• Structural Engineering and Mechanics
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• v.55 no.1
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• pp.29-46
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the natural frequencies of a truncated shallow and deep conical shell with linearly varying thickness along the meridional direction free at its top edge and clamped at its bottom edge. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. Displacement components $u_r$, $u_{\theta}$, and $u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be periodic in ${\theta}$ and in time, and algebraic polynomials in the r and z directions. Strain and kinetic energies of the truncated conical shell with variable thickness 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. The frequencies from the present 3-D method are compared with those from other 3-D finite element method and 2-D shell theories.

• Structural Engineering and Mechanics
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• v.55 no.4
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• pp.785-799
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• 2015

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of hyperboloidal shells free at the top edge and clamped at the bottom edge like a hyperboloidal cooling tower by the Ritz method based upon the circular cylindrical coordinate system instead of related 3-D shell coordinates which are normal and tangent to the shell midsurface. The Legendre polynomials are used as admissible displacements. Convergence to four-digit exactitude is demonstrated. Natural frequencies from the present 3-D analysis are also compared with those of straight beams with circular cross section, complete (not truncated) conical shells, and circular cylindrical shells as special cases of hyperboloidal shells from the classical beam theory, 2-D thin shell theory, and other 3-D methods.

• Journal of the Korean Institute of Electrical and Electronic Material Engineers
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• v.34 no.2
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• pp.90-98
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• 2021

Piezoelectric ceramic fiber composite (PCFC) was fabricated using a planar electrode printed piezoelectric ceramic fiber driven in transverse mode for small-scale wind energy harvester applications. The PCFC consisted of an epoxy matrix material and piezoelectric ceramic fibers sandwiched by interdigitated electrode (IDE) patterned polyimide films. The PCFC showed an excellent mechanical performance under a continuous stress. For the fabrication of PCB cantilever harvester, five -PCFCs were vertically attached onto a flexible printed circuit board (PCB) substrate, and then PCFCs were serially connected through a printed Cu circuit. The energy harvesting performance was evaluated applying an inverted structure, which imples its free leading edge located at an open end but the trailing edge at a clamped end, to enhance strain energy in a wind tunnel. The output voltage of the PCB cantilever harvester was increased as the wind speed increased. The maximum output power was 17.2 ㎼ at a resistance load of 200 ㏀ and wind speed of 9 m/s. It is considered that the PCB cantilever energy harvester reveals a potential use for wind energy harvester applications.

• Journal of Korean Ophthalmic Optics Society
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• v.6 no.1
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• pp.13-29
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• 2001

A mathematical model was proposed to analyze the vibration of diaphragm, such as the contact lenses fitted on the eyes, being subjected to the external sinusoidal pressure. The model incorporates the differential equations and their numerical solution program, based on the wave equations. Turbo-C and graphic software, formulated to describe the dependence of the various parameters involved in the vibration. The model predicts the radial distribution of amplitude, frequency dependence of both average displacement amplitude and the power of diaphragm whose edge is being either simply supported or rigidly clamped in vibration. The effect of variables such as thickness, radius, damping coefficients on the vibration characteristics was illustrated by the computer simulation of the derived program. As the frequency of driving pressure increases above the certain value determined by the boundary conditions and parameters the wave shape or pattern changes from simple arc to belly or loops having double antinode. It seems that the effect of outer antinode progressively increases as the frequency increases. If this kind of phenomena occurs to the contact lens on the cornea in vivo, it may cause an abnormal correction power in the lenses or pull off the eye due the increased rise of outer part of the lens.

• International Journal of Aeronautical and Space Sciences
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• v.7 no.2
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• pp.42-49
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• 2006

In this paper, an efficient piezoelectric passive damper is newly devised to suppress the multi-mode vibration of plates. To construct the passive damper, the piezoelectric materials are utilized as energy transformer, which can transform the mechanical energy to electrical energy. To dissipate the electrical energy transformed from mechanical energy, multiple resonant shunted piezoelectric circuits are applied. The dynamic governing equations of a coupled electro-mechanical piezoelectric with multiple piezoelectric patches and multiple resonant shunted circuits is derived and solved for the one edge clamped plate. The equations of motion of the piezoelectrics and shunted circuits as well as the plate are discretized by finite element method to estimate more exactly the effectiveness of the piezoelectric passive damper. The method to find the optimal location of a piezoelectric is presented to maximize effectiveness for desired modes. The electro-mechanical coupling term becomes important parameter to select the optimal location.

• Structural Engineering and Mechanics
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• v.61 no.2
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• pp.295-316
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• 2017

Element based differential quadrature method (EDQM) has been applied to analyze static, stability and free vibration of non-homogeneous orthotropic rectangular plates of variable or stepped thickness. The Young's modulus and the density are assumed to vary in exponential form in X-direction whereas the thickness is assumed to vary linear, parabolic or exponential variation in one or two directions. In-plane loading is assumed to vary linearly. Various combinations of clamped, simply supported and free edge conditions (regular and irregular boundary) have been considered. Continuous plates could also be handled with ease. In this paper, formulation for equilibrium, buckling and free vibration problems is discussed and several numerical examples are solved using EDQM and compared with the published results.

• Journal of KSNVE
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• v.8 no.2
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• pp.324-330
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• 1998

The forced vibration analysis of the outer-clamped spinnig annular disk with arbitrary in-plane is formulated to investigate the influence of non-uniform tension on the cutting accuracy of wafer cutting machine. The arbitrary in-plan force along the outer edge of an annular plate is expressed as a Fourier series. Galerkin method and modal superposition method are employed to obtain the forced responses under the static force and the impulse force in astationary coordinate. Through qualitative and quantitative analyses, it can be found that forced and impulse responses are sensitive to the non-uniformity of in-plane force, which can bring a bad effect to the accuracy of wafer cutting process. Also, in case of a spinning disk with non-uniform in-plane force, critical speed is required to define in a different way, compared with conventional definition in axi-symmetrical spinning disk.

• Structural Engineering and Mechanics
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• v.74 no.5
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• pp.711-722
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• 2020

In this study, on-site testing was carried out to investigate the vibration serviceability of a composite steel-bar truss slab with steel girder system. Impulse excitations (heel-drop and jumping) and steady-state motion (walking and running) were performed to capture the primary vibration parameters (natural frequency and damping ratio) and distribution of peak acceleration. The composite floor possesses low frequency (<8.3Hz) and damping ratio (<2.47%). Based on experimental, theoretical, and numerical analyses on fundamental natural frequency, the boundary condition of SCSS (i.e., three edges simply supported and one edge clamped) is deemed more comparable substitutive for the investigated composite floor. Walking and running excitations by one person (single excitation) were considered to evaluate the vibration serviceability of the composite floor. The measured acceleration results show a satisfactory vibration perceptibility. For design convenience and safety, a crest factor β_rp describing the ratio of peak acceleration to root-mean-square acceleration induced from the walking and running excitations is proposed. The comparisons of the modal parameters determined by walking and running tests reveal the interaction effect between the human excitation and the composite floor.