• Communications of the Korean Mathematical Society
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• v.35 no.1
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• pp.321-338
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• 2020

In this paper, we investigate the viscoelastic plate equation with a constant delay term and logarithmic nonlinearities. Under some conditions, we will prove the global existence. Furthermore, we use weighted spaces to establish a general decay rate of solution.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.27 no.3
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• pp.472-477
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• 2003

A piezo-actuator is an important component for an E-beam lithography system. But it is very difficult to model its characteristics due to nonlinearities such as hysteresis and creep, to the input voltage. In this paper, one-axis micro stage with a piezo-actuator is modeled including the nonlinear properties. Hysteresis and creep are modeled as the first order differential equation and a time-dependent logarithmic function, respectively. The dynamic motion of the stage is also modeled as a mass-spring-damper system and the parameters are determined by utilizing the system identification technique. The simulation tool for a micro stage is constructed using the commercial software and its simulation results are compared with the experimental data.

• Transactions of the Korean Society of Mechanical Engineers A
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• v.28 no.10
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• pp.1541-1548
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• 2004

A nano-stage simulation tool is developed for an advanced E-beam lithography system. Even if piezo-actuators are believed to be compatible fer the E-beam lithograpy system it is difficult to predict their characteristics due to their nonlinearities such as hysteresis and creep. In this paper, the nonlinear properties are modeled for a piezo-actuator by considering the voltage range and speed variations. The hysteresis is described as the first order differential equation with 24 sets of parameters and the creep is modeled as a time-dependent logarithmic function with 2 sets of a parameter. A two-axis nano stage with piezo-actuators are investigated for realizing nano scale motions. The characteristics of flexure guide mechanisms are analyzed based on the finite element method using the ANSYS software. The simulation tool for the nano stage is constructed by using the RecurDyn software. The dynamic response of the nano stage is obtained in simulations and compared with the experimental data.