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An Analysis and Modeling of the Dynamic Stability of the Cutting Process Against Self-Excited Vibration

dynamic equations of the system consisting of 8 equations varying with time and space are solved using the method of separation of variables with respect to time and space. The dynamic effect of the temporal term appears in these equations in the form of a frequency term. By eliminating the temporal dependence from dynamic equations governing the behavior of the system, we arrive at 8 spatial equations for positions along the beam, which can be solved by applying boundary constraints (conditions) with respect to space, as shown in Figure 4.2a . Figure 2 The

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Elastodynamical disturbances due to laser irradiation in a microstretch thermoelastic medium with microtemperatures

_{j,i},\, i, j, m=1,2,3 \end{array} $$ (9) Figure 1 Temporal profile of f ( t ) Figure 2 Profile of g ( x 1 ) Figure 3 Profile of h ( x 3 ) Figure 4 Geometry of the problem The surface of the medium is irradiated by laser heat input (following Al Qahtani and Dutta [ 20 ]): Q = I 0 f ( t ) g ( x 1 ) h ( x 3 ) , $$\begin{array}{} Q=I_{0}f\,(t)g\,(x_{1})h\,(x_{3}), \end{array} $$ (10) f ( t ) = t t 0 2 e − ( t t 0 ) , $$\begin{array}{} f\,(t)=\displaystyle \frac{t}{t_{0}^{2}}e^{-\big(\frac{{t}}{{t}_{0

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Response of thermoelastic microbeam with double porosity structure due to pulsed laser heating

^{\star}\,\bigg(\displaystyle \frac{\partial^{2}T}{\partial x^{2}}+\frac{\partial^{2}T}{\partial z^{2}}\bigg) = \bigg(1+\displaystyle \tau_{0}\frac{\partial}{\partial t}\bigg)\\\displaystyle\,\left[-\beta T_{0}z\frac{\partial}{\partial t}\bigg(\frac{\partial^{2}w}{\partial x^{2}}\bigg)+\gamma_{1}T_{0}\dot{\varphi}+\gamma_{2}T_{0}\dot{\psi}+\rho C^{\star}\dot{T}-Q\right]. \end{array} $$ (13) The initial temperature distribution T ( x , z , 0) = T 0 . For t = 0, the upper surface, z = h /2, of the beam is heated uniformly by a laser pulse with non-Gaussian form temporal profile, which can

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