• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2006년도 춘계학술대회논문집
• /
• pp.1354-1359
• /
• 2006

A modeling method for the vibration analysis of rotating multi-blade systems considering the coupling stiffness effect is presented in this paper. Blades are assumed as cantilever beams and the coupling stiffness effect originates from disc or shroud between blades. As the angular speed, hub radius ratio, and the coupling stiffness vary, the natural frequencies of the system vary. Numerical results show that the coupling stiffness is very important to estimate the natural frequencies. Along with the natural frequencies, associated mode shapes, critical angular speed, and critical hub radius ratio are obtained through the analysis.

• Structural Engineering and Mechanics
• /
• 제33권6호
• /
• pp.747-763
• /
• 2009

In this work, the linear vibration characteristics of $90^{\circ}$ pipe bends and their cylindrical and toroidal shell components are studied. The finite element method, based on shear-deformation shell elements, is used to carry out a vibration analysis of metallic multiple $90^{\circ}$ mitred pipe bends. Single, double, and triple mitred bends are considered, as well as a smooth bend. Sample natural frequencies and mode shapes are given. To validate the procedure, comparison of the natural frequencies is made with existing results for cylindrical and toroidal shells. The influence of the multiplicity of the bend, the boundary conditions, and the various geometric parameters on the natural frequency is described. The differential quadrature method, based on classical shell theory, is used to study the vibration of components of these bends. Regression formulas are derived for cylindrical shells (straight pipes) with one or two oblique edges, and for sectorial toroidal shells (curved pipes, pipe elbows). Two types of support are considered for each case. The results given provide information about the vibration characteristics of pipe bends over a wide range of the geometric parameters.

• Structural Engineering and Mechanics
• /
• 제9권5호
• /
• pp.449-467
• /
• 2000

The natural frequencies and the corresponding mode shapes of a non-uniform beam carrying multiple point masses are determined by using the analytical-and-numerical-combined method. To confirm the reliability of the last approach, all the presented results are compared with those obtained from the existing literature or the conventional finite element method and close agreement is achieved. For a "uniform" beam, the natural frequencies and mode shapes of the "clamped-hinged" beam are exactly equal to those of the "hinged-clamped" beam so that one eigenvalue equation is available for two boundary conditions, but this is not true for a "non-uniform" beam. To improve this drawback, a simple transformation function ${\varphi}({\xi})=(e+{\xi}{\alpha})^2$ is presented. Where ${\xi}=x/L$ is the ratio of the axial coordinate x to the beam length L, ${\alpha}$ is a taper constant for the non-uniform beam, e=1.0 for "positive" taper and e=1.0+$|{\alpha}|$ for "negative" taper (where $|{\alpha}|$ is the absolute value of ${\alpha}$). Based on the last function, the eigenvalue equation for a non-uniform beam with "positive" taper (with increasingly varying stiffness) is also available for that with "negative" taper (with decreasingly varying stiffness) so that half of the effort may be saved. For the purpose of comparison, the eigenvalue equations for a positively-tapered beam with five types of boundary conditions are derived. Besides, a general expression for the "normal" mode shapes of the non-uniform beam is also presented.

• Journal of KSNVE
• /
• 제7권6호
• /
• pp.1049-1058
• /
• 1997

To verify the Finite Element Method(FEM) model of an Exhaust System, Frequency Response Function(FRF) is utilized. Up to now, generally, comparisons of natural frequencies and mode shapes of the Exhaust System between numerical analysis and experimental results are adopted to prove completion of the FEM model. However, the comparisons of natural frequencies and mode shapes are not sufficient to have the perfect FEM model of the Exhaust system. Instead of these comparisons. FRF method is introduced for the more accurate FEM model.

• Transactions of the Korean Society of Mechanical Engineers
• /
• 제10권3호
• /
• pp.383-391
• /
• 1986

Mode shapes and natural frequencies of the bell type shell are analyzed numerically by the finite element method. The impulse hammer method and the Fast Fourier Transform analyzer are used for the experimental test. All types of mode shapes are expressed by the computer graphics. Numerical solutions are good agreement with the experimental results. The sustaining sound of the typical bell-type shell depend upon the first flexural mode (0-2 mode) and the second flexural mode (0-3 mode), and their mode shapes are independent upon thickness Dangjwas, holes, and added mass effects. Asymmetric effects by Dangjwas, holes and added mass give rise to beat frequencies, and the added mass is found to be most effective.

