esa-sceva/satcom-chunk-collection huggingface dataset:
## 2 The Basis of Derivation
### Equivalent Equation in the Form of Principal Stress of the Joint Strength  
The ultimate equilibrium state of the joint strength on the \(\sigma\)-\(\tau\) plane is shown in Figure 3, where \(\sigma_{1}\) is major principal stress and \(\sigma_{3}\) is minor principal stress.  
Figure 3: Ultimate equilibrium state in the joint strength.  
Figure 2: M–C strength and the joint strength.  
The stress Circle \(O_{1}\) is tangent to the joint strength line, with the assumption that the coordinates of tangent Point \(F\) are \((\sigma_{\rm F},\tau_{\rm F})\), because tangent Point \(F\) is on the joint strength line. Thus,  
\[\tau_{\rm F}^{2}=(c+\sigma_{\rm F}\tan\varphi)^{2}-\beta^{2} \tag{3}\]  
Or  
\[\tau_{\rm F}=\sqrt{(c+\sigma_{\rm F}\tan\varphi)^{2}-\beta^{2}} \tag{4}\]  
In Formulas (3) and (4),  
\[\beta=c+\sigma_{\rm t}\tan\varphi \tag{5}\]  
The tangent slope \(k_{\rm F}\) at the differentiable Point \(F\) of Formula (4) is  
\[k_{\rm F}=\frac{\mathrm{d}\tau_{\rm F}}{\mathrm{d}\sigma_{\rm F}}=\frac{(c+ \sigma_{\rm F}\tan\varphi)\tan\varphi}{\sqrt{(c+\sigma_{\rm F}\tan\varphi)^{2 }-\beta^{2}}} \tag{6}\]  
Then, the slope of the normal Line \(O_{1}F\) at Point \(F\) is \(k_{\rm N}\):  
\[k_{\rm N}=-\frac{1}{k_{\rm F}}=-\frac{\sqrt{(c+\sigma_{\rm F}\tan\varphi)^{2}- \beta^{2}}}{(c+\sigma_{\rm F}\tan\varphi)\tan\varphi} \tag{7}\]  
According to the coordinates of Point \(F\) and Formula (7), the equation of straight Line \(O_{1}F\) is  
\[\tau-\tau_{\rm F}=k_{\rm N}(\sigma-\sigma_{\rm F}) \tag{8}\]  
The intersection of Formula (8) and the \(\sigma\) coordinate axis is the central coordinate of the Circle \(O_{1}\)\((\sigma_{\rm F}+(c+\sigma_{\rm F}\tan\varphi)\tan\varphi,\ \ 0)\).  
The distance between Points \(O_{1}\) and \(F\) is the radius of Circle \(O_{1}\). Thus, the equation of Circle \(O_{1}\) is  
\[\sqrt{\left[(c+\sigma_{\rm F}\tan\varphi)\tan\varphi\right]^{2}+\tau_{\rm F}^{ 2}}=\frac{\sigma_{1}-\sigma_{3}}{2} \tag{9}\]  
According to the half relation between the abscissa of centre of Circle \(O_{1}\) and the value of \((\sigma_{1}+\sigma_{3})\), we have  
\[\sigma_{\rm F}+(c+\sigma_{\rm F}\tan\varphi)\tan\varphi=\frac{\sigma_{1}+ \sigma_{3}}{2} \tag{10}\]  
Introducing Formula (4) into Formula (9) yields  
\[\sqrt{\frac{(c+\sigma_{\rm F}\tan\varphi)^{2}}{\cos^{2}\varphi}-\beta^{2}}= \frac{\sigma_{1}-\sigma_{3}}{2} \tag{11}\]  
With the simultaneous solution of Formulas (10) and (11) and the elimination of \(\sigma_{\rm F}\), the equivalent equation in the form of principal stress of the joint strength can be obtained as  
\[\frac{\sigma_{1}-\sigma_{3}}{2}=\sqrt{\left[\left(\frac{\sigma_{1}+\sigma_{3} }{2}\right)\sin\varphi+c\cos\varphi\right]^{2}-\beta^{2}} \tag{12}\]
## 3 Overview of the Research Project and Monitoring Plan
\begin{table}
\begin{tabular}{c c c c c} \hline
**Index or Layers** & **\textbackslash{1} (4000 kN.m)** & **\textbackslash{2} (6000 kN.m)** & **\textbackslash{3} (8000 kN.m)** & **\textbackslash{4} (12,000 kN.m)** \\ \hline Natural moisture content \(W\) (\%) & 18.5 & 18.7 & 19.0 & 18.2 \\ Natural unit weight \(\gamma\) (KN/m\({}^{3}\)) & 18.9 & 18.9 & 18.9 & 18.9 \\ Dry unit weight \(\gamma_{d}\) (KN/m\({}^{3}\)) & 16.0 & 16.0 & 15.9 & 16.0 \\ Specific gravity \(G_{\text{s}}\) & 2.71 & 2.71 & 2.71 & 2.71 \\ Natural void ratio \(e\) & 0.662 & 0.664 & 0.676 & 0.664 \\ Saturation of soil \(S_{r}\) (\%) & 76 & 76 & 76 & 75 \\ Liquid limit \(W_{L}\) (\%) & 30.6 & 30.5 & 30.0 & 30.1 \\ Plastic limit \(W_{p}\) (\%) & 18.4 & 18.4 & 18.1 & 18.2 \\ Plasticity index \(I_{p}\) & 12.2 & 12.1 & 11.9 & 11.9 \\ Liquidity index \(I_{L}\) & 0.08 & 0.11 & 0.12 & 0.08 \\ Coefficient of compressibility \(a\) (MPa\({}^{-1}\)) & 0.19 & 0.21 & 0.20 & 0.21 \\ \hline \end{tabular}
\end{table} 
