Free vibration analysis of partially connected parallel beams with elastically restrained ends

Abstract

In the present paper, the problem of transverse free vibration of two parallel beams partially connected to each other by a Winkler-type elastic layer is investigated. Euler–Bernoulli beam hypothesis has been applied, and translational and rotational elastic springs in each end considered as support. The motion of the system is described by coupled, piece-wise differential equations. The differential transform method (DTM) is employed to derive natural frequencies and mode shapes. DTM is a semi-analytical approach based on Taylor expansion series which does not require any admissible functions and yields rapid convergence and computational stability. After validation of the DTM results with results reported by well-known references and finite elements solution, the influences of the inner layer connection length, boundary conditions, the coefficient of elastic inner layer and ratio of beam’s flexural rigidity on natural frequencies as well as influences of the inner layer connection length on mode shapes are discussed. This problem is treated for the first time, and results are completely new which candidate them to being considered for practical engineering applications.

Damage detection in a double-beam system using proper orthogonal decomposition and teaching-learning based algorithm

“…According to the results of Ref. [19], a partial removal of the elastic layer was considered as damage at the core did not a ect the odd mode frequencies of the system; consequently, through the usual methods of modal parameters, detecting the core damage is not easily possible and, so far, no research has been done in this area, while damage at the core is detected by the current method, even in the presence of excessive noise; 5. The accuracy of the method in the presence of noise depends on the location of the damage.…”

“…In fact, their study deals with the e ect of damage in the inner elastic layer on natural frequencies and mode shapes. Results in [19] showed that for similar boundary conditions of upper and lower beams, damage to the core did not a ect odd mode frequencies. Nguyen [20] addressed the e ect of crack on the double-beam system by applying Finite Elements (FE) method.…”

“…In these studies, the beams and core remained intact, and e ects of damage were neglected. Mirzabeigy and Madoliat [19] investigated the free vibration of the partially connected double-beam system. In fact, their study deals with the e ect of damage in the inner elastic layer on natural frequencies and mode shapes.…”

Explicit formula to estimate natural frequencies of a double-beam system with crack

“…In fact, their study deals with effect of damage in the inner elastic layer on natural frequencies and mode shapes. Results of [29] show that for similar boundary conditions of upper and lower beams, damage in core does not affect odd mode frequencies. Nguyen [30] addressed effect of crack on double beam system by using finite elements method and used results to crack detection.…”

“…In these researches, the beams and core are intact and effects of damage are neglected. Mirzabeigy and Madoliat [29] investigate the free vibration of the partially connected double-beam system. In fact, their study deals with effect of damage in the inner elastic layer on natural frequencies and mode shapes.…”