• Proceedings of the KSR Conference
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• 2010.06a
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Structural Engineering and Mechanics
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• v.21 no.6
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• pp.635-658
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• 2005

The possibility of detecting a crack in L-shaped pipes filled with fluid based on measurement of transverse natural frequencies is examined. The problem is solved by representing the crack by a massless rotational spring, simulating the out-of-plane transverse vibration only without solving the coupled torsional vibration and using the transfer matrix method for solution of the governing equation. The theoretical solutions are verified by experiments. The cracks considered are external, circumferentially oriented and have straight front. Pipes made of aluminium and mild steel are tested with water as internal fluid. Crack size to pipe thickness ratio ranging from 0.20 to 0.57 and fluid (gauge) pressure in the range of 0 to 10 atmospheres are examined. The rotational spring stiffness is obtained by an inverse vibration analysis and deflection method. The details of the two methods are given. The results by the two methods are presented graphically and show good agreement. Crack locations are also determined by the inverse analysis. The maximum absolute error in the location is 13.80%. Experimentally determined variation of rotational spring stiffness with ratio of crack size to thickness is utilized to predict the crack sizes. The maximum absolute errors in prediction of crack size are 17.24% and 16.90% for aluminium and mild steel pipes respectively.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.20 no.4
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• pp.417-425
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• 2007

The differential quadrature method(DQM) is applied to computation of eigenvalues of the equations of motion governing the free out-of-plane vibration for circular curved beams including the effects of rotatory inertia and transverse shearing deformation. Fundamental frequencies are calculated for the members with clamped-clamped end conditions and various opening angles. The results are compared with exact solutions or numerical solutions by other methods for cases in which they are available. The DQM provides good accuracy even when only a limited number of grid points is used.

• Structural Engineering and Mechanics
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• v.75 no.2
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• pp.247-269
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• 2020

A finite strip formulation was developed for buckling and free vibration analysis of laminated composite plates based on different shear deformation plate theories. The different shear deformation theories such as Zigzag higher order, Refined Plate Theory (RPT) and other higher order plate theories by variation of transverse shear strains through plate thickness in the parabolic form, sine and exponential were adopted here. The two loaded opposite edges of the plate were assumed to be simply supported and remaining edges were assumed to have arbitrary boundary conditions. The polynomial shape functions are applied to assess the in-plane and out-of-plane deflection and rotation of the normal cross-section of plates in the transverse direction. The finite strip procedure based on the virtual work principle was applied to derive the stiffness, geometric and mass matrices. Numerical results were obtained based on various shear deformation plate theories to verify the proposed formulation. The effects of length to thickness ratios, modulus ratios, boundary conditions, the number of layers and fiber orientation of cross-ply and angle-ply laminates were determined. The additional results on the same effects in the interaction of biaxial in-plane loadings on the critical buckling load were determined as well.

• Steel and Composite Structures
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• v.26 no.6
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• pp.673-691
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• 2018

The main goal of this research is to examine the in-plane and out-of-plane forced vibration of a curved nanocomposite microbeam. The in-plane and out-of-plane displacements of the structure are considered based on the first order shear deformation theory (FSDT). The curved microbeam is reinforced by functionally graded carbon nanotubes (FG-CNTs) and thus the extended rule of mixture is employed to estimate the effective material properties of the structure. Also, the small scale effect is captured using the strain gradient theory. The structure is rested on a nonlinear orthotropic viscoelastic foundation and is subjected to concentrated transverse harmonic external force, thermal and magnetic loads. The derivation of the governing equations is performed using energy method and Hamilton's principle. Differential quadrature (DQ) method along with integral quadrature (IQ) and Newmark methods are employed to solve the problem. The effect of various parameters such as volume fraction and distribution type of CNTs, boundary conditions, elastic foundation, temperature changes, material length scale parameters, magnetic field, central angle and width to thickness ratio are studied on the frequency and force responses of the structure. The results indicate that the highest frequency and lowest vibration amplitude belongs to FGX distribution type while the inverse condition is observed for FGO distribution type. In addition, the hardening-type response of the structure with FGX distribution type is more intense with respect to the other distribution types.

