• Proceedings of the Korean Society For Composite Materials Conference
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• 1999.11a
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• pp.5-14
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• 1999

Free vibration characteristics of a cantilevered laminated composite beam with multiple non-propagating transverse open cracks are investigated. In the present analysis a special ply-angle distribution referred to as asymmetric stiffness configuration inducing the elastic coupling between chord-wise bending and extension is considered. The multiple open cracks are modelled as equivalent rotational springs whose spring constants are calculated based on the fracture mechanics of composite material structures. Governing equations of a composite beam with open cracks are derived via Hamilton's Principle and Timoshenko beam theory encompassing transverse shear and rotary inertia effect is adopted. The effects of various parameters such as the ply angle, fiber volume fraction, crack numbers, crack positions and crack depthes on the free vibration characteristics of the beam with multiple cracks are highlighted. The numerical results show that the existence of the multiple cracks in an anisotropic composite beam affects the free vibration characteristics in a more complex fashion compared with the beam with a single crack.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.161-169
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• 2017

In this paper, using consistent couple stress theory and Hamilton's principle, the free vibration analysis of Euler-Bernoulli nano-beams made of bi-directional functionally graded materials (BDFGMs) with small scale effects are investigated. To the best of the researchers' knowledge, in the literature, there is no study carried out into consistent couple-stress theory for free vibration analysis of BDFGM nanostructures with arbitrary functions. In addition, in order to obtain small scale effects, the consistent couple-stress theory is also applied. These models can degenerate into the classical models if the material length scale parameter is taken to be zero. In this theory, the couple-tensor is skew-symmetric by adopting the skew-symmetric part of the rotation gradients as the curvature tensor. The material properties except Poisson's ratio are assumed to be graded in both axial and thickness directions, which it can vary according to an arbitrary function. The governing equations are obtained using the concept of Hamilton principle. Generalized differential quadrature method (GDQM) is used to solve the governing equations for various boundary conditions to obtain the natural frequencies of BDFG nano-beam. At the end, some numerical results are presented to study the effects of material length scale parameter, and inhomogeneity constant on natural frequency.

• Steel and Composite Structures
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• v.26 no.3
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• pp.273-287
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• 2018

Buckling and free vibration analysis of sandwich micro plate (SMP) integrated with piezoelectric layers embedded in orthotropic Pasternak are investigated in this paper. The refined Zigzag theory (RZT) is taken into consideration to model the SMP. Four different types of functionally graded (FG) distribution through the thickness of the SMP core layer which is reinforced with single-wall carbon nanotubes (SWCNTs) are considered. The modified couple stress theory (MCST) is employed to capture the effects of small scale effects. The sandwich structure is exposed to a two dimensional magnetic field and also, piezoelectric layers are subjected to external applied voltages. In order to obtain governing equation, energy method as well as Hamilton's principle is applied. Based on an analytical solution the critical buckling loads and natural frequency are obtained. The effects of volume fraction of carbon nanotubes (CNTs), different distributions of CNTs, foundation stiffness parameters, magnetic and electric fields, small scale parameter and the thickness of piezoelectric layers on the both critical buckling loads and natural frequency of the SMP are examined. The obtained results demonstrate that the effects of volume fraction of CNTs play an important role in analyzing buckling and free vibration behavior of the SMP. Furthermore, the effects of magnetic and electric fields are remarkable on the mechanical responses of the system and cannot be neglected.

• Journal of Power System Engineering
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• v.19 no.6
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• pp.60-67
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• 2015

While designing and operating machines, it is very important to understand the dynamic characteristic of the machines. Authors developed the Sylvester-transfer stiffness coefficient method in order to analyze effectively the free vibration of machines or structures. The Sylvester-transfer stiffness coefficient method was derived from the combination of the Sylvester's inertia theorem and the transfer stiffness coefficient method. In this paper, the authors formulate the computational algorithm for flexural free vibration analysis of axisymmetric annular plate using the Sylvester-transfer stiffness coefficient method. To confirm the usefulness of the Sylvester-transfer stiffness coefficient method, the natural frequencies and modes for two computational models computed using the Sylvester-transfer stiffness coefficient method are compared with those computed using the exact solution and the finite element method.

• Journal of Korean Society of Steel Construction
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• v.13 no.6
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• pp.651-659
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• 2001

The main purpose of this paper is to present an analytical method for free vibration of stepped horizontally curved members on two-parameter elastic foundation. The ordinary differential equations governing the free vibration of such beams are derived as non-dimensional forms including the effects of rotatory inertia and shear deformation. The governing equations are solved numerically for the circular, parabolic, sinusoidal and elliptic curved beams with hinged-hinged, hinged-clamped and clamped-clamped end constraints. As the numerical results, the lowest four natural frequency parameters are presented as the functions of various non-dimensional system parameters. Also the typical mode shapes are presented.

