• Journal of applied mathematics & informatics
• /
• 제17권1_2_3호
• /
• pp.495-508
• /
• 2005

We investigated both classical and quantum properties of a damped harmonic oscillator with a time-variable elastic coefficient using invariant operator method. We acquired the energy eigenvalues, uncertainties and probability densities for several types of wave packet. The probability density corresponding to the displaced minimum wave packet expressed in terms of the time-dependent Gaussian function. The displaced minimum wave packet not only be attenuated but also oscillates about x = 0. We confirmed that there exist correspondence between quantum and classical behaviors for the time-dependent damped harmonic oscillator.

• Current Optics and Photonics
• /
• 제7권4호
• /
• pp.449-456
• /
• 2023

The localized surface-plasmon resonance has drawn great attention, due to its unique optical properties. In this work a general theoretical description of the dipole mode is proposed, using the forced damped harmonic oscillator model of free charges in an ellipsoid. The restoring force and driving force are derived in the quasistatic approximation under general conditions. In this model, metal is regarded as composed of free charges and bound charges. The bound charges form the dielectric background which has a dielectric function. Those free charges undergo a collective motion in the dielectric background under the driving force. The response of free charges will not be included in the dielectric function like the Drude model. The extinction and scattering cross sections as well as the damping coefficient from our model are verified to be consistent with those based on the Drude model. We introduce size effects and modify the restoring and driving forces by adding the dynamic depolarization factor and the radiation damping term to the depolarization factor. This model provides an intuitive physical picture as well as a simple theoretical description of the dipole mode of the localized surface-plasmon resonance based on free-charge collective motion.

• 대한전기학회논문지:시스템및제어부문D
• /
• 제52권4호
• /
• pp.205-211
• /
• 2003

In this paper we propose a disturbance design method to test a system's stability. It is shown that the time maximum disturbance is represented in bang-bang and state feedback form. To maximize the time severity index, the value of disturbance is determined by the associated switch curve. The original switch curve is vulnerable to model uncertainties and takes much calculation time. We propose an improved method to approximate the original switch curve. This reduces the computational time and implements sufficiently to test the stable system. Simulation results show how the approximate switch curve can be used to stress a system by driving it to oscillation along the maximum limit cycle.

• 한국정밀공학회지
• /
• 제10권1호
• /
• pp.134-141
• /
• 1993

Electro-Rheological(ER) fluids undergo a phase-change when subjected to an external electic field, and this phase-change typically manifests itself as a many-order-of-magnitude change in the rheological behavior. This phenomenon permits the global stiffness and energy- dissipation properties of the beam structures to be tuned in order to synthesize the desired vibration characteristics. This paper reports on a proof-of-concept experimental investigation focussed on evaluation the vibration properties of hollow cantilevered beams filled with an ER fluid. and consequently deriving an empirical model for predicting field-dependent vibration characteristics. A hydrous-based ER fluid consisting of corn starch and silicone oil is employed. The beams are considered to be uniform viscoelastic materials and modelled as a viscously-damped harmonic oscillator. Natural frequency, damping ratio and elastic modulus are evaluated with respect to the electric field and compared among three different beams: two types of different volume fraction of ER fluid and one type of different particle concentration of ER fluid by weight. Transient and forced vibration responses are examined in time domain to demonstrate the validity of the proposed empirical model and to evaluate the feasibility of using the ERfluid as an actuator in a closed-loop control system.

• 대한기계학회논문집
• /
• 제17권7호
• /
• pp.1649-1657
• /
• 1993

This paper reports on a proof-of-concept experimental investigation focused on evaluating the vibration characteristics and control of smart hollow cantilever beams filled with an electro-rheological(ER) fluid. The beams are considered to be of uniform viscoelastic materials and modelled as a viscously-damped harmonic oscillator. Electric field-dependent natural frequencies, loss factors and complex moduli are evaluated and compared among three different beams : two types of different volume fraction of ER fluid and one type of different particle concentration of ER fluid by weight. Modal characteristics of the beams are observed in both the absence and the presence of electric potentials. It is also shown that by constructing active control algorithm the removal of structural resonances and the suppression of tip deflection are obtained. This result provides the feasiblility of ER fluids as an active vibration control element.

• 대한조선학회논문집
• /
• 제52권1호
• /
• pp.25-33
• /
• 2015

Following the previous works on the natural frequency of heaving circular cylinder, i.e. Lee and Lee (2013) and Kim and Lee (2013), an investigation of the same spirit on the 2-dimensional cylinder of Lewis form has been conducted. As before, the natural frequency is defined as that corresponding to the local maximum of the MCFR (Modulus of Complex Frequency Response), which is given by the equation of motion in the frequency domain analysis. Hydrodynamic coefficients were found by using the Ursell-Tasai method, and numerical results for them were obtained up to much higher frequencies than before, for which the method was known as numerically unstable in the past. For a wide range of H, the beam-draft ratio, and ${\sigma}$, the sectional area coefficient, including their practical ranges for a ship, results for the natural frequency were computed and presented in this work. Two approximate values for the natural frequency, one proposed by Lee (2008) and another one by the damped harmonic oscillator, were also compared with the current results, and for most cases it was observed that the current result is between the two values. Our numerical results showed that the values of the local maximum of MCFR as well as the natural frequencye increase as ${\sigma}$ increases while H decreases. At present, extension of the present finding to the 3-dimensional ship via the approximate theory like the strip method looks promising.