Jordan Journal of Civil Engineering

Paper Detail

Analysis of geometrically non-linear free in-plane vibration of a circular arch with damages

Volume 16, No. 4, 2022
Received: 2022/03/12, Accepted: 2022/06/27


omar outassafte; Yassine El khouddar Yassine El khouddar;


The geometrically nonlinear vibration problems in the plane vibration of a circular arch with damages are studied in this paper. Due to damages, which can occur inside structures as a result of various factors or during fabrication, it is necessary to examine the vibration behavior of curved beams in this study. Indeed, the damage is modeled by a rotational elastic spring connecting two adjacent sections of the arch. The theoretical formulation is constructed on the basis of the geometric nonlinearity of von K�rm�n and the Euler-Bernoulli beam theory. Based on Hamilton's principle, the nonlinear equilibrium equations are determined by solving the linear problem. An approximate method called the second formulation is used to numerically solve the nonlinear algebraic system of the free nonlinear vibrational response. The effects of varying the position, damage intensity, and the number of damages on the linear and nonlinear dynamic behavior of the arch are presented and discussed in detail


Geometrically nonlinear vibration, damages, rotational elastic spring, Hamilton principle, second formation