• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2008.04a
• /
• pp.132-139
• /
• 2008

The blade vibration problem of bladed disk is the most critical subject to consider since it directly affects the stable performance of the engine as well as life of the engine. Especially, due to complicated vibration pattern of the bladed disk, more effort was required for vibration analysis and test. The research of measuring the vibration of the bladed disk, using NSMS(Non-intrusive stress measurement) instead of Aeromechanics testing method requiring slip ring or telemetry system with strain gauge, was successful. These testing can report the actual stresses seen on the blades; detect synchronous resonances that are the source of high cycle fatigue (HCF) in blades; measure individual blade mis-tuning and coupled resonances in bladed disks. In order to minimize the error being created due to heat expansion, the tip timing sensor is installed parallel to the blade trailing edge, yielding optimal result. Also, when working on finite element analysis, the whole bladed disk has gone through three-dimensional analysis, evaluating the family mode. The result of the analysis matched well with the test result.

• Steel and Composite Structures
• /
• v.20 no.3
• /
• pp.623-649
• /
• 2016

Most of the early studies on plates vibration are focused on two-dimensional theories, these theories reduce the dimensions of problems from three to two by introducing some assumptions in mathematical modeling leading to simpler expressions and derivation of solutions. However, these simplifications inherently bring errors and therefore may lead to unreliable results for relatively thick plates. The main objective of this research paper is to present 3-D elasticity solution for free vibration analysis of continuously graded carbon nanotube-reinforced (CGCNTR) rectangular plates resting on two-parameter elastic foundations. The volume fractions of oriented, straight single-walled carbon nanotubes (SWCNTs) are assumed to be graded in the thickness direction. In this study, an equivalent continuum model based on the Eshelby-Mori-Tanaka approach is employed to estimate the effective constitutive law of the elastic isotropic medium (matrix) with oriented, straight carbon nanotubes (CNTs). The proposed rectangular plates have two opposite edges simply supported, while all possible combinations of free, simply supported and clamped boundary conditions are applied to the other two edges. The formulations are based on the three-dimensional elasticity theory. A semi-analytical approach composed of differential quadrature method (DQM) and series solution is adopted to solve the equations of motion. The fast rate of convergence of the method is demonstrated and comparison studies are carried out to establish its very high accuracy and versatility. The 2-D differential quadrature method as an efficient and accurate numerical tool is used to discretize the governing equations and to implement the boundary conditions. The convergence of the method is demonstrated and to validate the results, comparisons are made between the present results and results reported by well-known references for special cases treated before, have confirmed accuracy and efficiency of the present approach. The novelty of the present work is to exploit Eshelby-Mori-Tanaka approach in order to reveal the impacts of the volume fractions of oriented CNTs, different CNTs distributions, various coefficients of foundation and different combinations of free, simply supported and clamped boundary conditions on the vibrational characteristics of CGCNTR rectangular plates. The new results can be used as benchmark solutions for future researches.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2005.05a
• /
• pp.196-200
• /
• 2005

Piezoelectric underwater acoustic transducer is a kind of device for underwater detection working as not only an actuator but also a sensor. The technique that can predict acoustical characteristics of transducer is important for robust design of transducer in harsh underwater environment. This paper represents the dynamic analysis of piezoelectric acoustic transducers based on finite element method through USAP software. Two dimensional model of Tonpilz transducer and three dimensional model of Flextensional transducer are generated for the dynamic analysis and some results obtained by USAP are compared with those by ANSYS.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.16 no.4
• /
• pp.419-429
• /
• 2003

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies of thick, hyperboloidal shells of revolution. 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/sub r/, u/sub θ/, u/sub z/ in the radial, circumferential, and axial directions, respectively, we taken to be sinusoidal in time, periodic in θ, and algebraic polynomials in the r and z directions. Potential(strain) and kinetic energies of the hyperboloidal shells 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 hyperboloidal shells of revolution. Numerical results are tabulated for eighteen configurations of completely free hyperboloidal shells of revolution having two different shell thickness ratios, three variant axis ratios, and three types of shell height ratios. Poisson's ratio (ν) is fixed at 0.3. Comparisons we made among the frequencies for these hyperboloidal shells and ones which ate cylindrical or nearly cylindrical( small meridional curvature. ) The method is applicable to thin hyperboloidal shells, as well as thick and very thick ones.

