• Structural Engineering and Mechanics
• /
• v.40 no.5
• /
• pp.689-703
• /
• 2011

A new perturbation method is introduced to study the undamped free vibration of a non-prismatic Timoshenko beam for its natural frequencies and vibration modes. For simplicity, the natural modes of vibration of its corresponding prismatic Euler-Bernoulli beam with the same length and boundary conditions are used as Ritz base functions with necessary modifications to account for shear strain in the Timoshenko beam. The new method can transform two coupled partial differential equations governing the transverse vibration of the non-prismatic Timoshenko beam into a set of nonlinear algebraic equations. It significantly simplifies the solution process and is applicable to non-prismatic beams with various boundary conditions. Three examples indicated that the new method is more accurate than the previous perturbation methods. It successfully takes into account the effect of shear deformation of Timoshenko beams particularly at the free end of cantilever structures.

• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.12 no.12
• /
• pp.1001-1009
• /
• 2002

In this paper, we analyse and present mechanical dynamic characteristics of a micro-machined vibrating silicon ring gyroscope which can measure angular velocities about three orthogonal axes. The ring gyroscope has a ring connected to the gyroscope main body by support-ligaments which are arranged with cyclic symmetry. The natural modes of its vibration can be distinguished into the in-plane motion and the out-of-plane motion which are coupled by the gyro-effect due to the rotation of the gyroscope main body. The equations of motion, the response to angular velocities, and the relationships between the natural modes of vibration are derived and compared with the previous studies for the design of a micro three-axis ring gyroscope.

• Ocean and Polar Research
• /
• v.42 no.3
• /
• pp.249-261
• /
• 2020

This study details grain-size distributions (GSDs) of carbonate and biogenic opal fractions of the sediments retrieved from the South Korea Plateau in the East Sea and draws paleocanographic implications from them. The opal-fraction GSDs show fine modes of 10.3 ㎛ and coarse modes of 102.5 ㎛ on average. The fine-mode grains of opal fractions mainly consist of small diatoms and radiolarians including their broken frustules, while the coarse-mode grains are mostly comprised of large warm-water diatoms and radiolarians. Significant positive correlation between opal contents and abundances of the coarse-mode GSDs in the total GSDs suggests that the abundances of the coarse-mode GSDs were controlled by the increased surface productivity of warm-water diatoms during interglacial stages. The carbonate-fraction GSDs show fine modes of 2.4 ㎛ and coarse modes of 99.1 ㎛ on average. The fine-mode grains mainly consist of coccolithophores, while the coarse-mode grains are mostly comprised of intact or broken planktonic foraminifera. The abundances of coarse-mode and fine-mode GSDs were not correlated with carbonate contents, suggesting a complex control exerted by both the degree of carbonate dissolution and the productivity of coccolithophores on the carbonate-fraction GSDs.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 1994.10a
• /
• pp.21-28
• /
• 1994

The forced vibration with the symmetric boundary condition in nonlinear structure is studied by utilizing the characteristic of the free vibration which have two modes with the similar natural frequency. Two linear modes exist to have no concern with the amplitude. It is found that the normal mode or elliptic orbit as the newly coupled modes is generated in accordance with changing the stability. It is also known that responses for forced vibration having the small external force and damping are near mode of free vibration and the stability for each response is determined according to the stability for each response is determined according to the stability in mode of free vibration. Finally the stability and bifurcation are analyzed in proportion to increment of external force and damping.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.05a
• /
• pp.722-728
• /
• 2001

Applying a general coupled lateral and torsional vibration finite element model of gear pair element this paper intends to look into in detail the coupled lateral and torsional vibration characteristics in a turbo-chiller rotor bearing system, having a bull-pinion speed increasing gear. Investigations have been carried out systematically by comparing the uncoupled and coupled analyses natural vibration frequencies and their mode shapes upon varying the gear mesh stiffness, and also by comparing the strain energies of lateral and torsional vibration modes. Results have shown that some modes may have coupled lateral and torsional mode characteristics as the gear mesh stiffness increases over a certain value, and moreover that their associated dominant modes may be different from their initial modes, i.e., the dominant mode changes from an initial torsional one to a lateral one or from an initial lateral one to a torsional one.