• Structural Engineering and Mechanics
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• v.58 no.5
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• pp.847-868
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• 2016

In this study, the free vibration analysis of axially moving beams is investigated according to Reddy-Bickford beam theory (RBT) by using dynamic stiffness method (DSM) and differential transform method (DTM). First of all, the governing differential equations of motion in free vibration are derived by using Hamilton's principle. The nondimensionalised multiplication factors for axial speed and axial tensile force are used to investigate their effects on natural frequencies. The natural frequencies are calculated by solving differential equations using analytical method (ANM). After the ANM solution, the governing equations of motion of axially moving Reddy-Bickford beams are solved by using DTM which is based on Finite Taylor Series. Besides DTM, DSM is used to obtain natural frequencies of moving Reddy-Bickford beams. DSM solution is performed via Wittrick-Williams algorithm. For different boundary conditions, the first three natural frequencies that calculated by using DTM and DSM are tabulated in tables and are compared with the results of ANM where a very good proximity is observed. The first three mode shapes and normalised bending moment diagrams are presented in figures.

• Structural Engineering and Mechanics
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• v.42 no.3
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• pp.409-424
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• 2012

Since relatively low elasticity modulus of the FRP materials results in lower natural frequencies, it is necessary to study the free vibration of FRP transmission poles. In this paper, the free vibration of tapered FRP transmission poles with thin-walled circular cross-section is investigated by a tapered beam element. To model the flexible joints of the modular poles, a rotational spring model is used. Modal analysis is performed for typical FRP poles with/without joint and they are also modeled by ANSYS commercial finite element software. There is a good correlation between the results of the tapered beam finite element model and those obtained from ANSYS as well as the existing experimental results. The effects of different geometries, material lay-ups, concentrated masses at the pole tip, and joint flexibilities are evaluated. Moreover, it is concluded that using tougher fibres at the inner and outer layers of the cross-section, results in higher natural frequencies, significantly.

• Structural Engineering and Mechanics
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• v.19 no.5
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• pp.477-501
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• 2005

In this study, a new smart beam finite element is proposed for the finite element modeling of beam-type smart structures that are equipped with bonded plate-type piezoelectric sensors and actuators. Constitutive equations for the direct piezoelectric effect and converse piezoelectric effect of piezoelectric materials are considered in the formulation. By using a variational principle, the equations of motion for the smart beam finite element are derived. The proposed 2-node beam finite element is an isoparametric element based on Timoshenko beam theory. The proposed smart beam finite element is applied to the free vibration control adopting a constant gain feedback scheme. The electrical force vector, which is obtained in deriving an equation of motion, is the control force equivalent to that in existing literature. Validity of the proposed element is shown through comparing the analytical results of the verification examples with those of other previous researchers. With the use of smart beam finite elements, simulation of free vibration control is demonstrated by sensing the voltage of the piezoelectric sensors and by applying the voltages to the piezoelectric actuators.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.719-742
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• 2015

This paper dealt the free vibration analysis of thick truncated conical composite sandwich shells with transversely flexible cores and simply supported boundary conditions based on a new improved and enhanced higher order sandwich shell theory. Geometries were used in the present work for the consideration of different radii curvatures of the face sheets and the core was unique. The coupled governing partial differential equations were derived by the Hamilton's principle. The in-plane circumferential and axial stresses of the core were considered in the new enhanced model. The first order shear deformation theory was used for the inner and outer composite face sheets and for the core, a polynomial description of the displacement fields was assumed based on the second Frostig's model. The effects of types of boundary conditions, conical angles, length to radius ratio, core to shell thickness ratio and core radius to shell thickness ratio on the free vibration analysis of truncated conical composite sandwich shells were also studied. Numerical results are presented and compared with the latest results found in literature. Also, the results were validated with those derived by ABAQUS FE code.

• The Journal of the Convergence on Culture Technology
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• v.5 no.3
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• pp.305-310
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• 2019

This paper proposes the method of exactly identifying both viscous and friction damping from free vibration response to SDOF structure. Both displacement and acceleration free vibration responses to SDOF system, in which both viscous and friction damping are considered as its damping mechanism, are discussed to verify the proposed method. The relationship for identifying both viscous and friction damping is derived from two consecutive amplitudes of displacement or acceleration peak response. The proposed method is verified through the numerical simulation for an assumed SDOF system consisting of mass, both viscous and friction damping and spring components.