• Journal of the Korean Society for Railway
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• v.15 no.6
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• pp.588-596
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• 2012

This paper presents a new semi-analytical annular Mindlin plate element with which out-of-plane natural vibration of thick disks can be analyzed simply, efficiently, and accurately through FEM by including effects of rotary inertia and transverse shear deformation. Using static deformation modes which are exact solutions of equilibrium equations of annular Mindlin plate, the element interpolation functions, stiffness and mass matrices corresponding to each number of nodal diameters are derived. The element is capable of representing out-of-plane rigid-body motions exactly and free from shear locking. Natural frequencies of uniform and multi-step disks with or without concentric ring support are analyzed by applying the presented element. Such results are compared with theoretical predictions of previous works or FEA results obtained by using two-dimensional shell element to investigate the convergence and accuracy of the presented element.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.5 s.176
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• pp.1261-1270
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• 2000

This paper is concerned with the development of a general model for predicting material damping in laminates based on the strain energy method. In this model, the effect of interlaminar stress on damping is taken into accounts along with those of in-plane extension/compression and in-plane shear. The model was verified by carrying out the damping measurements on $90^0$ unidirectional composite beams varying length and thickness. The analytical predictions were favorably compared with the experimental data. The transverse shear($$\sigma$_{yz}$) appears to have a considerable influence on the damping behaviors in $90^0$ unidirectional polymer composites. However, the other interlaminar stresses($$\sigma$_{xz}$, $$\sigma$_z$) were shown to have little impact on vibration damping in $90^0$ laminated composite beam.

• International Journal of Aerospace System Engineering
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• v.3 no.1
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• pp.10-16
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• 2016

A trigonometric Layerwise higher order shear deformation theory (TLHSDT) is developed and implemented for free vibration and buckling analysis of laminated composite and sandwich plates by analytical and finite element formulation. The present model assumes parabolic variation of out-plane stresses through the depth of the plate and also accomplish the zero transverse shear stresses over the surface of the plate. Thus a need of shear correction factor is obviated. The present zigzag model able to meet the transverse shear stress continuity and zigzag form of in-plane displacement continuity at the plate interfaces. Hence, botheration of shear correction coefficient is neglected. In the case of analytical method, the governing differential equation and boundary conditions are obtained from the principle of virtual work. For the finite element formulation, an efficient eight noded $C^0$ continuous isoparametric serendipity element is established and employed to examine the dynamic analysis. Like FSDT, the considered mathematical model possesses similar number of variables and which decides the present models computationally more effective. Several numerical predictions are carried out and results are compared with those of other existing numerical approaches.

• Structural Engineering and Mechanics
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• v.13 no.6
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• pp.695-711
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• 2002

Here, the dynamic response characteristics of thick cross-ply laminated composite cylindrical shells are studied using a higher-order displacement model. The formulation accounts for the nonlinear variation of the in-plane and transverse displacements through the thickness, and abrupt discontinuity in slope of the in-plane displacements at any interface. The effect of inplane and rotary inertia terms is included. The analysis is carried out using finite element approach. The influences of various terms in the higher-order displacement field on the free vibrations, and transient dynamic response characteristics of cylindrical composite shells subjected to thermal and mechanical loads are analyzed.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.24 no.6 s.177
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• pp.1363-1370
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• 2000

Dynamic stability of a flexible spinning disk with angular acceleration is considered. To avoid the coupling between the in-plane and out-of-plane displacements, the linearized strain-displacement relations are used in the Kirchhoff plate theory. The uncoupled governing equations are derived by using Hamilton's principle with considering the angular acceleration. Numerical tests show that existence of the angular acceleration makes a spinning disk dynamically unstable.