Forced vibration of multi-span cracked Euler–Bernoulli beams using dynamic Green function formulation

Ghannadiasl, Amin; Ajirlou, Saeid Khodapanah

doi:10.1016/j.apacoust.2018.12.021

Cited by 19 publications

(5 citation statements)

References 31 publications

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“…A typical homogeneous solution 'u a,H (x a , ω)' to Equation (A4) comprises a linear combination of the hyperbolic and trigonometric functions. A nonhomogeneous solution 'u a,NH (x a , ω)' to Equation (A4) can be expressed using Green's function [49,50]. Equation (A4) represents the introduction of two spatially concentrated bending moments in the opposite direction but with the same magnitude as κ P v(ω).…”

Section: Conflicts Of Interestmentioning

confidence: 99%

Defect-Band Splitting of a One-Dimensional Phononic Crystal with Double Defects for Bending-Wave Excitation

Jo,

Lee,

Youn

2023

Mathematics

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Extensive prior research has delved into the localization of elastic wave energy through defect modes within phononic crystals (PnCs). The amalgamation of defective PnCs with piezoelectric materials has opened new avenues for conceptual innovations catering to energy harvesters, wave filters, and ultrasonic receivers. A recent departure from this conventional paradigm involves designing an ultrasonic actuator that excites elastic waves. However, previous efforts have mostly focused on single-defect scenarios for bending-wave excitation. To push the boundaries, this research takes a step forward by extending PnC design to include double piezoelectric defects. This advancement allows ultrasonic actuators to effectively operate across multiple frequencies. An analytical model originally developed for a single-defect situation via Euler–Bernoulli beam theory is adapted to fit within the framework of a double-defect set-up, predicting wave-excitation performance. Furthermore, a comprehensive study is executed to analyze how changes in input voltage configurations impact the output responses. The ultimate goal is to create ultrasonic transducers that could have practical applications in nondestructive testing for monitoring structural health and in ultrasonic imaging for medical purposes.

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Section: Conflicts Of Interestmentioning

confidence: 99%

Defect-Band Splitting of a One-Dimensional Phononic Crystal with Double Defects for Bending-Wave Excitation

Jo,

Lee,

Youn

2023

Mathematics

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“…A crack creates a discontinuity on the slope of the beam at the crack position. It can be expressed as [15,[21][22][23]:…”

Section: Cracked Beamsmentioning

confidence: 99%

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Hossain¹,

Lellep²

2022

Eng. Res. Express

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In the study, the Maclaurin series technique is presented to analyse the vibration of cracked tapered double nanobeams. The equation of motion is derived from the Euler-Bernoulli beam theory based on the Hamiltonian principle and Eringen's nonlocal theory of elasticity. The double-nanobeam system consists of two parallel nanobeams attached by a Winkler elastic layer. Both beams are identical and their widths vary along the x-axis. A single crack is considered at the upper beam of the system. The mechanical behaviour of cracked cross-sections is simulated by the local stiffness model. According to the model, the cracked double-beam system is divided into two intact segments. A numerical investigation is carried out to scrutinize the effects of nonlocal parameters, crack severity, taper ratio, and spring constant on the vibration of the double nanobeam. The results reveal that the effects of crack depth, crack location, nonlocal parameters, taper ratio, and spring constant influence the natural frequency and dynamic response of the system significantly. This study highlights that a crack at the upper beam influences the mode shape of the upper beam as well as the intact lower beam. Numerical results have been examined with the previously published works and found a good agreement with them.

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“…Ghannadiasl and Ajirlou [21] investigated the dynamics of damped structure under a transit mass using Green function method. In another paper of Ghannadiasl and Ajirlou [22] the solution has been given analitically with the help of dynamic Green function. The response of damaged structure under concentrated mass has been obtained and the numerical results have been validated with experimental tests.…”

Section: Introductionmentioning

confidence: 99%

Experimental and computational study on dynamic analysis of cracked simply supported structures under moving mass

Jena¹,

Bulut

Kurt

2022

Frattura Ed Integrità Strutturale

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In this study, the influences of crack parameters like crack location from the left end, crack height, number of cracks and the magnitude of mass and the velocity of the transit load on the vertical displacements of the cracked simply supported beams subjected to transit mass are investigated. The transverse open cracks with numerous damage scenerios are considered for the mathematical modelling of the system. The governing equations of motion for the system have been obtained and the equations have been solved by the help of Duhamel integral technique. The theoretical formulation has been exemplified with numerical studies. By utilizing ANSYS Workbench 2020, transient structural analysis has been carried out. The mode shapes and the frequency ratios of damaged simply supported beam have also been determined. To validate the numerical and FEM models, the experiments with damaged beams have been carried out in the laboratory. It has been proven that the results of the theoretical and FEM models are well convergent with the experimental data. The results gathered from the numerical analysis, FEA as well as experimental study have been presented with comparative graphs and tables. The outcomes of the examinations have been interpreted in the conclusions part. It has been observed that subject parameters are of considerable significance on the time dependent response of the cracked beams.

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Forced vibration of multi-span cracked Euler–Bernoulli beams using dynamic Green function formulation

Cited by 19 publications

References 31 publications

Defect-Band Splitting of a One-Dimensional Phononic Crystal with Double Defects for Bending-Wave Excitation

Defect-Band Splitting of a One-Dimensional Phononic Crystal with Double Defects for Bending-Wave Excitation

Analysis of free vibration of tapered cracked double nanobeams using Maclaurin series

Experimental and computational study on dynamic analysis of cracked simply supported structures under moving mass

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