Table 2: Physical and mechanical properties of the filling. Figure 3: Typical section of the filling body. Figure 5: Time history curve of settlement in each phase. Figure 6: Time history curve of cumulative settlement. Figure 7: Scatter plot of settlement deformation rate and time.
## 6 Comparative Analysis of Experimental and Numerical Outcomes  
A comparison with the numerical data obtained by Plaxis 3D was also conducted to validate the experimental results. The failure mechanism was similar in both cases, which can be very well observed from Figures 5 and 6. The deformation was higher in unreinforced soil than reinforced soil (OSC). However, the failure of the OSC was due to bulging, which was controlled by providing an encasement around the OSC. The encasement provided was both vertical and horizontal layering of a geotextile. Both the experimental and numerical analyses exhibited the same trend regarding failure mechanisms.  
A graph was plotted, as shown in Figures 11 and 12, to study the load-settlement behaviour. A factor, 'load ratio (LR)', was devised for an effective comparison; it is defined as the ratio of the load capacity of the experimental results to that of the numerical results. For unreinforced soft soil, the LR value obtained was 1.12. In OSCs, for \(D\) = 50, 75, and 100 mm, the LR value was calculated as 1.03, 1.13, and 1.17, respectively. In VESCs, for \(D\) = 50 m, \(Lr\) = 0.25 L, 0.5 L, 0.75 L, and \(L\), the LR value was found to be 1.006, 1.02, 1.03, and 1.04, respectively. Similarly, for the same length of reinforcement in \(D\) = 75 mm, the LR value was calculated as 1.06, 1.03, 1.08, and 1.05. The LR values for \(D\) = 100 mm were 1.04, 1.04, 1.05, and 1.09. In the HRSC case, for \(D\) = 50 mm, when \(Lr\) = 0.5 L from centre to end, 0.5 L from top to centre, and L throughout the length of the column, the LR values were obtained as 1.10, 1.05, and 1.03, respectively. Similarly, for \(D\) = 75 mm, the LR values were 1.09, 1.06, and 1.05. Moreover, for \(D\) = 100 mm, the LR values were 1.02, 1.05, and 1.05. All the cases in our study revealed a slightly lower value of the load-carrying capacity at 50 mm settlement for the numerical results compared to the experimental results. A potential cause of this issue may be the inherent constraint of replicating stone columns without accounting for the effects of installation, which results in an inability to accurately replicate the altered characteristics of the soil that arise during model testing. Moreover, the Rinter value of 0.8 was used; this is a soil reduction factor that is applied to the strength and stiffness of the interface. Rinter = 1.00 reflects a rigid interface between the structure and the soil; therefore, the nodes of the interface and soil are coupled and show the same behaviour (and deformations). A Rinter value of 0.8 was used to simulate the relative relation at the interface, which resulted in a lower value. Additionally, Table 5 demonstrates that the load-carrying capability, as determined by laboratory testing and numerical analysis, was in accordance, with a maximum 11.08% coefficient of variance (COV).
