• Transactions of the Korean Society for Noise and Vibration Engineering
• /
• v.20 no.11
• /
• pp.1058-1063
• /
• 2010

The vibration analysis of a rotating cantilever beam with tip mass was studied by using DTM(differential transformation method). DTM is one of the numerical methods, for finding series solutions by transforming differential equations to algebraic ones similar with Laplace transform. The advantages of the DTM are that it is easy to understand and is effective in finding numerical solutions. Applying DTM, the natural frequencies of a rotating cantilever beam were obtained taking into consideration the effects of tip mass. Also, convergence study of DTM was performed to decide the number of terms used in eigenvalue problems. Numerical results obtained by DTM show good agreement with those by other methods. As a result, it is expected that DTM can be a useful method in vibration analysis such as that of a rotating cantilever beam with tip mass.

• Smart Structures and Systems
• /
• v.25 no.6
• /
• pp.669-678
• /
• 2020

This paper focuses on the free vibration analysis of axially functionally graded (FG) Euler-Bernoulli beams. The material properties of the beams are assumed to obey the linear law distribution. The complexities in solving differential equation of transverse vibration of composite beams which limit the analytical solution to some special cases are overcome using the Differential Transformation Method (DTM). Natural frequencies and corresponding normalized mode shapes are calculated. Validation targets are experimental data or finite element results. Different parameters such as reinforcement distribution, ratio of the reinforcement Young's modulus to the matrix Young's modulus and ratio of the reinforcement density to the matrix density are taken into investigation. The delivered results prove the capability and the robustness of the applied method. The studied parameters are demonstrated to be very crucial for the normalized natural frequencies and mode shapes.

• Proceedings of the Korean Society of Precision Engineering Conference
• /
• 2006.05a
• /
• pp.87-88
• /
• 2006

The phase transformation behaviors of Ni-Ti shape memory alloys were investigated through a DSC(Differential Scanning Calorimetry). The annealing temperatures were applied from $600^{\circ}C,\;700^{\circ}C,\;800^{\circ}C,\;and\;900^{\circ}C$ for their effects on the phase transformation behaviors. Based on the results of DSC, phase transformation behaviors of shape memory alloys can be predicted by Liang's phase transformation model or Tanaka's phase transformation model.

• Journal of applied mathematics & informatics
• /
• v.27 no.3_4
• /
• pp.757-762
• /
• 2009

In allelic model $X\;=\;(x_1,\;x_2,\;{\cdots},\;x_d)$, $$M_f(t)\;=\;f(p(t))\;-\;{\int}^t_0\;Lf(p(t))ds$$ is a P-martingale for diffusion operator L under the certain conditions. We can also obtain a new diffusion operator $L^*$ for diffusion coefficient and we prove that unique solution for $L^*$-martingale problem exists. In this note, we define new symmetric preserving transformation. Uniqueness for martingale problem and symmetric property will be proved.

• Proceedings of the KSR Conference
• /
• 2004.10a
• /
• pp.611-615
• /
• 2004

To obtain material properties of NiTi shape memory alloy showing pseudoelastic or shape memory effect, tensile test was conducted for various temperatures. Transformation temperature also was measured by using DSC(Differential Scanning Calorimeter), and crystallographic feature of transformation was observed by XRD(X-ray Diffraction).

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1165-1176
• /
• 2009

This paper is concerned with the interval oscillation of the second order nonlinear ordinary differential equation (r(t)|y'(t)|$^{{\alpha}-1}$ y'(t))'+p(t)|y'(t)|$^{{\alpha}-1}$ y'(t)+q(t)f(y(t))g(y'(t))=0. By constructing ageneralized Riccati transformation and using the method of averaging techniques, we establish some interval oscillation criteria when f(y) is not differetiable but satisfies the condition $\frac{f(y)}{|y|^{{\alpha}-1}y}$ ${\geq}{\mu}_0$ > 0 for $y{\neq}0$.

• Honam Mathematical Journal
• /
• v.38 no.4
• /
• pp.693-699
• /
• 2016

The purpose of this note is to provide an alternative proof of two quadratic transformations contiguous to that of Kummer using a differential equation approach.

• Journal of KSNVE
• /
• v.10 no.5
• /
• pp.800-805
• /
• 2000

To determine the modal matrix and modal frequency of engine mount system, we most solve so-called eigen-value problem. However eigen-value problem of engine mount system with hydraulic mount can not be solved by general eigne-analysis algorithm because the properties of hydraulic mount vary with frequency. so in this paper the method for modal analysis of rigid body motions of an engine supported by hydraulic mount is proposed. Natural frequencies and mode shapes of this nonlinear system are obtained by using complex exponential method and Laplace transformation method. In time domain, impulse response functions are calculated by (two-sided) discrete inverse Fourier Transformation of forced frequency response functions achieved by Laplace transformation of the differential equation of motion. Considering the fact that frequency response functions synthesized by modal parameters form proposed method are in good agreement with original FRFs, it is proved that the proposed method is very efficient and useful for the analysis of eigne-value problem of hydraulic engine mount system.

• Journal of Powder Materials
• /
• v.8 no.1
• /
• pp.42-49
• /
• 2001

Ti-50Ni(at%) and Ti-40Ni-10Cu(at%) alloy powders have been fabricated by ball milling method, and their microstructure and phase transformation behavior were investigated by means of scanning electron microscopy/energy dispersive spectrometry, differential scanning calorimetry (DSC), X-ray diffractions and transmission electron microscopy. In order to investigate the effect of ball milling conditions on transformation behavior, ball milling speed and time were varied. Ti-50Ni alloy powders fabricated with the milling speed more than 250 rpm were amorphous, while those done with the milling speed of 100rpm were crystalline. In contrast to Ti-50Ni alloy powders, Ti-40Ni-10Cu alloy powders were crystalline, irrespective of ball milling conditions. DSC peaks corresponding to martensitic transformation were almost discernable in alloy powders fabricated with the milling speed more than 250 rpm, while those were seen clearly in alloy powders fabricated with the milling speed of 100 rpm. This was attributed to the fact that a strain energy introduced during ball milling suppressed martensitic transformation.

• Bulletin of the Society of Naval Architects of Korea
• /
• v.13 no.3
• /
• pp.11-19
• /
• 1976

Grillages are abundant in ship structures and in many other types of structures such as bridges and building floors. Clarkson has shown that plated grillages can be satisfactorily analyzed as gridworks if an appropriate effective breadth is taken into account. Also, it has previously been pointed out, by Nielsen, that grillage calculations could be simplified by use of the Laplace transformation. In this paper, it is assumed that the torsional rigidity of the members and axial load are negligible, also that girders have the same scantling and spacing each other and so stiffeners do. Then the grillages composed of both-end-fixed girders and both-end-hinged stiffeners, which are subjected only to uniform normal loads are investigated. The calculus of variation is used to set up the differential equations and the Laplace transformation is applied to solve the differential equations. The program has been tested by FACOM 28 and the results show good agreements with those by the STRESS, which was developed in M.I.T.. The amount of the data input and computing time are much less than those of the STRESS. But this program has so much restrictions that it is urgent to extend the program to the grillage problems of arbitrary loading and boundary conditions.