• Structural Engineering and Mechanics
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• v.40 no.4
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• pp.501-515
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• 2011

Sandwich elements have high flexural rigidity and high strength per density. They also have excellent anti-vibration and anti-noise characteristics. Therefore, they are used for structures of airplanes and high speed ships that must be light, as well as strong. In this paper, the Reissner-Mindlin's plate theory is studied from a Hamilton's principle point of view. This theory is modified to include the influence of shear deformation and rotary inertia, and the equation of motion is derived using energy relationships. The theory is applied to a rectangular sandwich model which has isotropic, asymmetrical faces and an isotropic core. Investigations are conducted for five different plate thicknesses. These plates are identical to the sandwich plates currently used in various structural elements of surface effect ships (SES). The boundary conditions are set to simple supports and fixed supports. The elastic and shear moduli are obtained from the four-point bending tests on the sandwich beams.

• Steel and Composite Structures
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• v.42 no.3
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• pp.397-405
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• 2022

The existing researches on the dynamics of the fluid-conveying pipes only focus on stability and vibration problems, and there is no literature report on the wave propagation of the fluid-conveying pipes. Therefore, the purpose of this paper is to explore the propagation characteristics of longitudinal and flexural waves in the fluid-conveying pipes. First, it is assumed that the material properties of the fluid-conveying pipes vary based on a power function of the thickness. In addition, it is assumed that the material properties of both the fluid and the pipes are closely depended on temperature. Using the Euler-Bernoulli beam equation and based on the linear theory, the motion equations considering the thermal-mechanical-fluid coupling is derived. Then, the exact expressions of phase velocity and group velocity of longitudinal waves and bending waves in the fluid-conveying pipes are obtained by using the eigenvalue method. In addition, we also studied the free vibration frequency characteristics of the fluid-conveying pipes. In the numerical analysis, we successively studied the influence of temperature, functional gradient index and liquid velocity on the wave propagation and vibration problems. It is found that the temperature and functional gradient exponent decrease the phase and group velocities, on the contrary, the liquid flow velocity increases the phase and group velocities. However, for vibration problems, temperature, functional gradient exponent parameter, and fluid velocity all reduce the natural frequency.

• Structural Engineering and Mechanics
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• v.87 no.3
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• pp.283-296
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• 2023

Free-vibration and buckling analyses of plate problems are investigated with the aid of the strain gradient notation finite element method (SGN-FEM). As SGN-FEM employs physically interpretable polynomials in developing finite elements, parasitic shear sources, which are the cause of shear locking, can be precisely identified and subsequently eliminated. This allows two mutually complementary objectives to be defined in this work, namely, evaluate the efficiency of free-vibration and buckling results provided by corrected models, and study the severity of parasitic shear effects on plate models performance. Parasitic shear are flexural terms erroneously present in shear strain polynomials. It is reviewed here that six parasitic shear terms arise during the formulation of the four-node Mindlin plate element. Two parasitic shear terms have been identified in the in-plane shear strain polynomial while other two have been identified in each of the transverse shear strain polynomials. The element is corrected a-priori, i.e., during development, by simply removing the spurious terms from the shear strain polynomials. The computational implementation of the element in its two versions, namely, containing the parasitic shear terms (PS) and corrected for parasitic shear (SG), allows for assessments of the accuracy of results and of the deleterious effects of parasitic shear in free vibration and buckling analyses. This assessment of the parasitic shear effects is a novelty of this work. Validation of the SG model is done comparing its results with analytical results and results provided by other numerical procedures. Analyses are performed for square plates with different thickness-to-length ratios and boundary conditions. Results for thin plates provided by the PS model do not converge to the correct solutions, which indicates that parasitic shear must be eliminated. That is, analysts should not rely on refinement alone. For thick plates, PS model results can be considered acceptable as deleterious effects are really critical in thin plates. On the other hand, results provided by the SG model converge well for both thin and thick plates. The effectiveness of the SG model is established via high-accuracy results obtained in several examples. It is concluded that corrected SGN-FEM models are efficient alternatives for free-vibration and buckling analysis of Mindlin plate problems, and that precise elimination of parasitic shear is a requirement for sound analyses.

• Steel and Composite Structures
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• v.29 no.4
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• pp.527-544
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• 2018

The paper presents the study on a change in modal parameters and structural stiffness of cable-stayed Fiberline Bridge made entirely of Glass Fiber Reinforced Polymer (GFRP) composite used for 20 years in the fjord area of Kolding, Denmark. Due to this specific location the bridge structure was subjected to natural aging in harsh environmental conditions. The flexural properties of the pultruded GFRP profiles acquired from the analyzed footbridge in 1997 and 2012 were determined through three-point bending tests. It was found that the Young's modulus increased by approximately 9%. Moreover, the influence of the temperature on the storage and loss modulus of GFRP material acquired from the Fiberline Bridge was studied by the dynamic mechanical analysis. The good thermal stability in potential real temperatures was found. The natural vibration frequencies and mode shapes of the bridge for its original state were evaluated through the application of the Finite Element (FE) method. The initial FE model was created using the real geometrical and material data obtained from both the design data and flexural test results performed in 1997 for the intact composite GFRP material. Full scale experimental investigations of the free-decay response under human jumping for the experimental state were carried out applying accelerometers. Seven natural frequencies, corresponding mode shapes and damping ratios were identified. The numerical and experimental results were compared. Based on the difference in the fundamental natural frequency it was again confirmed that the structural stiffness of the bridge increased by about 9% after 20 years of service life. Data collected from this study were used to validate the assumed FE model. It can be concluded that the updated FE model accurately reproduces the dynamic behavior of the bridge and can be used as a proper baseline model for the long-term monitoring to evaluate the overall structural response under service loads. The obtained results provided a relevant data for the structural health monitoring of all-GFRP bridge.

