• 한국철도학회:학술대회논문집
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• 한국철도학회 2010년도 춘계학술대회 논문집
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• pp.13-17
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• 2010

This presentation examines the characteristics of torsional vibration in axisymmetric out-of-plane vibrations of an annular Mindin plate. The out-of-plane vibration of circular or annular plates have been investigated since a long years ago by many researchers. When the classical Kirchhoff plate theory neglecting the effect of transverse shear deformation is applied to a thick plate, its out-of-plane natural frequencies are much different from reality. And so, since Minlin presented a plate theory considering the effect of rotary inertia and transverse shear deformation, many researches for the out-of-plane natural vibration of circular or annular Mindin plates have been performed. But almost all researchers missed the torsional vibration due to transverse shear deformation in axisymmetric out-of-plane vibrations of the circular or annular Mindin plate. Therefore, in this presentation, we verify the existence of torsional vibration of an annular plate and present the natural frequencies of an annular plate with free outer boundary surface.

• Wind and Structures
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• 제9권1호
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• pp.1-22
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• 2006

The response characteristics and suppression of flow-induced vibrations of rectangular prisms with various width-to-depth ratios were experimentally investigated. The prisms were rigid and elastically mounted at both ends to enable constrained torsional vibrations only. The present study focused on torsional vibrations, one of the three types of flow-induced vibrations generated in a rectangular prism. First, the response characteristics of torsional vibrations generated in rectangular prisms were investigated by free-vibration tests. It was found that the response characteristics of torsional vibrations generated in rectangular prisms could be classified into six patterns depending on the width-to-depth ratio. Next, the response characteristics of torsional vibrations observed in the free-vibration tests were reproduced by forced-vibration tests, and the mechanisms by which the three types of flow-induced vibrations, low-speed torsional flutter, vortex excitation and high-speed torsional flutter, are generated in the rectangular prisms were elucidated on the basis of characteristics of fluid forces and visualized flow patterns. Experiments were also carried out to establish an effective method for suppressing flow-induced vibrations generated in the rectangular prisms, and it was found that low-speed torsional flutter and high-speed torsional flutter could be suppressed by placing a small normal plate upstream of the prism, which results in suppression of the alternating rolling-up of the shear layers separating from the leading edges of the prism. It was also found that vortex excitation could be suppressed by placing a splitter plate downstream of the prism, which results in suppression of the generation of wake vortices.

• 한국소음진동공학회:학술대회논문집
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• 한국소음진동공학회 2001년도 춘계학술대회논문집
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• pp.295-301
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• 2001

An investigation into asymmetric vibrations of a clamped circular plate under a hannonic excitation is made. We examine a primary resonance, in which the frequency of excitation is near the natural frequency of an asymmetric mode of the plate. We found not only a response having the form of standing wave but also one having the form of traveling wave, which was not observed by Sridhar, Mook and Nayfeh(1978; Journal of Sound and Vibration 59(2), pp. 159-170).

• Structural Engineering and Mechanics
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• 제83권4호
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• pp.451-463
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• 2022

The present study deals with forced vibrations of an elastic circular plate supported along its circular edge by unilateral elastic springs. The plate is assumed to be subjected to a uniformly distributed and a concentrated load. Under the combination of these loads, equations of motion are explicitly derived for static and dynamic response analyses by assuming a series of the displacement functions of time and other unknown parameters which are to be determined by employing Lagrangian functional. The approximate solution is sought by applying the Lagrange equations of motions by using the potential energy of the external forces that includes the contributions of the edge forces and the external moments, i.e., those of the effects of the boundary condition to the analysis. For the numerical treatment of the problem in the time domain, the linear acceleration procedure is adopted. The tensionless character of the support is taken into account by using an iterative process and, the coordinate functions for the displacement field are selected to partially fulfill the boundary conditions so that an acceptable approximation can be achieved faster. Numerical results are presented in the figures focusing on the nonlinearity of the problem due to the plate lift-off from the unilateral springs at the edge support.