• Structural Engineering and Mechanics
• /
• 제61권5호
• /
• pp.617-624
• /
• 2017

Piezoelectric nanobeams are used in several nano electromechanical systems. The first step in designing these systems is conducting a vibration analysis. In this research, the free vibration of a piezoelectric nanobeam is analyzed by using the nonlocal elasticity theory. The nanobeam is modeled based on Euler-Bernoulli beam theory. Hamilton's principle is used to derive the equations of motion and also the boundary conditions of the system. The obtained equations of motion are solved by using both Galerkin and the Differential Quadrature (DQ) methods. The clamped-clamped and cantilever boundary conditions are analyzed and the effects of the applied voltage and nonlocal parameter on the natural frequencies and mode shapes are studied. The results show the success of Galerkin method in determining the natural frequencies. The results also show the influence of the nonlocal parameter on the natural frequencies. Increasing a positive voltage decreases the natural frequencies, while increasing a negative voltage increases them. It is also concluded that for the clamped parts of the beam and also other parts that encounter higher values of stress during free vibrations of the beam, anti-nodes in voltage mode shapes are observed. On the contrary, in the parts of the beam that the values of the induced stress are low, the values of the amplitude of the voltage mode shape are not significant. The obtained results and especially the mode shapes can be used in future studies on the forced vibrations of piezoelectric nanobeams based on Galerkin method.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2001년도 춘계학술대회논문집
• /
• pp.668-674
• /
• 2001

An experimental study was performed for two types of co-axial cylindrical shell structures in order to establish the relationship between in-air dynamic characteristics and in-water ones and to observe hydrodynamic mass effects on their mode shapes when submerged. The outer cylinders are prepared with two kinds to get more insights on the fluid-structure interaction phenomena: one is flexible, which means that the outer cylinder has almost same stiffness as the inner one, and the other is a rigid one whose stiffness is more than ten times of the inner one's(it might be regarded as the scaled-down model of the reactor internals). The finite element. analyses were also implemented to support the experimental results. The results show that the natural frequencies of a co-axial cylindrical shell structure in water are remarkably lower than those in air due to the fluid mass effects. In case of the flexible-to-flexible cylinders, there exist in-phase and out-of-phase mode shapes and they are affected by the annular gap between the. co-axial cylinders. For the in-phase mode the in-water natural frequency decreases exponentially as the gap increases, while it slightly increases in case of the out-of-phase mode due to the squeezing effect of the gap fluid. In the flexible-to-rigid case, the normalized natural frequency(in-water frequency/in-air one) of the inner cylinder(core barrel model) ranges between in-phase and out-of-phase mode frequencies of the flexible-to-flexible co-axial cylindrical structure having identical dimensions. Also the normalized natural frequency of the inner cylinder of the flexible-to-rigid one moves from near of the in-phase mode frequency into the out-of-phase mode value of the flexible-to-flexible case as circumferential mode number(n) increases.

• Transactions of the Korean Society of Mechanical Engineers A
• /
• 제27권3호
• /
• pp.424-431
• /
• 2003

The spacer grid is one of the main structural components in the fuel assembly, which supports the fuel rods and maintains coolable geometry from an external load. A vibration test and a finite element analysis using ABAQUS on a dummy fuel rod continuously supported by Optimized H type(OHT) and New Doublet (ND) spacer grids arc performed to obtain the vibration characteristics such as natural frequencies and mode shapes an(1 to verify a finite element model. The results from the test and the finite element analysis are compared by modal assurance criteria (MAC) values. It is resulted that MACs for the first, the third and the fifth mode shapes are relatively good as compared with those of the second an(1 fourth ones. The natural frequency differences between two methods as well as the mode comparison results for the rod with OHT spacer grid are better than those with ND spacer grid. It is judged that the FE model for the ND spacer grid spring should be modified to consider the long contact length which actually happen when the spring supports the rod.

• Transactions of the Korean Society of Mechanical Engineers
• /
• 제16권5호
• /
• pp.849-863
• /
• 1992

A very simple and computationally efficient numerical method is developed for the free vibration of isotropic and orthotropic composite triangular plates. A set of two-dimensional simple series functions is used as an admissible displacement functions in the Rayleigh-Ritz method to obtain the natural frequencies, nodal patterns and mode shapes for the plates. From the prescribed starting function satisfying only the geometric boundary conditions, the higher terms in the series functions are constructed with adding order of polynominal. Natural frequencies, nodal patterns and mode shapes are obtained for right triangular plates with three different support conditions. The obtained numerical results are presented, and the isotropic and some orthotropic cases are verified with other numerical methods in the liternature.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 한국소음진동공학회 2002년도 춘계학술대회논문집
• /
• pp.429-434
• /
• 2002

The differential equations governing in-plane free vibrations of stepped circular arcs, including the effects of axial deformation, rotatory inertia and shear deformation, are derived and solved numerically to obtain frequencies and mode shapes. Numerical results are calculated for the clamped-clamped symmetric and unsymmetric circular arcs with thickness varying in a discontinuous fashion. The lowest four natural frequencies and mode shapes are presented over a range of non-dimensional system parameters: the subtended angle, the slenderness ratio, the section ratio and the ratio of discontinuous section.