• Structural Engineering and Mechanics
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• v.60 no.3
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• pp.489-505
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• 2016

Sinusoidal shear deformation theory (SSDT) is developed here for dynamic buckling of functionally graded (FG) nano-plates. The material properties of plate are assumed to vary according to power law distribution of the volume fraction of the constituents. In order to present a realistic model, the structural damping of nano-structure is considered using Kelvin-Voigt model. The surrounding elastic medium is modeled with a novel foundation namely as orthotropic visco-Pasternak medium. Size effects are incorporated based on Eringen'n nonlocal theory. Equations of motion are derived from the Hamilton's principle. The differential quadrature method (DQM) in conjunction with Bolotin method is applied for obtaining the dynamic instability region (DIR). The detailed parametric study is conducted, focusing on the combined effects of the nonlocal parameter, orthotropic visco-Pasternak foundation, power index of FG plate, structural damping and boundary conditions on the dynamic instability of system. The results are compared with those of first order shear deformation theory and higher-order shear deformation theory. It can be concluded that the proposed theory is accurate and efficient in predicting the dynamic buckling responses of system.

• Structural Engineering and Mechanics
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• v.55 no.2
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• pp.435-459
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• 2015

Parametric resonance of shear deformable composite skew plates subjected to non-uniform (parabolic) and linearly varying periodic edge loading is studied for different boundary conditions. The skew plate structural model is based on higher order shear deformation theory (HSDT), which accurately predicts the numerical results for thick skew plate. The total energy functional is derived for the skew plates from total potential energy and kinetic energy of the plate. The strain energy which is the part of total potential energy contains membrane energy, bending energy, additional bending energy due to additional change in curvature and shear energy due to shear deformation, respectively. The total energy functional is solved using Rayleigh-Ritz method in conjunction with boundary characteristics orthonormal polynomials (BCOPs) functions. The orthonormal polynomials are generated for unit square domain using Gram-Schmidt orthogonalization process. Bolotin method is followed to obtain the boundaries of parametric resonance region with higher order approximation. These boundaries are traced by the periodic solution of Mathieu-Hill equations with period T and 2T. Effect of various parameters like skew angle, span-to-thickness ratio, aspect ratio, boundary conditions, static load factor on parametric resonance of skew plate have been investigated. The investigation also includes influence of different types of linearly varying loading and parabolically varying bi-axial loading.

• Advances in nano research
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• v.9 no.3
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• pp.133-145
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• 2020

In this study, nonlinear vibrations and dynamic instabilities of a smart embedded micro shell conveying varied fluid flow and subjected to the combined electro-thermo-mechanical loadings are investigated. With the aim of designing new hydraulic sensors and actuators, the piezoelectric materials are employed for the body and the effects of applying electric field on the stability of the system as well as the induced voltage due to the dynamic behavior of the system are studied. The nonlocal piezoelasticity theory and the nonlinear cylindrical shell model in conjunction with the energy approach are utilized to mathematically modeling of the structure. The fluid flow is assumed to be isentropic, incompressible and fully develop, and for more generality of the problem both steady and time dependent flow regimes are considered. The mathematical modeling of fluid flow is also carried out based on a scalar potential function, time mean Navier-Stokes equations and the theory of slip boundary condition. Employing the modified Lagrange equations for open systems, the nonlinear coupled governing equations of motion are achieved and solved via the state space problem; forth order numerical integration and Bolotin's method. In the numerical results, a comprehensive discussion is made on the dynamical instabilities of the system (such as divergence, flutter and parametric resonance). We found that applying positive electric potential field will improve the stability of the system as an actuator or vibration amplitude controller in the micro electro mechanical systems.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2004.05a
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• pp.601-606
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• 2004

This paper deals with friction-induced vibration of disc brake system under constant friction coefficient. A linear, lumped and distributed parameter model to represent the floating caliper disc brake system is proposed. The complex eigenvalues are used to investigate the dynamic stability and in order to verify simulations which are based on the theoretical model, the experimental modal test and the dynamometer test are performed. The comparison of experimental and theoretical results shows a good agreement and the analysis indicates that mode coupling due to friction force is responsible for disc brake squeal. And squeal type instability is investigated by using the parametric analysis. This indicates parameters which have influence on the propensity of brake squeal. This helped to validate the analysis model and establish confidence in the analysis results. Also they may be useful during system development or diagnostic analysis.