## 2 G-R for HSRs
### Handover Measurement of SCell and NCell  
#### 2.3.1 SS-RSRP  
The command of the handover is triggered when the measured value of NCell is higher than the preset threshold of the measured value of SCell and this state lasts for a certain time. Two gNodeBs with a spacing of 1.2 km were selected in the section of an HSR from Lanzhou station to Jiayquan Station in China. Based on the actual measurement data of a handover period, 1610 sampling points of the SS-RSRP of SCell and 1500 sampling points of the SS-RSRP of NCell are shown in Figure 6. According to the fitting curve, it is found that the measured values of SS-RSRP of SCell decrease gradually, while that of NCell increase gradually.
# PUF and Chaotic Map-Based Authentication Protocol for Underwater Acoustic Networks
## 3 The Proposed Scheme
### Authentication and Key Management Phase
\begin{table}
\begin{tabular}{|c|c|c|} \hline \(U_{i}\) & \(GWN_{k}\) & \(St_{ij}\) \\ \hline insert SC and input \(id_{i},pw_{i}\) & \\ RC compute \(M_{i}^{\prime}=h(id_{i}\parallel M_{0}\parallel pw_{i})mod\ n_{0}\) & \\ Checks whether \(M_{3}^{\prime}=M_{3}\) & \\ \(M_{2}=M_{1}\bigoplus h(id_{i}\parallel pw_{i})\) & \\ choose two random numbers \(rug\) and \(ru\) & \\ \(K_{U}=T_{ru}(x)mod\ q\) & \\ \(K_{U-C}=T_{ru}(M_{0})mod\ q\) & \\ \(M_{4}=h(T_{1}\parallel M_{2}\parallel rug\parallel id_{i})\) & \\ \(M_{5}=E_{k_{U-C}}(id_{i}\parallel Sid_{i}\parallel rug\parallel M_{4})\) & \\ \(\underset{\left(K_{U},M_{5},T_{1}\right)}{\underbrace{\left(K_{U},M_{5},T_{1} \right)}}\) & check the freshness of T\({}_{1}\) \\  & \\ \(M_{6}=D_{K_{U-C}}(M_{5})\) & \\ \(S_{K}=GSK\bigoplus h(PUF1(C_{G}))\) & \\ \(M_{2}^{\prime}=h(id_{i}\parallel S_{K})\) & \\ \(M_{4}^{\prime}=h\left(T_{1}\parallel M_{2}\parallel rug\parallel id_{i}\right)\) & \\ check whether \(M_{4}^{\prime}=M_{4}\) & \\ \(S_{j}=h(Sid_{j}\parallel Gid_{k}\parallel S_{K})\) & \\ choose a random number \(r\) & \\ \(M_{7}=E_{S_{j}}(h(id_{i}\parallel r)\parallel Gid_{k}\parallel Sid_{j} \parallel K_{U}\parallel T_{2})\) & check the freshness of T\({}_{2}\) \\  & \\ check the freshness of T\({}_{3}\) & \\ check the freshness of T\({}_{4}\) & \\ \(\underset{\left(M_{9},M_{10},M_{12},T_{3}\right)}{\underbrace{\left(M_{9},T_{ 10}\right)}}\) & \\ check the freshness of T\({}_{4}\) & \\ \(\underset{\left(M_{9},M_{10},M_{12},T_{3}\right)}{\underbrace{\left(M_{9},T_{ 10}\right)}}\) & \\ check the freshness of T\({}_{4}\) & \\ \(\underset{\left(M_{10},M_{10},M_{12},T_{3}\right)}{\underbrace{\left(M_{9},T_{ 10}\right)}}\) & \\ \(\underset{\left(M_{10},M_{10},M_{12},T_{3}\right)}{\underbrace{\left(M_{10},M_{ 10}\right)}}\) & \\ check the freshness of T\({}_{3}\) & \\  & \\ verify the correctness of \(M_{11}\) & \\  & \\  & \\ \(M_{12}=h(rug\parallel M_{0}\parallel M_{10}\parallel T_{4})\) & \\  & \\ check the freshness of T\({}_{4}\) & \\ \(\underset{\left\{\begin{array}{c}\text{decrypt}M_{13}\text{and obtain rand }M_{12}\\ \text{verify the correctness of }M_{12}\\ \text{SK}=h(T_{ru}(M_{0})\parallel K_{U}\parallel M_{0}\parallel Gid_{k} \parallel Sid_{j}\\ \parallel h(id_{i}\parallel r))\end{array}\right.}\) & \\ \(M_{10}^{\prime}=h(Gid_{k}\parallel Sid_{j}\parallel SK\parallel M_{9} \parallel T_{3})\) & \\ check \(M_{10}^{\prime}=M_{10}\) & \\ if it holds, the session key is SK. & \\ \hline \end{tabular}
\end{table} 
Table 2: Login and authentication phase.
