We present a new mathematical model and method for identifying the unknown flexural rigidity [Formula: see text] in the damped Euler-Bernoulli beam equation [Formula: see text] [Formula: see text], subject to the simply supported boundary conditions [Formula: see text], [Formula: see text], from the available measured boundary rotation [Formula: see text]. We prove the existence of a quasi-solution and derive an explicit gradient formula for the Fréchet derivative of the Tikhonov functional [Formula: see text]. The results obtained here also form the basis of gradient-based computational methods for solving this class of inverse coefficient problems. This article is part of the theme issue 'Non-smooth variational problems and applications'.
Keywords: Fréchet differentiability; damped Euler–Bernoulli beam; existence of a quasi-solution; gradient formula; inverse coefficient problem; measured boundary rotation.