• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2013.10a
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• pp.730-735
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• 2013

This paper contains various vibration analysis of multi-stage shaft shape such as the bending, torsional and axial vibration. The shaft system is modeled as Timoshenko beam with the transverse shear and rotary inertia effect and the equation of motion is derived by Hamilton's principle with considering clamped-free boundary condition. Then, eigenvalue problem of discrete equation of motion for multi-stage shaft model is solved and got results of the natural frequency through the numerical analysis. Obtained numerical analysis results through Matlab program were compared with those of FEM analysis to verify the results. This study suggests that design of shaft system be consider torsional and axial vibration as well as bending vibration.

• Advances in concrete construction
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• v.13 no.3
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• pp.255-264
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• 2022

Vibration is expected to occur in microtubules as tubular heterodimers. They oscillate like electric dipoles. Several research studies have estimated a frequency of vibration using the orthotropic model, a beam or rod like models and shell models, considering the surface forces. The effects of body forces on the dynamics of the microtubules were not yet taken into account. This study seeks to capture the body force effects on the vibration modes generated and on the corresponding frequency for microtubules. An orthotropic elastic shell model for the structural details of microtubules is used for the analysis. The tests are conducted out for microtubules, exposed to electro-magnetic and gravitational forces, the transverse vibration, radial mode vibration, and axial mode of vibration have accomplished. We therefore, evaluate and compare microtubules' frequencies with prior results of vibration frequency without the effects of body force.

• Steel and Composite Structures
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• v.22 no.2
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• pp.257-276
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• 2016

In this paper, a new simple higher-order shear deformation theory for bending and free vibration analysis of functionally graded (FG) plates is developed. The significant feature of this formulation is that, in addition to including a sinusoidal variation of transverse shear strains through the thickness of the plate, it deals with only three unknowns as the classical plate theory (CPT), instead of five as in the well-known first shear deformation theory (FSDT) and higher-order shear deformation theory (HSDT). A shear correction factor is, therefore, not required. Equations of motion are derived from Hamilton's principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The accuracy of the present solutions is verified by comparing the obtained results with those predicted by classical theory, first-order shear deformation theory, and higher-order shear deformation theory. Verification studies show that the proposed theory is not only accurate and simple in solving the bending and free vibration behaviours of FG plates, but also comparable with the other higher-order shear deformation theories which contain more number of unknowns.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.21 no.12
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• pp.2008-2018
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• 1997

In this study, free vibration analysis of double through-the-width split beam is studied based on the author's earlier work. Each segment which constructs double through-the-width split beam is considered as Timoshenko beam. The effect of coupling between longitudinal and transverse vibration on the natural frequencies of split beams is considered. Data acquisition and modal test of double split beam for clamped-free boundary condition are carried out. Experimental and numerical results obtained by ANSYS were compared with the calculated data by present theory and their comparisons give good agreement with one another. The influences of the size and location of double split, shear deformation, and boundary conditions on the natural frequencies are demonstrated for illustrative purpose. Effects of double split on the dynamic characteristics of beams can be used to detect the size and the location of damages in structures.

• Steel and Composite Structures
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• v.24 no.5
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• pp.603-613
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• 2017

In this research, the free vibration response of laminated composite plates is investigated using a novel and simple higher order shear deformation plate theory. The model considers a non-linear distribution of the transverse shear strains, and verifies the zero traction boundary conditions on the surfaces of the plate without introducing shear correction coefficient. The developed kinematic uses undetermined integral terms with only four unknowns. Equations of motion are obtained from the Hamilton's principle and the Navier method is used to determine the closed-form solutions of antisymmetric cross-ply and angle-ply laminates. Numerical examples studied using the present formulation is compared with three-dimensional elasticity solutions and those calculated using the first-order and the other higher-order theories. It can be concluded that the present model is not only accurate but also efficient and simple in studying the free vibration response of laminated composite plates.

• Steel and Composite Structures
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• v.46 no.2
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• pp.263-277
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• 2023

Free vibration analysis of multi-directional porous functionally graded (FG) sandwich plate has been performed for two cases namely: FG skin with homogeneous core and FG core with homogeneous skin. Hamilton's principle was employed and the solution was obtained using Navier's technique. This theory imposes traction-free boundary conditions on the surfaces and does not require shear correction factors. The results obtained are validated with those available in the literature. The composition of metal-ceramic-based functionally graded material (FGM) changes in longitudinal and transverse directions according to the power law. Imperfections in the functionally graded material introduced during the fabrication process were modeled with different porosity laws such as evenly, unevenly distributed, and logarithmic uneven distributions. The effect of porosity laws and geometry parameters on the natural frequency was investigated. On comparing the natural frequency of two cases for perfect and imperfect sandwich plates a reverse trend in natural frequency result was seen. The finding shows a multidirectional functionally graded structures perform better compared to uni-directional gradation. Hence, critical grading parameters and imperfection types have been identified which will guide experimentalists and researchers in selecting fabrication routes for improving the performance of such structures.