• Proceedings of the Korea Concrete Institute Conference
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• 1998.10a
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• pp.412-417
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• 1998

This paper provides accurate flexural vibration solutions for thick (Mindlin) sectorial plates. A Ritz method is employed which incorporates a complete set of admissible algebraic-trigonometric polynomials in conjunction with an admissible set of Mindlin “corner functions". These corner functions model the singular vibratory moments and shear forces, which simultaneously exist at the vertex of corner angle exceeding 180$^{\circ}$. The first set guarantees convergence to the exact frequencies as sufficient terms are taken. The second set represents the corner singularities, and accelerates convergence substantially. Numerical results are obtained for completely free sectorial plates. Accurate frequencies are presented for a wide spectrum of vertex angles (90$^{\circ}$, 180$^{\circ}$, 270$^{\circ}$, 300$^{\circ}$, 330$^{\circ}$, 350$^{\circ}$, 35 5$^{\circ}$,and 359$^{\circ}$)and thickness ratios.tios.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.11 no.2
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• pp.15-26
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• 1991

The lateral forces such as the earthquake and wind my cause the torsion to be coupled with the lateral bending in the gider, the cross-section of wich has only one axis of symmetry. This induces additional stresses especially in cables arranged in double-planes. Since this effect cannot be considered by using the conventional frame elements, the stiffness and the mass matrices of the geometrically nonlinear thin-walled frame element are developed in this study to model the girder. The equivalent modulus of elasticity proposed by Ernst is used for the cable elements. Verification of the present theory is made through a numerical example. Then, the free vibration of a three dimensional cable-stayed bridge is analyzed to study the coupled flexural-torsional behavior.

• Journal of the Korean Society of Fisheries and Ocean Technology
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• v.27 no.4
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• pp.313-320
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• 1991

The paper describes the formulation for the analysis of the flexural free vibration of rectangular plate structure by the transfer influence coefficient method, which was developed on the base of the concept of the successive transmission of dynamic influence coefficients. For the analysis of rectangular plate which two opposite sides are simply-supported edge condition, the results of simple numerical examples demonstrate the validity of the present method, that is, the numerical high accuracy, the high speed and the flexibility for programming, compared with results of the transfer matrix method and exact solution or Leissa's method.

• Journal of Korea Foresty Energy
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• v.17 no.1
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• pp.36-46
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• 1998

The aim of this study was to develop the noise and vibration damping wood-based composites by using viscoelastic polymer materials. Polyvinylchloride(PVC) was plasticized with 20-140 phr bis(2-ethylhexyl) phthalate(DOP) and the dynamic tensile mechanical properties were measured at 110Hz and approximate temperature range -100 to 150$^{\circ}$ using a Rheovibron Instrument. The PVC/DOP blends were shown to be compatible in all proportions, and both T(E”$_{max}$) and T(tan${\delta}_{max}$) shifted to the lower temperature side as the DOP content increased. The vibration damping properties of wood/polymer composites were measured using the Rheovibron instrument in a bending mode. The composite damping factor(tan ${\delta}_{c}$) of wood /PVC-DOP/wood sandwich structure correlated with the loss factor and that of the coated structure correlated with the loss modulus(E”) of the polymer layer. In addition, the sandwich structure was found to be more effective in damping than the coated structure. The logarithmic decrement (${\Delta}$c) curve of a sandwich structure, which was determined by the free-free flexural vibration method was similar in shape to the tan ${\delta}_{c}$ curve.

• Composites Research
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• v.29 no.6
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• pp.347-352
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• 2016

This work presents the free vibration characteristics of laminated composite corrugated rectangular plates using the analytical method. Because it is very difficult to determine its mechanical behavior of 3-dimensional corrugated structures analytically, the equivalent homogenization model is adapted to investigate the overall mechanical behavior of corrugated structures. The corrugated element can be homogenized as an orthotropic material. Both the effective extensional and flexural stiffness of this homogenized equivalent orthotropic material are considered in the analysis. The present analytical results are validated by those obtained from 3D finite element analysis based on shell elements. The natural frequencies and global vibration mode shapes obtained from present analytical and finite element analysis are presented. Some numerical results are presented to check the effect of the geometric properties.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.19 no.11
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• pp.1133-1143
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• 2009

Vibro-acoustic characteristics of a simplified disk-brake rotor containing a narrow radial slot are studied using a semi-analytical procedure. First, modal sound radiations for flexural and radial modes of a generic annular disk having identical key dimension and slot(with free boundaries) are defined using pre-developed analytical solutions based on the modal vibrations from finite element model. The analytical solutions are validated by fully computational methods. Second, sound radiation from a simplified brake rotor simulated using sound radiation solution of the generic disk based on the rotor eigensolutions computed using a finite element code. Predictions by the semi-analytical method matched well numerical calculations using finite element and boundary element method. Finally, sound radiation and vibration characteristics for the example rotor due to a harmonic excitation fixed to the rotor or rotating around the rotor are also obtained.