• Advances in nano research
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• v.14 no.2
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• pp.127-139
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• 2023

This paper studies the free vibration behavior of bi-dimensional functionally graded (BFG) nanobeams subjected to arbitrary boundary conditions. According to Eringen's nonlocal theory and Hamilton's principle, the underlying equations of motion have been obtained for BFG nanobeams. Moreover, the variable substitution method is utilized to establish the structure's state-space differential equations, followed by forming the dynamic stiffness matrix based on state-space differential equations. In order to compute the natural frequencies, the current study utilizes the Wittrick-Williams algorithm as a solution technique. Moreover, the nonlinear vibration frequencies calculated by employing the proposed method are compared to the frequencies obtained in previous studies to evaluate the proposed method's performance. Some illustrative numerical examples are also given in order to study the impacts of the nonlocal parameters, material property gradient indices, nanobeam length, and boundary conditions on the BFG nanobeam's frequency. It is found that reducing the nonlocal parameter will usually result in increased vibration frequencies.

• Advances in aircraft and spacecraft science
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• v.5 no.1
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• pp.107-128
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• 2018

Thermo-mechanical vibration of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) is investigated within the framework of Timoshenko beam theory. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture and are considered to be temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and are solved using an efficient semi-analytical technique of the differential transform method (DTM). Comparison between the results of the present work and those available in literature shows the accuracy of this method. A parametric study is conducted to study the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and various boundary conditions on free vibration behavior of sandwich beams with FG-CNTRC face sheets. It is explicitly shown that the vibration characteristics of the curved nanosize beams are significantly influenced by the surface density effects.

• Smart Structures and Systems
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• v.20 no.3
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• pp.351-368
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• 2017

To peruse the free vibration of curved functionally graded piezoelectric (FGP) nanosize beam in thermal environment, nonlocal elasticity theory is applied for modeling the nano scale effect. The governing equations are obtained via the energy method. Analytically Navier solution is employed to solve the governing equations for simply supported boundary conditions. Solving these equations enables us to estimate the natural frequency for curved FGP nanobeam under the effect of a uniform temperature change and external electric voltage. The results determined are verified by comparing the results by available ones in literature. The effects of various parameters such as nonlocality, uniform temperature changes, external electric voltage, gradient index, opening angle and aspect ratio of curved FGP nanobeam on the natural frequency are successfully discussed. The results revealed that the natural frequency of curved FGP nanobeam is significantly influenced by these effects.

• Structural Engineering and Mechanics
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• v.53 no.4
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• pp.625-644
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• 2015

In this paper, a two-layer partial interaction composite beams model considering the higher order shear deformation of sub-elements is built. Then, the governing differential equations and boundary conditions for static analysis of linear elastic higher order composite beams are formulated by means of principle of minimum potential energy. Subsequently, analytical solutions for cantilever composite beams subjected to uniform load are presented by Laplace transform technique. As a comparison, FEM for this problem is also developed, and the results of the proposed FE program are in good agreement with the analytical ones which demonstrates the reliability of the presented exact and finite element methods. Finally, parametric studies are performed to investigate the influences of parameters including rigidity of shear connectors, ratio of shear modulus and slenderness ratio, on deflections of cantilever composite beams, internal forces and stresses. It is revealed that the interfacial slip has a major effect on the deflection, the distribution of internal forces and the stresses.

• Transactions of the Korean Society of Mechanical Engineers
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• v.15 no.2
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• pp.455-462
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• 1991

This paper present an analysis method of crankshaft of four cylinder internal combustion engine for studying dynamic characteristics of the shaft. For simple analysis, uniform sections of journal, pin and arm parts were assumed. Transfer Matrix Method was used, considering branched part and coordinate transformation part. Natural frequencies, natural modes and transfer functions of crank shaft were investigated based upon the Timosenko beam theory: It was shown that the calculated natural frequencies, modeshapes agree well with the experimental results.

• Journal of Ocean Engineering and Technology
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• v.10 no.3
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• pp.3-13
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• 1996

An extensive research programme has been aimed at the effct of ship weight distribution on the ship responses applying ship hydroelasticity theory. In the previous works, consistent tendencies of the still-water and the wave bending moments. respectively, were found as the weight distribution was varied systematically. The paper is therefore concerned mainly with any correlation between still-water and wave bending moments with the variations of weight distribution. Although these bending moments share different features with each other, such a comparison of tendencies was plausible and informative. These and other matters for the future are discussed.

• Journal of the Korean Society of Manufacturing Technology Engineers
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• v.9 no.4
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• pp.99-107
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• 2000

In this study, a static and dynamic characteristics analysis system for machine tool spindle systems with 3 lobe sliding bearing is developed based on Timoshenko theory, finite element method and windows programming techniques. And the characteristics value of 3 lobe sliding bearing such as eccentricity ratio, attitude angle, friction coefficient , stiffness coefficients, damping coefficients and so on, are determined by using the thermal equilibrium conditions of spindle systems. Since the developed system has various analysis modules related to static deformation analysis, modal analysis, frequency responses analysis and so on, it can be utilized to perform systematically the design an devaluation process of spindle systems with 3 lobe sliding bearing under windows GUI environment.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.846-851
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• 1995

A motor-integrated high-speed spindle system with .psi. 65*25, 000rpm is modeled for analytical and experimental studies related to the dynamic characteristics. And the systematic and rational identification processes for evaluating the material properties of spindle and built-in motor is introduced. The impulse excitation method is applied for the experimental model testing, and the dynamic characteristics of test model is theoretically analysed by using the finite element method based on Timoshenko theory. Especially, the experimental and theoetical results reveal that the test model under the required operational conditions has no critical problem for dynamic characteristics.

• Proceedings of the Korean Society of Precision Engineering Conference
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• 1995.10a
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• pp.836-840
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• 1995

Recently, the motor-integrated spindle spindle systems have been used to simplify the machine tool structure, to improve the motion flexibility of machine tool, and to perform the high-speed machining. In this study, a static and dynamic analysis system for motor-integrated high-speed spindle systems is developed based on Timoshenko theory, finite element method and windows programming techniques. Since the system has various analysis modules related to static deformation analysis, modal analysis, frequency response analysis, unbalance response analysis and so on, it is useful in performing systematically the design and evaluation processes of motor-integrated high-speed spindle systems under windows GUI encironment.

• Structural Engineering and Mechanics
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• v.51 no.1
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• pp.111-130
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• 2014

The aim of this study is to investigate the effects of the beam aspect ratio(L/h), hole diameter, hole location and stacking layer sequence ($[0/45/-45/90]_s$, $[45/0/-45/90]_s$ and $[90/45/-45/0]_s$) on natural frequencies of glass/epoxy perforated beams under room and high (40, 60, 80, and $100^{\circ}C$) temperatures for the common clamped-free boundary conditions (cantilever beam). The first three out of plane bending free vibration of symmetric laminated beams is studied by Timoshenko's first order shear deformation theory. For the numerical analyses, ANSYS 13.0 software package is utilized. The results show that the hole diameter, stacking layer sequence and hole location have important effect especially on the second and third mode natural frequency values for the short beams and the high temperatures affects the natural frequency values significantly. The results are presented in tabular and graphical form.