Dissipative Elements

Similarly, nonlinear relations are assumed for the dissipative elements RA and RB... 

Thermal noise, on the other hand, is a fundamental property of all dissipative elements such as resistors or transistors. For example, a thermal noise current source appears in parallel with all physical resistors. While the instantaneous value of the noise current cannot be predicted, physics accurately predicts its statistics. The mean of the noise current is zero, and the variance is given by... 

For the purposes of this discussion, we need only be concerned with electrical circuits that contain capacitances, C, and resistances, R. The resistance is the dissipative element, formally analogous to the dashpot in the mechanical model case. It is defined by Ohm s law ... 

Fulkerson, W. Goeller, H.E, "Cadmium the Dissipated Element", Oak Ridge National Laboratory Report ORNL-NSF-EP-21, 1973. 

Using Equation 68, four Q s will now be defined appropriate for a transmission Fabry-Perot cavity. The unloaded Q, Qq accounts for power dissipation in the cavity. Similarly, the input and output coupling Q s are labelled Qd and Qc2 The sum of all dissipative elements defines the loaded Q, Q ... 

The first two reduced models (reduced model 1 and reduced model 2) have almost identical predictions for the tire contact force as it is shown in Fig. 2.11 and have an error of 0.02 and 0.31 %, respectively. The third reduced model (reduced model 3) has some visible differences with an accuracy of 2.41%, while the last reduced model (reduced model 4) has an average error of 62.2% and fails to capture the system behavior. As can be seen in Fig. 2.11, the tire contact force prediction of the fourth reduced model has undamped oscillations and it is very different from the one of the full model. This prediction is expected, since this model has no dissipation elements included and consists of only a spring and mass connected in series. Note that in the top plot of Fig. 2.11 there are five curves plotted, one for the full model and one for each one of the four reduced models. However, only three curves (reduced 2, reduced 3, reduced 4) are visible, since the full and reduced 1 curves are almost identical with reduced 2. Similarly, in the bottom plot of Fig. 2.11 there are five curves plotted but only three are visible. 

The simplest linear viscous model is Newton s model. This is shown by a piston-dashpot element [10]. The dashpot is an energy dissipation element, and it represents a viscous damping force. It relates the translational and rotational velocity of a fluid (oil) between two points, and an applied load, by using a damping constant. 

When there are multiple heat paths from the dissipating element to the ambient, then the equivalent thermal resistance can be considered to be the parallel eqiuvalent of the individual resistances. This is analogous to electrical resistances in parallel. For N thermal paths, the is calculated using the formula ... 

A more exact spreading angle model uses 26.6° for cases when the ratio of heat-spreader thickness to heat-dissipating-element side is less than 2 [13]. 

On examining Equation 3.31, it is obvious that the key parameter in the amount of heat removed in forced convection is the linear velocity of the air current as it passes the dissipating element. 

In order to predict temperature rises in electronic components, a thermal model needs to be created, which shows all of the dissipating elements and the entire heat path. Starting at the junction of each dissipating semiconductor, the model needs to include all layers in the thermal path the die attach, substrate (if used and its attachment), package, thermal interface materials (if used), heat sink and circuit card assembly (CCA). The heat dissipated in each component, physical layout, and availability of cooling air are required to calculate the temperature-rise predictions. 

The bond-graph element for unimolecular reactions which we shall introduce in this section turns out to be the essential dissipative element of all types of networks to be discussed in the following chapters. It not only represents the basic description for unimolecular reactions but also for reactions of arbitrary order and for diffusion as well. Our starting point is an ansatz for the reaction flux J of... 

Let us apply now (7.39) to networks where the dissipative elements are reaction or diffusion 2-ports as was the case in the models of Chapters 5 and 6. For a reaction 2-port of the type... 

When the Ohm law is valid for the dissipative elements, then the dissipation potentials are Onsager s like. 

The dissipative elements of the devices, either hysteretic or frictional, are designed to be activated at the threshold of damage limitation, when cracks start opening and allow for the dissipative elements to become active. When the hysteretic devices enter the plastic field, or the friction devices start sliding, the connection between wall panels is still maintained, but the pullout of the head of the anchorage is prevented and drift controlled. 

The replaceable link concept (Fig. 11) effectively eliminates the aforementioned concerns instead of reducing the beam section size dismountable dissipative elements (Fig. 12)... 

---