## 2 Blockchain-Based Data Storage Methods: On-Chain, Off-Chain, and Hybrid Approaches
### Practical Integration of On-Chain, Off-Chain, and Hybrid Blockchain Storage Approaches
As summarized in Table 5, blockchain-based data storage methods offer distinct advantages across various application scenarios. On-chain storage is an ideal solution for data verification and integrity preservation, while off-chain storage provides performance advantages for managing large datasets. Hybrid approaches, combining both methodologies, ensure a balance between security and performance, maintaining data confidentiality and integrity while optimizing cost efficiency and operational scalability.
# Trends and Opportunities in the Dairy Industry: A2 Milk and Processing Methods
## 5 Milk Processing
### Thermal Methods
#### 5.1.2 Pasteurization and Sterilization  
The conditions used during pasteurization are designed to inactivate the most heat-resistant, non-spore-forming pathogenic bacteria in milk--_Mycobacterium tuberculosis_ and _Coxiella burnetti_. It is a standard among methods for extending the storage life of milk and dairy products and ensuring their safety. However, it has limitations due to its high energy consumption, cost versus efficiency, and impact on the physicochemical properties of milk. Different types of pasteurization and sterilization are used depending on production needs: Low Temperature Long Time (LTLT: 30 min/63 \({}^{\circ}\)C), High Temperature Short Time/Continuous (HTST: 15 s/72 \({}^{\circ}\)C), Flash/Ultra Pasteurization (2 s/138 \({}^{\circ}\)C), and Ultra High Temperature (UHT: 2 s/150 \({}^{\circ}\)C) sterilization [62; 67; 68]. The combination of temperature and time will adequately reduce the bacterial population, which varies depending on the type and conditions (such as viscosity, percentage of protein and fat, and solids content) of the pasteurized product. Other types of pasteurization are also being designed to optimize the process and its cost, like Low Temperature Short Time (LTST: 0.02 s/\(\leq\)72.7 \({}^{\circ}\)C). In this process, milk is dispersed as droplets in a process chamber and heated for a fraction of a second at pasteurization temperature or lower [68; 69].  
Due to the temperatures used in these processes, changes occur in the milk: denaturation of proteins, the occurrence of Maillard reactions and the appearance of their products, and loss and changes of aroma, so attempts are being made to develop better methods for preserving milk quality [70].
## Materials and Methods
### Choice Tests  
For choice tests based on olfactory cues, a Y-shaped tube (2 cm inner diameter) consisting of a central tube (13 cm long) and two arms (10 cm long, offset by 60\({}^{\circ}\)) was connected to 36 L glass desicators. Five healthy, mock-inoculated, or MMWV-infected plants (10 days after inoculation) were placed in glass desiccators, respectively. The GC-grade air was pumped into the glass desiccators at a flow rate of 200 mL min\({}^{-1}\). The Y-tube was housed in an airtight cubical box (70 cm \(\times\) 45 cm \(\times\) 30 cm) with a 25 W filament lamp giving a constant light 25 cm above each arm. The temperature in the glass desiccators was 25 \({}^{\circ}\)C and the relative humidity was 70%. An _M. persicae_ aphid (starved for 1 h before tests) was individually placed in the central tube and allowed to choose between the two arms. A choice was registered if _M. persicae_ passed the threshold line located 3 cm away from the Y-junction. A \"no choice\" was marked if it failed to decide during the 5 min testing period [22]. Pairings for host preference tests were designed as follows: (i) Healthy vs. MMWV-infected, (ii) healthy vs mock-inoculated, and (iii) mock-inoculated vs. MMWV-infected. Thirty _M. persicae_ were tested for each pairing. When 5 _M. persicae_ individuals had been tested, the odor sources were interchanged. The Y-tube and plants were replaced after testing of 10 aphids. All Y-tubes were cleaned with 95% alcohol and dried in a 120 \({}^{\circ}\)C oven before use [20; 22]. A total of 150 aphids in 5 replicates  
Choice tests based on visual and contact cues followed the procedure of previous studies with minor modifications [14; 16; 23]. A glass Petri dish (12 cm diameter) lined with a filter paper was divided into two parts by pencil marks. Two leaves, each still attached to a differently treated plant, (i) healthy vs. MMWV-infected, (ii) healthy vs mock-inoculated, and (iii) mock-inoculated vs. MMWV-infected, were placed in the Petri dish, into which 50 alate _M. persicae_ were released. Petri dishes were sealed with Parafilm perforated to allow air movement. The number of aphids settled on each leaf was counted 30 min and 60 min later, respectively. A total of 750 aphids in 15 replicates were tested for each dual-choice bioassay.