• Smart Structures and Systems
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• 제12권5호
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• pp.547-577
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• 2013

To suppress vibration and noise of mechanical structures piezoelectric ceramics play an increasing role as effective, simple and light-weighted damping devices as they are suitable for sensing and actuating. Out of the various piezoelectric damping methods this paper compares mode based active control strategies to passive shunt damping for thin plates. Therefore, a new approach for the optimal placement of the piezoelectric sensors/actuators, or more general transducers, is proposed after intense theoretical investigations based on the Kirchhoff kinematical hypotheses of plates; in particular, modal and nilpotent transducers are discussed in detail. Based on the proposed distribution a discrete design for modal transducers is implemented, tested and verified on an experimental setup. For active control the modal sensors clearly identify the eigenmodes, whereas the modal actuators impose distributed eigenstrains in order to reduce the transverse plate vibrations. In contrast to the modal control, passive shunt damping works without requiring additional actuators or auxiliary power and can therefore act as an autonomous system, but it is less effective compensating the flexible vibrations. Exemplarily, an acryl glass plate disturbed by an arbitrary force initialized by a loudspeaker is investigated. Comparing the different methods their specific advantages are highlighted and a significant broadband reduction of the vibrations of up to -20dB is obtained.

• 대한조선학회지
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• 제24권3호
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• pp.35-42
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• 1987

For the analysis of natural vibrations of a rectangular stiffened plate with inner cutouts, an application of the Rayleigh-Ritz method is investigated. In construction of the trial function for the Rayleigh quotient, only the outer boundary conditions are satisfied with combination of Euler beam functions. As to the modeling of stiffened plates for the energy calculations, a lumping stiffener-effects method and the orthotropic plate analogy are considered for the purpose of comparison. Some numerical results obtained by the Rayleigh-Ritz method are compared with results by experiments and the finite element method. The following are major conclusions; (1) With the lumping stiffener-effects modeling the Rayleigh-Ritz method gives good results of both natural frequencies and mode shapes. The orthotropic plate analogy in cases of regularly stiffened plates is of restrictive use i.e. acceptable for a small cutout. (2) The natural frequency of a stiffened plate with inner cutouts between stiffeners is higher than that of without cutouts and increase as the hole area ratio increases as long as there are no discontinuous stiffeners due to the cutout.

• Computers and Concrete
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• 제25권6호
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• pp.575-585
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• 2020

Based on a refined shear deformation finite strip, transient vibrations of graphene oxide powder (GOP) reinforced plates due to external pulse loads have been investigated. The plate has uniformly and linearly distributed GOPs inside material structure. Applied pulse loads have been selected as sinusoidal, linear and blast types. Such pulse loads result in transient vibrations of the GOP-reinforced plates which are not explored before. Finite strip method (FSM) has been performed for solving the equations of motion and then inverse Laplace transform technique has been employed to derive transient responses due to pulse loading. It is reported in this study that the transient responses of GOP-reinforced plates are dependent on GOP dispersions, GOP volume fraction, type of pulse loading, loading time and load locations.

• Structural Engineering and Mechanics
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• 제90권6호
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• pp.551-568
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• 2024