• Structural Engineering and Mechanics
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• v.63 no.4
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• pp.551-565
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• 2017

In this paper, an analytical approach is proposed for determining vibration characteristics of cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems. This method is based on the Timoshenko beam theory, transfer matrix method and numerical assembly method to obtain natural frequencies and mode shapes. Firstly, the beam is considered to be divided into several segments by spring-mass systems and support points, and four undetermined coefficients of vibration modal function are contained in each sub-segment. The undetermined coefficient matrices at spring-mass systems and pinned supports are obtained by using equilibrium and continuity conditions. Then, the overall matrix of undetermined coefficients for the whole vibration system is obtained by the numerical assembly technique. The natural frequencies and mode shapes of a cracked non-uniform continuous Timoshenko beam carrying an arbitrary number of spring-mass systems are obtained from the overall matrix combined with half-interval method and Runge-Kutta method. Finally, two numerical examples are used to verify the validity and reliability of this method, and the effects of cracks on the transverse vibration mode shapes and the rotational mode shapes are compared. The influences of the crack location, depth, position of spring-mass system and other parameters on natural frequencies of non-uniform continuous Timoshenko beam are discussed.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.1
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• pp.56-63
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• 2004

Exact solutions are presented for the free vibration and buckling of rectangular plates haying two opposite edges ( x=0 and a) simply supported and the other two ( y=0 and b) clamped, with the simply supported edges subjected to a linearly varying normal stress $\sigma$$_{x}$=- $N_{0}$[1-a(y/b)]/h, where h is the plate thickness. By assuming the transverse displacement ( w) to vary as sin(m$\pi$x/a), the governing partial differential equation of motion is reduced to an ordinary differential equation in y with variable coefficients. for which an exact solution is obtained as a power series (the method of Frobenius). Applying the clamped boundary conditions at y=0 and byields the frequency determinant. Buckling loads arise as the frequencies approach zero. A careful study of the convergence of the power series is made. Buckling loads are determined for loading parameters a= 0, 0.5, 1, 1.5. 2, for which a=2 is a pure in-plane bending moment. Comparisons are made with published buckling loads for a= 0, 1, 2 obtained by the method of integration of the differential equation (a=0) or the method of energy (a=1, 2). Novel results are presented for the free vibration frequencies of rectangular plates with aspect ratios a/b =0.5, 1, 2 when a=2, with load intensities $N_{0}$ / $N_{cr}$ =0, 0.5, 0.8, 0.95, 1. where $N_{cr}$ is the critical buckling load of the plate. Contour plots of buckling and free vibration mode shapes ate also shown.shown.

• Earthquakes and Structures
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• v.2 no.1
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• pp.43-64
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• 2011

One-dimensional rod theory is very effective as a simplified analytical approach to large scale or complicated structures such as high-rise buildings, in preliminary design stages. It replaces an original structure by a one-dimensional rod which has an equivalent stiffness in terms of global properties. The mechanical behavior of structures composed of distinct constituents of different stiffness such as coupled walls with opening is significantly governed by the local variation of stiffness. Furthermore, in structures with setback the distribution of the longitudinal stress behaves remarkable nonlinear behavior in the transverse-wise. So, the author proposed the two-dimensional rod theory as an extended version of the rod theory which accounts for the two-dimensional local variation of structural stiffness; viz, variation in the transverse direction as well as longitudinal stiffness distribution. This paper proposes how to deal with the two-dimensional rod theory for structures with setback. Validity of the proposed theory is confirmed by comparison with numerical results of computational tools in the cases of static, free vibration and forced vibration problems for various structures. The transverse-wise nonlinear distribution of the longitudinal stress due to the existence of setback is clarified to originate from the long distance from setback.

• Proceedings of the Korean Society For Composite Materials Conference
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• 2000.11a
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• pp.161-164
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• 2000

In this paper, a finite element structural analysis for thin-walled open-section composite beams with elastic couplings has been performed. The analysis includes the effects of transverse shear across beam sections, torsion warping and constrained warping. Reissner's semi-complementary energy functional is used to obtain the beam st illness coefficients The bending and torsion related warpings and the shear correct ion factors are obtained as part of the analysis. The resulting theory describes the beam kinematics in terms of the axial, flap and lag bending, flap and lag shear, torsion and torsion-warping deformations. The static response has been validated against finite element predict ions, closed form solutions, and experimental data for rectangular sol id and I-beams with elastic couplings. The free vibration results are also compared with available literature.