![]() 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. In closed-loop mode, the slow response of the feedback loop puts another limit on the bandwidth.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). Also please note that these calculations only apply for open-loop systems. Note: For these calculations, it is assumed that the absolute maximum bandwidth of the driver is much higher than the bandwidths calculated, and thus, driver bandwidth is not a limiting factor. Hence, for an instantaneous voltage change from 0 V to 75 V, it would take 3 ms for the output voltage to reach 75 V. ![]() The larger the capacitance, the more current needed:įor example, if a 100 µm stack with a capacitance of 20 ♟ is being driven by a BPC Series piezo controller with a maximum current of 0.5 A, the slew rate is given by The change in charge, dV/dt, is called the slew rate. To drive the output capacitor, current is needed to charge it and to discharge it. The absolute maximum bandwidth of the driver, which is independent of the load being driven.The desired signal amplitude (V), which determines the length that the piezo extends.The higher the capacitance, the slower the system. This is 0.5 A for our BPC Series Piezo Controllers, which is the driver used in the examples below. The maximum amount of current the controllers can produce.The bandwidth of a piezo controller and stack can be estimated if the following is known: Knowing the rate at which a piezo is capable of changing lengths is essential in many high-speed applications.
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