The present study deals with static and dynamic behaviors including forced vibrations of an elastic rectangular nano plate on the two-parameter foundation. Firstly, the rectangular plate is assumed to be subjected to uniformly distributed and eccentrically applied concentrated loads. The governing equations of the problem are derived by considering the dynamic response of the plate, employing a series of the Chebyshev polynomials for the displacement function and applying the Galerkin method. Then, effects of the non-essential boundary conditions of the plate, i.e., the boundary conditions related to the shearing forces, the bending moments and the corner forces, are included in the governing equation of motion to compensate for the non-satisfied boundary conditions and increase the accuracy of the Galerkin method. The approximate numerical solution is accomplished using an iterative process due to the non-linearity of the unilateral property of the two-parameter foundation. The plate under static concentrated load is investigated in detail numerically by considering a wide range of parameters of the plate and the foundation stiffnesses. Numerical treatment of the problem in the time domain is carried out by assuming a stepwise variation of the concentrated load and the linear acceleration procedure is employed in the solution of the system of governing differential equations derived from the equation of motion. Time variations of the contact region and those of the displacements of the plate are presented in the figures for various numbers of the two-parameter of the foundation, as well as the classical and nano parameters of the plate particularly focusing on the non-linearity of the problem due to the plate lift-off from the unilateral foundation. The effects of classical and nonlocal parameters and loading are investigated in detail. Definition of the separation between the plate and the two-parameter foundation is presented and applied to the given problem. The effect of the lift-off on the static and dynamic behavior of the rectangular plate is studied in detail by considering various loading conditions. The numerical study shows that the effect of nonlocal parameters on the behavior of the plate becomes significant, when nonlinearity becomes more profound, due to the lift-off of the plate. It is seen that the size effects are significant in static and dynamic analysis of nano-scaled rectangular plates and need to be included in the mechanical analyses. Furthermore, the corner displacement of the plate is affected more significantly from the lift-off, whereas it is less marked in the time variation of the middle displacement of the plate. Several numerical examples are presented to examine the sensibility of various parameters associated with nonlocal parameters of the plate and foundation. Both stiffening and softening nonlocal parameters behavior of the plate are identified in the numerical solutions which show that increasing the foundation stiffness decreases the extent of the contact region, whereas the stiffness of the shear layer increases the contact region and reduces the foundation settlement considerably.

• Advances in aircraft and spacecraft science
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• 제6권6호
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• pp.515-528
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• 2019

The structural vibrations of a flat plate induced by fluctuating wall pressures within wall-bounded transonic jet flow downstream of a high-aspect ratio rectangular nozzle are simulated. The wall pressures are calculated using Hybrid RANS/LES CFD, where LES models the large-scale turbulence in the shear layers downstream of the nozzle. The structural vibrations are computed using modes from a finite element model and a time-domain forced response calculation methodology. At low flow speeds, the convecting turbulence in the shear layers loads the plate in a manner similar to that of turbulent boundary layer flow. However, at high nozzle pressure ratio discharge conditions the flow over the panel becomes transonic, and the shear layer turbulence scatters from shock cells just downstream of the nozzle, generating backward traveling low frequency surface pressure loads that also drive the plate. The structural mode shapes and subsonic and transonic surface pressure fields are transformed to wavenumber space to better understand the nature of the loading distributions and individual modal responses. Modes with wavenumber distributions which align well with those of the pressure field respond strongly. Negative wavenumber loading components are clearly visible in the transforms of the supersonic flow wall pressures near the nozzle, indicating backward propagating pressure fields. In those cases the modal joint acceptances include significant contributions from negative wavenumber terms.

• Advances in nano research
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• 제8권2호
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• pp.115-134
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• 2020

In this paper, the free vibrations analysis of the nanoplates made of three-directional functionally graded material (TDFGM) with small scale effects is presented. To study the small-scale effects on natural frequency, modified strain gradient theory (MSGT) has been used. Material properties of the nanoplate follow an arbitrary function that changes in three directions along the length, width and thickness of the plate. The equilibrium equations and boundary conditions of nanoplate are obtained using the Hamilton's principle. The generalized differential quadrature method (GDQM) is used to solve the governing equations and different boundary conditions for obtaining the natural frequency of nanoplate made of three-directional functionally graded material. The present model can be transformed into a couple stress plate model or a classic plate model if two or all parameters of the length scales set to zero. Finally, numerical results are presented to study the small-scale effect and heterogeneity constants and the aspect ratio with different boundary conditions on the free vibrations of nanoplates. To the best of the researchers' knowledge, in the literature, there is no study carried out into MSGT for free vibration analysis of FGM nanoplate with arbitrary functions.