Substructural Method for Vibration Analysis of the Elastically Connected Double-Beam System

Advances in Structural Engineering

Vahabi

2016

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.

Section: Numerical Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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

Advances in Structural Engineering

Vahabi

2016

“…Finite element solution using conventional two node elements has been developed to approve accuracy of DTM. In this way, each beam discritized by 100 elements and mass and stiffness matrices calculated as same as Huang and Liu 9 except the elastic layer matrix due to discontinuity. Results show accuracy and rapid convergence of DTM.…”

Section: Numerical Resultsmentioning

confidence: 99%

“…The proposed technique is capable to describe rate-dependent behavior of viscoelastic materials; furthermore, results show faster convergence of the proposed technique rather than a classical finite element method. Huang and Liu 9 analyzed free and forced vibration of a double beam system by using a substructural method. In this study, the forced vibration responses were obtained from Newmark direct integration and the effects of local damages on dynamic response were investigated.…”

Section: Introductionmentioning

confidence: 99%

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

Proceedings of the Institution of Mechanical Engineers, Part C:

2016

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.

“…By applying energy criterion in Eq. 15, the dominant POM of the structure before and after damage occurrence is determined, and the following damage indicator is used: P OM(i) = P OM u (i) P OM d (i); i = 1; 2; :::; M; (16) where P OM u (i) is the dominant proper orthogonal mode before a damage or undamaged case at the ith measurement point, and P OM d (i) is the dominant proper orthogonal mode after damage at the same point. Damage location is revealed by an abrupt change in the graph of P OM.…”

Section: The Proper Orthogonal Decomposition (Pod)mentioning

confidence: 99%

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

2019

Scientia Iranica

This study applies the inverse approach to damage detection in a doublebeam system. A double-beam system made of two parallel beams is connected through an elastic layer. Degradation of the sti ness of beams element, crack occurrence, and partial destruction of the inner layer are considered as di erent types of damage. The time domain acceleration response of the system is measured, and proper orthogonal decomposition is applied to the collected data in order to derive Proper Orthogonal Values (POVs) and Proper Orthogonal Modes (POMs) of the system. E ect of single damage in di erent locations on the POV has been analyzed, and an objective function is de ned using the dominant POV and POM of each beam separately. In order to increase the robustness of the method against noise, the objective function is enriched by adding statistical property of time domain response. The teaching-learning based optimization algorithm is employed to solve the optimization problem. The e ciency of the proposed method for detecting single and multiple damages in the system is demonstrated with and without noise. Simulation results verify the good accuracy of the proposed method for detecting single and multiple damages of di erent types in the system.