In GN-III model, a second sound may arise, but only when there is no dissipation, i.e., when the hyperbolic heat equation. The GN-III model includes the preceding two models as exceptional cases. The finite heat conduction speed without energy dissipation predicted by the GN-II model makes it the most controversial of the three. The linearized form of the GN-I model is the same as the CTE and displays the heat conduction paradox. For the homogenous isotropic material, the three new thermoelastic models depending on the energy dissipation and thermal signal, were developed by Green and Naghdi 4, 5, 6 and labeled as GN-I, GN-II, and GN-III. Green and Lindsay 3 developed the second generalized theory of thermoelasticity with two relaxation time parameters and included the temperature rate-dependent term in the heat equation. In 1967, to overcome this difficulty, Lord and Shulman (L–S) 2 developed the generalized thermoelastic theory by incorporating one relaxation time into Fourier’s heat transfer law. But the diffusion-type of heat conduction equation makes it difficult for the CTE and the Biot theory of thermoelasticity to describe the thermal signal velocity mechanism. Biot 1 proposed the model of coupled thermoelasticity, which stated that temperature changed independent of elastic variations and removed the first paradox of CTE. There are two shortcomings in the CTE: first, the mechanical state of an elastic body does not affect the temperature, and second, the parabolic heat equation predicts an infinite propagation speed of heat. Fourier’s law produces the famous heat equation as the partial differential equation regulating heat transfer when coupled with the energy conservation law. They are significant when considering theoretical research and real-world applications in industries like mining and acoustics.įourier’s law of heat conduction provides a framework for the classical theory of thermoelasticity (CTE), developed by Duhamel. Studies of these phenomena are crucial for revealing the interior makeup of the Earth’s structure. Many disciplines, including geophysics, earth-quake engineering, and seismology, have intensely interested in studying wave reflection and refraction phenomena. The model astutely captures diverse scenarios, showcasing its ability to interpret complex interface dynamics. This visual representation reveals the nuanced fluctuations of energy ratios with the incidence angle. A graphical representation effectively illustrates the impact of higher-order time differential parameters and memory to offer comprehensive insights. Upon encountering the interface, an intriguing dynamic unfolds: three waves experience reflection within the TS medium, while four waves undergo transmission into the HPS medium. These waves span various incident types, including longitudinal, thermal, and transversal, as they propagate through the TS and interact at the interface. This study explores the amplitude and energy ratios of reflected and transmitted waves. Taken into account the different boundary conditions and the mass of the platform, the first resonance in the application will be lower in the order of tens of kHz, enabling imaging in a few seconds.This paper investigates the intricate energy distribution patterns emerging at an orthotropic piezothermoelastic half-space interface by considering the influence of a higher-order three-phase lags heat conduction law, accompanied by memory-dependent derivatives (referred to as HPS) within the underlying thermoelastic half-space (referred to as TS). It provides 6µm of free displacement and an unloaded resonance of 200kHz (free-free). Usually a soft-doped ceramic ( NCE51 ) provides good results.įor example, a plate actuator stack such as NAC2012-H06 can be used. Depending on the required travel range, positioners can include single actuators or stacks. Multilayer actuators are preferred for their high strain and low operating voltage. Which piezo elements can be used for high frequency nanopositioning? Depending on the displacement range, resonance frequency can be of several kHz.įigure showing the basic functionality of the actuator directly pushing the platform Positioners usually include a sensor to achieve closed-loop control. The piezo actuator provides a few microns positioning range but with picometer resolution. This means that the actuator is directly pushing the platform without any conversion or amplification mechanism, which would drag the first resonance down. High frequency nanopositioning employs piezoelectric elements or stacks with direct action.
0 Comments
Leave a Reply. |
AuthorWrite something about yourself. No need to be fancy, just an overview. ArchivesCategories |