• International Journal of Naval Architecture and Ocean Engineering
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• v.8 no.2
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• pp.117-126
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• 2016

In this paper, a numerical procedure for the natural vibration analysis of plates with openings and carlings based on the assumed mode method is extended to assess their forced response. Firstly, natural response of plates with openings and carlings is calculated from the eigenvalue equation derived by using Lagrange's equation of motion. Secondly, the mode superposition method is applied to determine frequency response. Mindlin theory is adopted for plate modelling and the effect of openings is taken into account by subtracting their potential and kinetic energies from the corresponding plate energies. Natural and frequency response of plates with openings and carlings subjected to point excitation force and enforced acceleration at boundaries, respectively, is analysed by using developed in-house code. For the validation of the developed method and the code, extensive numerical results, related to plates with different opening shape, carlings and boundary conditions, are compared with numerical data from the relevant literature and with finite element solutions obtained by general finite element tool.

• Transactions of the Korean Society of Mechanical Engineers
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• v.9 no.2
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• pp.174-180
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• 1985

A new measuring technique for the rigidities of stiffened plated is presented. The equations relating the rigidities of stiffened plates and the natural frequencies of a cantilever plate are derived and the rigidities are determined using the measured natural frequencies of the plate. The static deflection tests are conducted for checking the validity of this method. For unstiffened plates the measured rigidities are good agreement with the theoretical values and the experimental results of deflection tests. In the case of stiffened plates the measured rigidities closely matched with the results of deflection tests. It has been also demonstrated that this measuring technique can be utilized in determining the rigidities of arbitrarily stiffened plates.

• Structural Engineering and Mechanics
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• v.65 no.5
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• pp.573-585
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• 2018

This article presents strain gradient elasticity-based procedures for static bending, free vibration and buckling analyses of functionally graded rectangular micro-plates. The developed method allows consideration of smooth spatial variations of length scale parameters of strain gradient elasticity. Governing partial differential equations and boundary conditions are derived by following the variational approach and applying Hamilton's principle. Displacement field is expressed in a unified way to produce numerical results in accordance with Kirchhoff, Mindlin, and third order shear deformation theories. All material properties, including the length scale parameters, are assumed to be functions of the plate thickness coordinate in the derivations. Developed equations are solved numerically by means of differential quadrature method. Proposed procedures are verified through comparisons made to the results available in the literature for certain limiting cases. Further numerical results are provided to illustrate the effects of material and geometric parameters on bending, free vibrations, and buckling. The results generated by Kirchhoff and third order shear deformation theories are in very good agreement, whereas Mindlin plate theory slightly overestimates static deflection and underestimates natural frequency. A rise in the length scale parameter ratio, which identifies the degree of spatial variations, leads to a drop in dimensionless maximum deflection, and increases in dimensionless vibration frequency and buckling load. Size effect is shown to play a more significant role as the plate thickness becomes smaller compared to the length scale parameter. Numerical results indicate that consideration of length scale parameter variation is required for accurate modelling of graded rectangular micro-plates.

• Computers and Concrete
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• v.25 no.3
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• pp.225-244
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• 2020

The influence of boundary conditions on the bending and free vibration behavior of functionally graded sandwich plates resting on a two-parameter elastic foundation is examined using an original novel high order shear theory. The Hamilton's principle is used herein to derive the equations of motion. The number of unknowns and governing equations of the present theory is reduced, and hence makes it simple to use. This theory includes indeterminate integral variables and contains only four unknowns in which any shear correction factor not used, with even less than the conventional theory of first shear strain (FSDT). Unlike any other theory, the number of unknown functions involved in displacement field is only four, as against five, six or more in the case of other shear deformation theories. Galerkin's approach is utilized for FGM sandwich plates with six different boundary conditions. The accuracy of the proposed solution is checked by comparing it with other closed form solutions available in the literature.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.39 no.2
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• pp.106-113
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• 2011

This paper was conducted on experimental analysis in the free vibration analysis of rectangular plates under uniform thermal loading. Materials of three rectangular plates were aluminum, steel and stainless-steel respectively. The dimension of rectangular plates was 0.1 $\times$ 0.1 $\times$ 0.002 m. Infrared quartz lamps were used for thermal loading. The PCS(Power Control System) electric control system was applied for control and scanning vibrometer (Poly Tech) was used for acquisition of frequency response function. Applied temperature was increased from room temperature to $300^{\circ}C$ by $50^{\circ}C$. Boundary condition was free-free condition using bungee cord. Front face of rectangular plate was heated uniformly.

