• Advances in nano research
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• 제5권4호
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• pp.281-301
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• 2017

In this disquisition, an exact solution method is developed for analyzing the vibration characteristics of magneto-electro-elastic functionally graded (MEE-FG) beams by considering porosity distribution and various boundary conditions via a four-variable shear deformation refined beam theory for the first time. Magneto-electroelastic properties of porous FG beam are supposed to vary through the thickness direction and are modeled via modified power-law rule which is formulated using the concept of even and uneven porosity distributions. Porosities possibly occurring inside functionally graded materials (FGMs) during fabrication because of technical problem that lead to creation micro-voids in FG materials. So, it is necessary to consider the effect of porosities on the vibration behavior of MEE-FG beam in the present study. The governing differential equations and related boundary conditions of porous MEE-FG beam subjected to physical field are derived by Hamilton's principle based on a four-variable tangential-exponential refined theory which avoids the use of shear correction factor. An analytical solution procedure is used to achieve the natural frequencies of porous-FG beam supposed to magneto-electrical field which satisfies various boundary conditions. A parametric study is led to carry out the effects of material graduation exponent, porosity parameter, external magnetic potential, external electric voltage, slenderness ratio and various boundary conditions on dimensionless frequencies of porous MEE-FG beam. It is concluded that these parameters play noticeable roles on the vibration behavior of MEE-FG beam with porosities. Presented numerical results can be applied as benchmarks for future design of MEE-FG structures with porosity phases.

• Smart Structures and Systems
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• 제19권6호
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• pp.625-631
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• 2017

In the fields of civil engineering and seismology, it is essential to detect and tracking the vibrations, and the fiber Bragg gratings (FBGs) are typically used as sensors to measure vibrations. Where, one of the most popular and detailed approaches to use FBGs as vibration sensors involves the use of cantilever beam designs, which adds a mass to measure low and moderate frequencies (from 20 Hz up to 1 kHz) with high sensitivities (greater than 10 pm/g). The design consists of a bending strain in the cantilever that is simultaneously transferred to the FBG, resulting in a shift in the wavelength that is proportional to the strain experienced by the cantilever. In this work, we present the experimental results of a vibration sensor design using a cantilever beam to generate an axial uniform strain in the FBG in-line with the vertical axis, which modifies the cantilever's natural frequency that allows the sensor to have a wide frequency broadband without losing sensitivity. This sensor achieved a sensitivity of about 339 pm/g and a natural frequency of 227.3 Hz. The presented design compared with the traditional cantilever beam-based FBG vibration sensors, has the advantages of a simple design for detection on vibration-sensitive structures and its physical parameters can be easily modified in order to satisfy the requirements of the desired vibration measurements.

• Structural Engineering and Mechanics
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• 제82권1호
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• pp.41-53
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• 2022

We developed an accurate and simple vibration model to calculate the natural frequencies and their corresponding vibration modes for multi-span beam bridges with non-uniform cross-sections. A closed set of characteristic functions of a single-span beam was used to construct the vibration modes of the multi-span bridges, which were considered single-span beams with multiple constraints. To simplify the boundary conditions, the restraints were converted into spring constraints. Then the functional of the total energy has the same form as the penalty method. Compared to the conventional penalty method, the penalty coefficients in the proposed approach can be calculated directly, which can avoid the iteration process and convergence problem. The natural frequencies and corresponding vibration modes were obtained via the minimum total potential energy principle. By using the symmetry of the eigenfunctions or structure, the matrix size can be further reduced, which increases the computational efficiency of the proposed model. The accuracy and efficiency of the proposed approach were validated by the finite element method.

• Advances in aircraft and spacecraft science
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• 제3권4호
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• pp.379-397
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• 2016

In this manuscript, free vibrations of a unidirectional composite orthotropic Timoshenko beam based on finite strain have been studied. Using Green-Lagrange strain tensor and comprising all of the nonlinear terms of the tensor and also applying Hamilton's principle, equations of motion and boundary conditions of the beam are obtained. Using separation method in single-harmonic state, time and locative variables are separated from each other and finally, the equations of motion and boundary conditions are gained according to locative variable. To solve the equations, generalized differential quadrature method (GDQM) is applied and then, deflection and cross-section rotation of the beam in linear and nonlinear states are drawn and compared with each other. Also, frequencies of carbon/epoxy and glass/epoxy composite beams for different boundary conditions on the basis of the finite strain are calculated. The calculated frequencies of the nonlinear free vibration of the beam utilizing finite strain assumption for various geometries have been compared to von Karman one.

