• Steel and Composite Structures
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• v.8 no.4
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• pp.281-296
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• 2008

Visco-elastic material and thin metals were adhered to plate structures, forming the composite components that are similar to the sandwich plates, called constrained layered damped (CLD) plates. Constrained layer damping has been utilized for years to reduce vibration, and advances in computation and finite element analysis software have enabled various problems to be solved by computer. However, some problems consume much calculation time. The vibration equation for a constrained layered damped plate with simple supports and an impact force is obtained theoretically herein. Then, the results of the vibration equation are compared with those obtained using the finite element method (FEM) software, ABAQUS, to verify the accuracy of the theory. Finally, the 3M constrained layer damper SJ-2052 was attached to plates to form constrained layered damped plates, and the vibration equation was used to elucidate the damping effects and vibration characteristics.

• Structural Engineering and Mechanics
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• v.68 no.2
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• pp.171-182
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• 2018

For the first time, nonlocal damped vibration and buckling analyses of arbitrary tapered bidirectional functionally graded solid circular nano-plate (BDFGSCNP) are presented by employing modified spectral Ritz method. The energy method based on Love-Kirchhoff plate theory assumptions is applied to derive neutral equilibrium equation. The Eringen's nonlocal continuum theory is taken into account to capture small-scale effects. The characteristic equations and corresponding first mode shapes are calculated by using a novel modified basis in spectral Ritz method. The modified basis is in terms of orthogonal shifted Chebyshev polynomials of the first kind to avoid employing adhesive functions in the spectral Ritz method. The fast convergence and compatibility with various conditions are advantages of the modified spectral Ritz method. A more accurate multivariable function is used to model two-directional variations of elasticity modulus and mass density. The effects of nanoscale, in-plane pre-load, distributed dashpot, arbitrary tapering, pinned and clamped boundary conditions on natural frequencies and buckling loads are investigated. Observing an excellent agreement between results of current work and outcomes of previously published works in literature, indicates the results' accuracy in current work.

• Korean Journal of Mathematics
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• v.24 no.3
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• pp.447-467
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• 2016

We prove the existence of random attractors for the continuous random dynamical systems generated by stochastic damped plate equations with linear memory and additive white noise when the nonlinearity has a critically growing exponent.

• Interaction and multiscale mechanics
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• v.5 no.2
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• pp.105-114
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• 2012

The study of rigid roadway pavement under dynamic traffic loads with variable velocity is investigated in this paper. Rigid roadway pavement is modeled as a rectangular damped orthotropic plate supported by elastic Pasternak foundation. The boundary supports of the plate are the steel dowels and tie bars which provide elastic vertical support and rotational restraint. The natural frequencies of the system and the mode shapes are solved using two transcendental equations, obtained from the solution of two auxiliary Levy's type problems, known as the Modified Bolotin Method. The dynamic moving traffic load is expressed as a concentrated load of harmonically varying magnitude, moving straight along the plate with a variable velocity. The dynamic response of the plate is obtained on the basis of orthogonality properties of eigenfunctions. Numerical example results show that the velocity and the angular frequency of the loads affected the maximum dynamic deflection of the rigid roadway pavement. It is also shown that a critical speed of the load exists. If the moving traffic load travels at critical speed, the rectangular plate becomes infinite in amplitude.

• Transactions of the Korean Society for Noise and Vibration Engineering
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• v.11 no.6
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• pp.193-199
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• 2001

Active control of forced vibration of the cantilevered laminated composite plates using collocated piezoceramic sensor/actuator is analyzed numerically and verified experimentally for various fiber orientations. Impact on the stiffness and the damping properties is studied by varying stacking sequence of [$\theta$$_{4}$O$_{2}$90$_{2}$]s for the laminated composite plate. For the forced vibration control, the plate is excited by one pair of collocated PZT exciters in resonance and its vibrational response is suppressed by the other collocated PZT sensor/actuator using direct negative velocity feedback. It is shown that the active control of forced vibration is more effective for the smart laminated plate with higher modal damped stiffness(2ζ$\omega$/aup 2/) .

• Proceedings of the Korean Society For Composite Materials Conference
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• 2001.05a
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• pp.5-8
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• 2001

A three node flat triangular element incorporating Layerwise Zig-Zag Theory(HZZT) is developed suitable for analyzing damped laminated composite structures. Using an interdependent kinematic relation, the higher order shear rotations are replaced by in-plane displacements, a transverse displacement and section rotations, which result in three translations and two rotations. Natural frequencies and modal loss factors of cantilevered laminated plates with embedded damping layers are calculated with the zig-zag triangular element and compared to the experimental results and MSC/NASTRAN results using a layered combination of plate and solid elements.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.10
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• pp.1778-1784
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• 2003

Vibration control of plates with a passive electrical damper is presented in this paper. This electrical absorber, piezoelectric patches connected with a resistor and an inductor in series, is analogous to the damped mechanical vibration absorber. For estimating the effectiveness of piezoelectric absorber, the governing equations of motion are derived using a classical laminate plate theory and Hamilton principle. The developed theoretical analysis is validated experimentally for a simply-supported aluminum plate in order to demonstrate the performance of passive electrical damper. The result shows that the vibration amplitude is reduced about 14dB for the targeted first vibration mode.

• Journal of KSNVE
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• v.10 no.6
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• pp.949-954
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• 2000

Applicability of the vibration signal phase for predicting the modal damping properties of structures is investigated. For uniform plates with different internal damping levels, the phase delay as a function of the frequency span as well as a function of the distance between the excitation and response measurement points are experimentally obtained. Dependence of the phase characteristics on the amount of structural damping is elucidated -more heavily damped plate shows notably reduced phase delay at intermediate distances. The experimental results compare favorably with analytical predictions, and show much promise for further refinement as a tool for estimating structural properties.

• Journal of the Korean Society for Precision Engineering
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• v.11 no.1
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• pp.166-176
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• 1994

The problem of reducing the vibration level of elastic plates driven by multiple random point forces is analyzed in this study. First, the analytical solution for the vibration level of finite thin plates with four simply supported edges under the action of multiple random point force is derived. By assuming the plates to be lightly damped, an approximate solution for the vibration level of the plate is obtained. A numerical study is carried out to determine an optimal spacing distance between the multiple point forces in order to produce a relative minimum in the plate's vibration level. The optimal spacing distance is shown to depend on the given excitation band. The effects of wave cancellation in the near field of the multiple point forces are discussed by using the equivalence of certain stationary random responses and deterministic pulse responese.

• Transactions of the Korean Society of Mechanical Engineers
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• v.17 no.1
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• pp.90-100
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• 1993

A finite element formulation of vibration control of a laminated plate with piezoelectric sensor/ actuators is presented. Classical lamination theory with the induced strain actuation and Hamilton's principle are used to formulate the equations of motion of the system. The total charge developed on the sensor layer is calculated from the direct piezoelectric equation. The equations of motion and the total charge are discretized with 4 node, 12 degrees of freedom quadrilateral plate bending elements with one electrical degree of freedom. The mass and stiffness of the piezoelectric layer are introduced by treating them as another layer in laminated plate. Piezoelectric sensor/actuators are distributed, but discrete due to the geometry of electrodes. By defining an i.d. number of electrode for each element, modelling of electrodes with variable geometry can be achieved. The static response of a piezoelectric bimorph beam to electrical loading and sensor voltage to given displacement are calculated. For a laminated plate under the negative velocity feedback control, the direct time response by the Newmark-.betha. method and damped frequencies and modal damping ratios by modal state space analysis are derived.