• Steel and Composite Structures
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• v.48 no.1
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• pp.1-17
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• 2023

The main goal of this paper is to study vibration of damaged core laminated sectorial plates with Functionally graded (FG) face sheets based on three-dimensional theory of elasticity. The structures are made of a damaged isotropic core and two external face sheets. These skins are strengthened at the nanoscale level by randomly oriented Carbon nanotubes (CNTs) and are reinforced at the microscale stage by oriented straight fibers. These reinforcing phases are included in a polymer matrix and a three-phase approach based on the Eshelby-Mori-Tanaka scheme and on the Halpin-Tsai approach, which is developed to compute the overall mechanical properties of the composite material. Three complicated equations of motion for the sectorial plates under consideration are semi-analytically solved by using 2-D differential quadrature method. Using the 2-D differential quadrature method in the r- and z-directions, allows one to deal with sandwich annular sector plate with arbitrary thickness distribution of material properties and also to implement the effects of different boundary conditions of the structure efficiently and in an exact manner. The fast rate of convergence and accuracy of the method are investigated through the different solved examples. The sandwich annular sector plate is assumed to be simply supported in the radial edges while any arbitrary boundary conditions are applied to the other two circular edges including simply supported, clamped and free. Several parametric analyses are carried out to investigate the mechanical behavior of these multi-layered structures depending on the damage features, through-the-thickness distribution and boundary conditions.

• Journal of the Computational Structural Engineering Institute of Korea
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• v.17 no.2
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• pp.119-129
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• 2004

A three dimensional (3D) method of analysis is presented for determining the free vibration frequencies and mode shapes of thick, circular and annular plates with nonlinear thickness variation along the radial direction. Unlike conventional plate theories, which are mathematically two dimensional (2D), the present method is based upon the 3D dynamic equations of elasticity. Displacement components u/sub s/, u/sub z/, and u/sub θ/ in the radial, thickness, and circumferential directions, respectively, are taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the s and z directions. Potential (strain) and kinetic energies of the plates are formulated, and the Ritz method is used to solve the eigenvalue problem thus yielding upper bound values of the frequencies by minimizing the frequencies. As the degree of the polynomials is increased, frequencies converge to the exact values. Convergence to four digit exactitude is demonstrated for the first five frequencies of the plates. Numerical results we presented for completely free, annular and circular plates with uniform linear, and quadratic variations in thickness. Comparisons are also made between results obtained from the present 3D and previously published thin plate (2D) data.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.05a
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• pp.312-317
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• 2005

Fluid-elastic instability and turbulence excitation for an under developing steam generator are investigated numerically. The stability ratio and the amplitude of turbulence excitation are obtained by using the PIAT (Program for Integrity Assessment of Steam Generator Tube) code from the information on the thermal-hydraulic data of the steam generator. The aspect ratio, the ratio between the height of U-tube from the upper most tube support plate (h) and the width of two vertical portion of U-tube (w), is defined for geometric parameter study. Several aspect ratios with relocation of tube support plates are adopted to study the effects on the mode shapes and characteristics of flow-induced vibration. When the aspect ratio exceeds value of 1, most of the mode shapes at low frequency are generated at the top of U-tube. It makes very high value of the stability ratio and the amplitude of turbulent excitation as well. We can consider that the local mode shape at the upper side of U-tube will develop the wear phenomena between the tube and the anti-vibration bars such as vertical, horizontal, and diagonal strips. It turns out that the aspect ratio reveals very important parameter for the design stage of the steam generator. The appropriate value of the aspect ratio should be specified and applied.

• Laser Solutions
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• v.14 no.2
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• pp.8-12
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• 2011

As the aged population grows around the world, many medical instruments and devices have been developed recently. Among the devices, a drug delivery stent is a medical device which requires precision machining. Conventional drug delivery stent has problems of residual polymer and decoating because the drug is coated on the surface of stent with the polymer. If the drug is impregnated in micro hole array on the surface of the stent, the problem can be solved. Micro sized holes are generally fabricated by laser machining; however, the fabricated holes do not have an enough aspect ratio to contain the drug or a good surface finish to deliver it to blood vessel tissue. To overcome these problems, we propose a vibration-assisted machining mechanism with PZT (Piezoelectric Transducers) for the fabrication of micro sized holes. If the mechanism vibrates the eyepiece of the laser machining head, the laser spot on the workpiece will vibrate vertically because objective lens in the eyepiece shakes by the mechanism's vibration. According to the former researches, the vibrating frequency over 20kHz and amplitude over 500nm are preferable. The vibration mechanism has cylindrical guide, hollowed PZT and supports. In the cylinder, the eyepiece is mounted. The cylindrical guide has upper and low plates and side wall. The shape of plates and side wall are designed to have high resonating frequency and large amplitude of motion. The PZT also is selected to have high actuating force and high speed of motion. The support has symmetrical and rigid characteristics.

• The Journal of the Acoustical Society of Korea
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• v.35 no.4
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• pp.253-260
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• 2016

In this paper, derivation of the STL (Sound Transmission Loss) of the double plates installed in an impedance tube is discussed using an analytic method, where an air cavity exists between the plates. Vibration of the plates and sound pressure field inside the tube are expressed in terms of infinite series of modal functions. Under the plane wave assumption, it is shown that consideration of the first few modes yields sufficiently accurate results, and locations of peaks and dips are investigated. It is determined that the peak frequencies of the double plates coincide with those of each single plate. When the two plates are identical, the STL of the double plates as well as that of the single plate become zero at the natural frequencies of the single plate. The location and amplitude of the dips are investigated using an approximation solution when the cavity depth is very small.