+(r(x)u_{xx})_{xx}=0} , ( x , t ) ∈ Ω T := ( 0 , ℓ ) × ( 0 , T ) {(x,t)\in\Omega_{T}:=(0,\ell)\times(0,T)} subject to the boundary conditions u ( 0 , t ) = u x ( 0
Authors: Alemdar Hasanov, Onur Baysal
Institutions: Kocaeli Üniversitesi, University of Malta
Language: English
Subfield: Control and Systems Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,712
OpenAlex ID: W7165201065