• Journal of the Korean Mathematical Society
• /
• v.46 no.5
• /
• pp.1105-1117
• /
• 2009

In this paper a parameter identification problem for a damped sine-Gordon equation is studied from the theoretical and numerical perspectives. A spectral method is developed for the solution of the state and the adjoint equations. The Powell's minimization method is used for the numerical parameter identification. The necessary conditions for the optimization problem are shown to yield the bang-bang control law. Numerical results are discussed and the applicability of the necessary conditions is examined.

• Journal of the Korean Mathematical Society
• /
• v.58 no.3
• /
• pp.633-642
• /
• 2021

In this paper we consider the following strongly damped wave equation with variable-exponent nonlinearity u_tt(x, t) - ∆u(x, t) - ∆u_t(x, t) = |u(x, t)|^p(x)-2u(x, t), where the exponent p(·) of nonlinearity is a given measurable function. We establish finite time blow-up results for the solutions with non-positive initial energy and for certain solutions with positive initial energy. We extend the previous results for strongly damped wave equations with constant exponent nonlinearity to the equations with variable-exponent nonlinearity.

• Honam Mathematical Journal
• /
• v.40 no.4
• /
• pp.771-783
• /
• 2018

This paper, we investigate a strongly damped nonlinear Klein-Gordon equation with nonlinearities of variable exponent type $$u_{tt}-{\Delta}u-{\Delta}u_t+m^2u+{\mid}u_t{\mid}^{p(x)-2}u_t={\mid}u{\mid}^{q(x)-2}u$$ associated with initial and Dirichlet boundary conditions in a bounded domain. We obtain a nonexistence of solutions if variable exponents p (.), q (.) and initial data satisfy some conditions.

• Computational Structural Engineering
• /
• v.6 no.1
• /
• pp.127-135
• /
• 1993

This paper summarizes a study on the application of viscoelastic dampers as an energy dissipation device in the frame structure. It can be concluded that, even at high temperatures, the viscoelastically damped structure can achieve a significant reduction of structural response as compared to the case with no dampers added. Empirical formulae for estimating the dynamic properties of the viscoelastic damper are established based on the regression analysis using data obtained from component tests of the damper. The structural damping with added dampers can be satisfactorily estimated by the modal strain energy method and the derived empirical formulae. Numerical simulations using conventional modal analysis methods are also carried out to predict the dynamic response of viscoelastically damped structures under seismic excitations. Comparison between numerical simulations and test results shows very good agreement. Based on the above studies, a design procedure for viscoelastically damped structures is present . This design procedure fits naturally into the conventional structural design flow-chart by including damping ratio an additional design parameter.

• Geophysics and Geophysical Exploration
• /
• v.22 no.1
• /
• pp.12-20
• /
• 2019

The first-arrival traveltime calculation method based on the damped wave equation overcomes the shortcomings of ray-tracing methods. Since this algorithm needs to solve the damped wave equation, numerical modeling is essential. However, it is not desirable to use the finite-difference method (FDM), which has good computational efficiency, for simulating the land seismic data because of irregular topography. Thus, the finite-element method (FEM) which requires higher computational cost than FDM has been used to correctly describe the irregular topography. In this study, we computed first-arrival traveltimes in an irregular topographic model using FDM incorporating embedded boundary method (EBM) to overcome this problem. To verify the accuracy and efficiency of the proposed algorithm, we compared our results with those of FEM. As a result, the proposed method using EBM not only provided the same accuracy as the FEM but also showed the improved computational efficiency.

• Smart Structures and Systems
• /
• v.11 no.5
• /
• pp.435-451
• /
• 2013

High-rise buildings are a common feature of urban cities around the world. These flexible structures frequently exhibit large vibration due to strong winds and earthquakes. Structural control has been employed as an effective means to mitigate excessive responses; however, structural control mechanisms that can be used in tall buildings are limited primarily to mass and liquid dampers. An attractive alternative can be found in outrigger damping systems, where the bending deformation of the building is transformed into shear deformation across dampers placed between the outrigger and the perimeter columns. The outrigger system provides additional damping that can reduce structural responses, such as the floor displacements and accelerations. This paper investigates the potential of using smart dampers, specifically magnetorheological (MR) fluid dampers, in the outrigger system. First, a high-rise building is modeled to portray the St. Francis Shangri-La Place in Philippines. The optimal performance of the outrigger damping system for mitigation of seismic responses in terms of damper size and location also is subsequently evaluated. The efficacy of the semi-active damped outrigger system is finally verified through numerical simulation.

• Smart Structures and Systems
• /
• v.25 no.2
• /
• pp.123-133
• /
• 2020

Compressive sensing (CS) is a newly developed data acquisition and processing technique that takes advantage of the sparse structure in signals. Normally signals in their primitive space or format are reconstructed from their compressed measurements for further treatments, such as modal analysis for vibration data. This approach causes problems such as leakage, loss of fidelity, etc., and the computation of reconstruction itself is costly as well. Therefore, it is appealing to directly work on the compressed data without prior reconstruction of the original data. In this paper, a direct approach for modal analysis of damped systems is proposed by decomposing the compressed measurements with an appropriate dictionary. The damped free vibration function is adopted to form atoms in the dictionary for the following sparse decomposition. Compared with the normally used Fourier bases, the damped free vibration function spans a space with both the frequency and damping as the control variables. In order to efficiently search the enormous two-dimension dictionary with frequency and damping as variables, a two-step strategy is implemented combined with the Orthogonal Matching Pursuit (OMP) to determine the optimal atom in the dictionary, which greatly reduces the computation of the sparse decomposition. The performance of the proposed method is demonstrated by a numerical and an experimental example, and advantages of the method are revealed by comparison with another such kind method using POD technique.

• Journal of Power Electronics
• /
• v.18 no.5
• /
• pp.1567-1576
• /
• 2018

The reliability of grid-connected inverters can be improved by algorithms capable of diagnosing faults in LCL filters. A fault diagnostic method during inverter startup is proposed. The proposed method can accurately generate and monitor information on the peak value and the location of the peak frequency component of the step response of a damped LCL filter. To identify faults, the proposed method compares the evaluated response with the response of a healthy higher-order damped LCL filter. The frequency components in the filter voltage response are first analytically obtained in closed form, which yields the expected trends for the filter faults. In the converter controller, the frequency components in the filter voltage response are computed using an appropriately designed fast Fourier transform and compared with healthy LCL response parameters using a finite state machine, which is used to sequence the proposed startup diagnostics. The performance of the proposed method is validated by comparing analytical results with the simulation and experimental results for a three-phase grid-connected inverter with a damped LCL filter.

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

• Journal of the Korean Society for Aeronautical & Space Sciences
• /
• v.41 no.2
• /
• pp.85-90
• /
• 2013

A numerical analysis for the internal flow was carried out in order to analyze the leakage flow characteristics inside the damped bypass valve. This research has found that the valve characteristics became stable at above a specific temperature. Very small amount of leakage flow was occurred. But there was no effect in temperature. The more temperature fell, the more maximum pressure rate was increased.