Free vibration analysis of two parallel beams connected together through variable stiffness elastic layer with elastically restrained ends

Abstract

In this study, free transverse vibration of two parallel beams connected together through variable stiffness Winkler-type elastic layer is investigated. Euler–Bernoulli beam hypothesis has been applied and the support is considered to be translational and rotational elastic springs in each ends. Linear and parabolic variation has been considered for connecting layer. The equations of motion have been derived in the form of coupled differential equations with variable coefficients. The differential transform method has been applied to obtain natural frequencies and normalized mode shapes of system. Differential transform method is a semi-analytical approach based on Taylor expansion series which converts differential equations to recursive algebraic equations and does not need domain discretization. The results obtained from differential transform method have been validated with the results reported by well-known references in the case of two parallel beams connected through uniform elastic layer. The effects of variation type and total stiffness of connecting layer, flexural rigidity ratio of beams, and boundary conditions on behavior of system are investigated and discussed in detail.

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

“…External excitation is considered in Eq. (18), and damage is shown to be reducing the sti ness of the beams' elements or the destruction of the core elements. In this case, the design variables of the optimization process are four, of which two variables are related to damage location and the other two correspond to the severity of damages.…”

“…The rst excitation frequency, Excitation (1), is lower than the rst natural frequency of the system as in Eq. (18). The second excitation frequency, Excitation (2), is close to the rst and second natural frequencies of the system and is considered as follows: F = 2000 sin(40 t):…”

“…The external excitation is considered in Eq. (18). According to the obtained results of the previous sections, the optimization algorithm is terminated after 300 iterations, and its output considered is as damage.…”

Influence of a Moving Mass on the Dynamic Behaviour of Viscoelastically Connected Prismatic Double-Rayleigh Beam System Having Arbitrary End Supports

“…Equations. In this subsection, we seek to simplify the coupled transformed second-order ordinary differential equations (16). To this end, a system consisting of two unconnected Rayleigh beams is, in the time being, considered.…”

“…As a third example, it is remarked that the coupled behaviour of paper translating with the paper cloth (wire screen) during paper making process is usually studied by modeling the system as two axially translating tensioned beams interconnected by an elastic foundation. Some other significant applications of double-beam system are in (i) passive vibration control, (ii) weight reduction, and (iii) strength and stiffness increase [15,16]. It is, nevertheless, observed from literature that, unlike the single-beam system, relatively few works have been carried out for the non-single-beam system carrying moving loads.…”