• Journal of KSNVE
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• v.9 no.6
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• pp.1210-1217
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• 1999

This paper presents schematic process of identifying the principal cause to make the vibration problem of rotating circular saws. In the tandem pencil slat saw lines, feeding of cedar blocks is often stopped because excessive motro current is required in a saw motor. These events are called "kick-offs" in technical reports. Research on saw behavior at kick-offs is required to understand are reduce the frequency and severity of kick-offs events. This research aims at finding out the principal cause of kick-offs, and evloving design improvements for high cutting performance with fewer and less severe kick-offs. Measurements of critical speed, cutting force, cutting temeprature and dynamic displacements are carried out to observe the instability mechanism and also to obtain saw design parameters for the numerical analyses. And the numerical analyses involving FEM and multiple scale method are utilized to show the possibility of the principal cause.pal cause.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.14 no.8
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• pp.702-708
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• 2004

This paper deals with friction-induced vibration of disc brake system under constant friction coefficient. A linear, lumped and distributed parameter model to represent the floating caliper disc brake system is proposed. The complex eigenvalues are used to investigate the dynamic stability and in order to verify simulations which are based on the theoretical model, the experimental modal test and the dynamometer test are performed. The comparison of experimental and theoretical results shows a good agreement and the analysis indicates that mode coupling due to friction force is responsible for disc brake squeal. And squeal type Instability is Investigated by using the parametric analysis. This indicates parameters which have influence on the propensity of brake squeal. This helped to validate the analysis model and establish confidence in the analysis results. Also they may be useful during system development or diagnostic analysis.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2006.05a
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• pp.171-176
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• 2006

An experimental study on a fuel-rich gas generator was carried out. Thirty seven double-swirl injectors with recess number of 1.5 were distributed and installed in the injector head, which significantly influences the combustion performance. In the paper, the characteristics of combustion stability are inspected by the parametric varations such as changing length and diameter of a combustion chamber and installing a turbulence ring. The experimental results show that as a resonant frequency took place in a high region, the amplitude of the dynamic pressure generally diminished, however, the combustion instability could not be suppressed perfectly.

• Advances in aircraft and spacecraft science
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• v.3 no.3
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• pp.271-298
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• 2016

In this paper, we study a problem of passive suppression of helicopter Ground Resonance (GR) using a single degree freedom Nonlinear Energy Sink (NES), GR is a dynamic instability involving the coupling of the blades motion in the rotational plane (i.e. the lag motion) and the helicopter fuselage motion. A reduced linear system reproducing GR instability is used. It is obtained using successively Coleman transformation and binormal transformation. The analysis of the steadystate responses of this model is performed when a NES is attached on the helicopter fuselage. The NES involves an essential cubic restoring force and a linear damping force. The analysis is achieved applying complexification-averaging method. The resulting slow-flow model is finally analyzed using multiple scale approach. Four steady-state responses corresponding to complete suppression, partial suppression through strongly modulated response, partial suppression through periodic response and no suppression of the GR are highlighted. An algorithm based on simple criterions is developed to predict these steady-state response regimes. Numerical simulations of the complete system confirm this analysis of the slow-flow dynamics. A parametric analysis of the influence of the NES damping coefficient and the rotor speed on the response regime is finally proposed.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2000.06a
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• pp.718-723
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• 2000

Dynamic stability of an axially oscillating cantilever beam with a concentrated mass is investigated in this paper. The equations of motion are derived and the derived equations include harmonically oscillating parameters which originate from the motion-induced stiffness variation. Under certain conditions of the frequency and the amplitude of oscillating motion, parametric instabilities may occur. The multiple scale perturbation method is employed to obtain the stability analysis results. It is found that the system stability varies with the magnitude or the location of the concentrated mass. Instability increases as the concentrated mass approaches to the free-end or its magnitude increases.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.26 no.12
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• pp.2647-2655
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• 2002

This research presents an analytical model to investigate the stability due to the ball bearing waviness i n a rotating system supported by two ball bearings. The stiffness of a ball bearing changes periodically due to the waviness in the rolling elements as the rotor rotates, and it can be calculated by differentiating the nonlinear contact forces. The linearized equations of motion can be represented as a parametrically excited system in the form of Mathieu's equation, because the stiffness coefficients have time -varying components due to the waviness. Their solution can be assumed as a Fourier series expansion so that the equations of motion can be rewritten as the simultaneous algebraic equations with respect to the Fourier coefficients. Then, stability can be determined by solving the Hill's infinite determinant of these algebraic equations. The validity of this research is proved by comparing the stability chart with the time responses of the vibration model suggested by prior researches. This research shows that the waviness in the rolling elements of a ball bearing generates the time-varying component of the stiffness coefficient, whose frequency is called the frequency of the parametric excitation. It also shows that the instability takes place from the positions in which the ratio of the natural frequency to the frequency of the parametric excitation corresponds to i/2 (i=1,2,3..).