## 2 Designed Methodology
### Degradation Model  
Once the SOC data are obtained, the model described in [21] is used to calculate the BESS degradation cost. Only the degradation due to cycles is considered, without taking into account the calendar degradation. Indeed, even though the ageing mechanism of BESSs is complex, it is mainly related to the depth of discharge (DOD) and to the charge as well as discharge cycles. The higher the battery's DOD, the fewer cycles it will endure, and the greater the degradation of the battery [21]. This relation is represented by Equation (7):  
\[N_{cycle}=\beta_{0}\cdot DOD^{-\beta_{1}}\cdot e^{\beta_{2}(1-DoD)} \tag{7}\]  
where \(N_{cycle}\) is the number of cycles of the BESS, and \(\beta_{0}=1.05\times 10^{7}\), \(\beta_{1}=0.8159\), and \(\beta_{2}=0.098\) are parameters that depend on the chemistry of the battery (values taken from the specific battery of the project).  
The operation or degradation cost of the BESS depends on the number of cycles the battery performs with a given DOD and the total BESS capital cost. As \(DOD~{}=~{}1~{}-~{}SOC\), from Equation (7), the operation cost can be defined as follows:  
\[C_{BESSop}(SOC)=\frac{C_{BESScap}}{N_{cycle}} \tag{8}\]  
where \(C_{BESScap}\) is the total capital cost of the BESS and \(C_{BESSop}\) is the operation or degradation cost of the BESS.  
This equation is valid only if two assumptions are taken into account: (i) the charge and discharge operation for a given DOD has a uniform impact on cell degradation and (ii) the charge or discharge cycle is independent of the previous cycles.  
In order to relate the partial charge/discharge cycles of the BESS, the rainflow-counting algorithm is used [21]. This method considers all of the partial charge/discharge profiles and relates them to some charge/discharge cycles that start from full capacity until the minimum SOC reached on the respective partial charge/discharge. Therefore, the cost of the partial charge/discharge is calculated as illustrated in Figure 4 (taken from [21]), and the total BESS operation cost is the sum of each cycle cost.  
Thus, the total degradation cost is calculated as follows, adding the degradation related to each partial cycle and relating it to a full cycle:  
\[C_{BESSop}(SOC)=\sum_{t=1}^{T}C_{E}(SOC_{t}) \tag{9}\]  
where \(C_{E}\) is the partial cycles of the BESS.  
Constraints  
Four constraints related to the BESS are considered:  
1. The battery SOC, \(SOC_{BESS}\), has to be between the minimum, \(SOC_{BESSmin}\), and maximum, \(SOC_{BESSmax}\), values provided by the manufacturer: \[SOC_{BESSmin}\leq SOC_{BESS}(t)\leq SOC_{BESSmax}\] (10)
2. The power consumed (considered as positive power) by the EVCS, \(P_{EVCS}\), and the BESS, \(P_{BESS}\), cannot be greater than the contracted power, \(P_{Gmax}\): \[P_{BESS}(t)+P_{EVCS}(t)\leq P_{Gmax}\] (11)
3. The maximum power variation in the BESS in one sample interval is limited to \(P_{BESSstep\_max}\): \[|P_{BESS}(t)-P_{BESS}(t-1)|\leq P_{BESSstep\_max}\] (12)
4. The BESS power does not have to exceed a limit, \(P_{BESSmax}\): \[|P_{BESS}(t)|\leq P_{BESSmax}\] (13)
# A Review of Counter-UAS Technologies for Cooperative Defensive Teams of Drones
## 6 Technological Challenges
### Team Communication Network  
Considering the mobility characteristics of the drones belonging to a team, the communication network will be a FANET with certain requirements of throughput, latency, transmission robustness, multiple access, flexibility and with constraints of available energy in relation to the mobile nodes (i.e., drones). A review on the communications perspectives of FANETs, with key enabling wireless technologies, applications, challenges and open research topics, is shown in [111]. In particular, the following key elements must be taken care of.  
* Routing--the algorithms used must be able to support a routing table capable of rapidly adapting to the continuous topological variations of the network due to the mobility of drones. A survey of routing techniques in FANETs is shown in [112].