• Structural Engineering and Mechanics
• /
• v.55 no.1
• /
• pp.29-46
• /
• 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
• /
• v.55 no.5
• /
• pp.1015-1035
• /
• 2015

A three-dimensional (3D) numerical analysis for the train-bridge interaction (TBI) system is actively developed in this study in order to investigate the vibration characteristics of rigid-frame reinforced concrete (RC) viaducts in both vertical and lateral directions respectively induced by running high-speed trains. An analytical model of the TBI system is established, in which the high-speed train is described by multi-DOFs vibration system and the rigid-frame RC viaduct is modeled with 3D beam elements. The simulated track irregularities are taken as system excitations. The numerical analytical algorithm is established based on the coupled vibration equations of the TBI system and verified through the detailed comparative study between the computation and testing. The vibration responses of the viaducts such as accelerations, displacements, reaction forces of pier bottoms as well as their amplitudes with train speeds are calculated in detail for both vertical and lateral directions, respectively. The frequency characteristics are further clarified through Fourier spectral analysis and 1/3 octave band spectral analysis. This study is intended to provide not only a simulation approach and evaluation tool for the train-induced vibrations upon the rigid-frame RC viaducts, but also instructive information on the vibration mitigation of the high-speed railway.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2008.03a
• /
• pp.871-876
• /
• 2008

The blade vibration problem of bladed disk is the most critical subject to consider since it directly affects the stable performance of the engine as well as life of the engine. Especially, due to complicated vibration pattern of the bladed disk, more effort was required for vibration analysis and test. The research of measuring the vibration of the bladed disk, using NSMS(Non-intrusive stress measurement) instead of Aeromechanics testing method requiring slip ring or telemetry system with strain gauge, was successful. These testing can report the actual stresses seen on the blades; detect synchronous resonances that are the source of high cycle fatigue(HCF) in blades; measure individual blade mis-tuning and coupled resonances in bladed disks. In order to minimize the error being created due to heat expansion, the tip timing sensor is installed parallel to the blade trailing edge, yielding optimal result. Also, when working on finite element analysis, the whole bladed disk has gone through three-dimensional analysis, evaluating the family mode. The result of the analysis matched well with the test result.

• KIEE International Transaction on Electrical Machinery and Energy Conversion Systems
• /
• v.3B no.4
• /
• pp.159-164
• /
• 2003

In this paper, a three-dimensional finite element method and construction of equivalent-circuit for a linear ultrasonic motor are presented. The validity of three-dimensional finite element routine in this paper is experimentally confirmed by analyzing impedance of a piezoelectric transducer. Using this confirmed finite element routine, impedance and vibration mode of a linear ultrasonic motor are calculated. Elliptical motion of contact point between vibrator and rail of the linear ultrasonic motor is shown for determination of contact points. By using the finite element method and analytic equations, characteristics of the linear ultrasonic motor, such as thrust force, speed, losses, powers and efficiency, are calculated. The results are confirmed by experiment. Finally, equivalent circuit parameters of the linear ultrasonic motor are obtained using the three-dimensional finite element method and analytic equations.

• Transactions of the Korean Society of Mechanical Engineers
• /
• v.18 no.11
• /
• pp.2922-2931
• /
• 1994

We propose a modified 6-node element, where the sampling point of Gauss quadrature moved in the thickness direction. The modified 6-node element has been applied to static problems and forced motion analyses. In this study, this method is extended to the finite element analysis of the natural frequencies of two dimensional problems. We also propose a modified 16-node element for three dimensional problems, which behaves much like a 20-node element with smaller degree of freedom. The modified 6-node and 16-node elements have been applied to the modal analyses of beams and plates, respectively. The results agree well with the results of the 8-node or 20-node element models.

• Journal of Korean Association for Spatial Structures
• /
• v.4 no.4 s.14
• /
• pp.113-128
• /
• 2004

A three-dimensional (3-D) method of analysis is presented for determining the free vibration frequencies and mode shapes of solid paraboloidal and complete (that is, without a top opening) paraboloidal shells of revolution with variable wall thickness. Unlike conventional shell theories, which are mathematically two-dimensional (2-D), the present method is based upon the 3-D dynamic equations of elasticity. The ends of the shell may be free or may be subjected to any degree of constraint. Displacement components $u_r,\;u_{\theta},\;and\;u_z$ in the radial, circumferential, and axial directions, respectively, are taken to be sinusoidal in time, periodic in ${\theta}$, and algebraic polynomials in the r and z directions. Potential (strain) and kinetic energies of the paraboloidal shells of revolution 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 complete, shallow and deep paraboloidal shells of revolution with variable thickness. Numerical results are presented for a variety of paraboloidal shells having uniform or variable thickness, and being either shallow or deep. Frequencies for five solid paraboloids of different depth are also given. Comparisons are made between the frequencies from the present 3-D Ritz method and a 2-D thin shell theory.