• 한국생산제조학회지
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• 제6권4호
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• pp.118-123
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• 1997

The study suggests a method to analyze the vibration of the multi-stepped beam having the different circular cross-sections. The rotatory inertia, the shear deformation and the torque applied at both ends of the beam are considered in the governing equation. The complex displacement and the variable separation are introduced to derive the solution of the equation of each uniform beam element having constant cross-section. Then boundary conditions are applied to solve the total system. This method uses the mathematically exact solutions unlike numerical method such as the finite element method in solving the problem having the simultaneous differential equations of Timoshenko beam theory. the natural frequencies and the corresponding mode shapes are precise, especially the mode shapes are continuous.

• International Journal of Precision Engineering and Manufacturing
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• 제4권1호
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• pp.15-22
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• 2003

Beams are often subject to bending-torsion coupled vibration due to mass coupling and/or stiffness coupling. This paper proposes a dynamic analysis method using the exact dynamic element for bending-torsion coupled vibration of general plane beam structures with joints. The exact dynamic element matrix for a bending-torsion coupled beam is derived, and the detailed procedure of using the exact dynamic element matrix is also presented. Three examples are provided for validating and illustrating the proposed method. The numerical study proves the proposed method to be useful for dynamic analysis of bending-torsion coupled beam structures with joints.

• Steel and Composite Structures
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• 제26권5호
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• pp.607-620
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• 2018

Vibration analysis of deep curved FG nano-beam has been carried out based on modified couple stress theory. Material properties of curved Timoshenko beam are assumed to be functionally graded in radial direction. Governing equations of motion and related boundary conditions have been obtained via Hamilton's principle. In a parametric study, influence of length scale parameter, aspect ratio, gradient index, opening angle, mode number and interactive influences of these parameters on natural frequency of the beam, have been investigated. It was found that, considering geometrical deepness term leads to an increase in sensitivity of natural frequency about variation of aforementioned parameters.

• 한국소음진동공학회논문집
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• 제17권10호
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• pp.936-945
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• 2007

We studied the influences of open cracks in free vibrating beam with rectangular section using a numerical model. The crack was assumed to be single and always open during the free vibration and equivalent bending stiffness of a cracked beam was calculated based on the strain energy balance. By Galerkin's method, the frequencies of cantilever beam could be obtained with respect to various crack depths and locations. Also, the experiments on the cracked beams were carried out to find natural frequencies. The cracks were initiated at five locations and the crack depths were increased by five steps at each location. The experimental results were compared with the numerical results and the comparison results were discussed.

• Structural Engineering and Mechanics
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• 제42권1호
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• pp.13-24
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• 2012

There are a large number of papers in the literature dealing with the free vibration analysis of single/multi-span uniform beam with multiple spring-mass systems, but that of coupled multi-span beams carrying spring-mass attachments is rare. In this note, free vibration analysis of a weakly coupled beam system with spring-mass attachments is conducted. The mode localization and frequency loci veering phenomena of the coupled beam system are investigated. Studies show that for weakly coupled beam system with spring-mass attachments, the mode localization and frequency loci veering will occur once there is a disorder in the system.

• Structural Engineering and Mechanics
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• 제43권1호
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• pp.15-30
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• 2012

A damped Timoshenko beam element is introduced for the DOF-efficient forced vibration analysis of beam-like structures coated with viscoelastic damping layers. The rotary inertia as well as the shear deformation is considered, and the damping effect of viscoelastic layers is modeled as an imaginary loss factor in the complex shear modulus. A complex composite cross-section of structures is replaced with a homogeneous one by means of the transformed section approach in order to construct an equivalent single-layer finite element model capable of employing the standard $C^{0}$-continuity basis functions. The numerical reliability and the DOF-efficiency are explored through the comparative numerical experiments.