* Reliability and security--the network must ensure availability and integrity (and, depending on the application, confidentiality) of the communication between the nodes, characteristics that can be obtained both by operating at a physical level and at some higher levels.  
Scalability--some network drones competing in the execution of a task may need to be replaced for technical reasons or due to the exhaustion of their energy resources, so it is necessary to add other drones to the team to efficiently complete the assigned task.
* Quality of service--different performances must be guaranteed according to the type of information transmitted and the level of criticality.
* Placement--the drones may need to be appropriately arranged in the 3D space in order to maximize the amount of information exchanged and minimize the time required for the exchange, so as to satisfy any energy constraints characterizing the nodes themselves. Clearly, this aspect also falls within the problem of coordination.
# A Review of Fault Diagnosing Methods in Power Transmission Systems
## 7 Fault Location Finding Methods
### Fault Location Finding Algorithm for Series Compensated TLs  
Typically, series compensation is achieved through series capacitors and metal oxide varistors. The non-linear nature of series compensation devices adds difficulty to locate the faulty segment and hence the fault location. Thus traditional approaches [126; 127] need to be modified to address such cases. The generalized procedure for FL finding for series compensated TLs is shown in Figure 10. In [128], an impedance-based approach is proposed using double end voltage and current samples. [PERSON] et al. used an artificial intelligence-based algorithm to locate single and multi-fault locations [129]. Third level wavelet coefficients (62.5-125 kHz) are extracted by DWT from two post-fault and one pre-fault cycles. The features based on standard deviation in coefficients of voltage and current signals serve as input for ANN. [PERSON] used synchronized measurements from ends of distributed transmission line and transient resistance nature of thyristor controlled series capacitor as an indicator of the faulty section [130].
# Effect of Tuned Spring on Vibration Control Performance of Modified Liquid Column Ball Damper
## 3 Parameter Optimization
### Response of the Structure Subjected to Harmonic Loading  
Figure 7 shows the normalized frequency responses of the structure subjected to harmonic loading with and without dampers. The response of the structure improved with the TLCBD, TLCBSSD, and TLCBSRD in the resonance region and was almost constant in the remaining zones. However, the reduction in the response of the structure with the TLCBSSD and TLCBSRD was significantly better than with the TLCBD. The qualitative measure of the responses of the TLCBSSD and TLCBSRD are tabulated in Table 4. It can be observed that the performance of the TLCBSSD and TLCBSRD in the resonance region was around 24% and 25% better over the TLCBD, respectively. The maximum reduction in the response in the TLCBSSD and TLCBSRD over TLCBD was 30% and 32% at \(w_{\varpi}/w_{s}=0.9\), respectively. The better performance of the TLCBSSD and TLCBSRD compared to the TLCB was due to better energy dissipation mechanisms, because in the case of the TLCBD, the energy was dissipated in three ways: (1) as heat due to friction between the ball and fluid, (2) due to the translational motion of the ball, and (3) due to the rotational motion of the ball. However, in addition to these three ways, the energy in the TLCBSD was also dissipated due to the spring interaction with the ball and fluid.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & **Structure** & **Structure** & **Structure** & **Percentage** & **Percentage** \\ \(\frac{\omega_{\text{ext}}}{\omega_{\text{s}}}\) & **Response** & **Response** & **Response** & **Improvement** & **Improvement** \\ \(\frac{\omega_{\text{ext}}}{\omega_{\text{s}}}\) & **Ratio with** & **Ratio with** & **Ratio with** & **of TLCBSSD** & **of TLCBSRD** \\  & **TLCBD** & **TLCBSSD** & **TLCBRD** & **over TLCB** & **over TLCB** \\ \hline
0.90 & 1.00 & 0.70 & 0.68 & 30.35 & 32.44 \\
0.92 & 0.80 & 0.57 & 0.55 & 28.63 & 31.27 \\
0.94 & 0.66 & 0.50 & 0.49 & 24.30 & 25.38 \\
0.96 & 0.66 & 0.50 & 0.49 & 24.93 & 25.52 \\
0.98 & 0.66 & 0.49 & 0.49 & 25.16 & 25.44 \\
1.00 & 0.65 & 0.49 & 0.49 & 25.00 & 25.13 \\
1.02 & 0.64 & 0.48 & 0.48 & 24.50 & 24.63 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Percentage performance improvement of the TLCBSSD and TLCBSRD over the TLCBD.  
Figure 7: Normalized frequency responses of the primary structure without a damper, with the TLCB, with the TLCBSSD, and with the TLCBSRD.