• International Journal of Precision Engineering and Manufacturing
• /
• v.9 no.2
• /
• pp.28-33
• /
• 2008

In a scanning electron microscope (SEM), outside acoustic noise causes image noise that distorts observations of the specimen being examined. A SEM that is less sensitive to acoustic noise is highly desirable. This paper investigates the image noise problem by addressing the mode shapes of the base plate and the transmission path of the acoustic noise and vibration. By arranging the position of the rib, a new SEM base plate was developed that had twisting as the 1st and 2nd modes. In those two twisting modes, vibration nodes existed near the center of the base plate where the specimen chamber is placed. Less vibration was transmitted to the chamber and to the specimen by the twisting modes compared to bending ones, which are the 2nd and 3rd modes for a rectangular plain base plate. An SEM with the developed base plate installed exhibited a significant reduction of image noise when exposed to acoustic noises below 250 Hz.

• Proceedings of the Korean Society of Propulsion Engineers Conference
• /
• 2007.04a
• /
• pp.7-12
• /
• 2007

Swirl injector with multi-stage tangential entry was analyzed to suppress high-frequency combustion instability in Liquid Rocket Engines. In order to analyze the effect of swirl injector as an acoustic absorber, swirl injector was regarded as a quarter-wave resonator and it's damping capacity is verified in atmospheric temperature. It has a finite mode of vibration and natural frequencies which can be tuned to the natural frequencies of a model combustion chamber. When the targeted injector for each modes is located at anti-node point, the amplitude of modes was decreased. And when the injector of large diameter is mounted, the split of mode which accompanies the decrease of amplitude appeared. From the experimental data, it is proved that if the location of injector mounted is located at an anti-node position of the targeted modes with proper volume, the amplitude of modes is decreased and the split of modes occurs at anti-node point.

• Structural Engineering and Mechanics
• /
• v.40 no.5
• /
• pp.637-654
• /
• 2011

The present paper studies the variation of the natural frequencies and mode shapes of rectangular plates carrying a three degree-of-freedom spring-mass system (subsystem), when the subsystem changes (stiffness, mass, moment of inertia, location). An analytical approach based on Lagrange multipliers as well as a finite element formulation are employed and compared. Numerically reliable results are presented for the first time, illustrating the convenience of using the present analytical method which requires only the solution of a linear eigenvalue problem. Results obtained through the variation of the mass, stiffness and moment of inertia of the 3-DOF system can be understood under the effective mass concept or Rayleigh's statement. The analysis of frequency values of the whole system, when the 3-DOF system approaches or moves away from the center, shows that the variations depend on each particular mode of vibration. When the 3-DOF system is placed in the center of the plate, "new" modes are found to be a combination of the subsystem's modes (two rotations, traslation) and the bare plate's modes that possess the same symmetry. This situation no longer exists as the 3-DOF system moves away from the center of the plate, since different bare plate's modes enable distinct motions of the 3-DOF system contributing differently to the "new' modes as its location is modified. Also the natural frequencies of the compound system are nearly uncoupled have been calculated by means of a first order eigenvalue perturbation analysis.

• Proceedings of the Computational Structural Engineering Institute Conference
• /
• 2004.04a
• /
• pp.41-47
• /
• 2004

The objective of this paper is to monitor damage in beam-type structures by using time history of natural frequencies. First, numerical experiments on test beams are described, Dynamic responses of the test structures are obtained for several damage scenarios in a consequent order. Next, the time history of natural frequencies are extracted for the first four modes from the dynamic responses of the test structures. Finally, damage detection in the test structures is performed using the time-history of natural frequencies.

• Structural Engineering and Mechanics
• /
• v.6 no.5
• /
• pp.517-527
• /
• 1998

This paper describes an exact method of analysis for natural vibration of diagonal networks by considering an equivalent cyclic periodic structure and adopting the double U-transformation technique. Both a lumped mass system and a distributed mass system are considered to investigate the diagonal networks. The exact solution for the frequency equations and the natural modes of the networks can be derived. As numerical examples, square diagonal cable networks with different meshes are worked out.