esa-sceva/satcom-chunk-collection huggingface dataset:
## 3 Provisions for Effective Flange Width of the Composite Beam in Current Design Specifications
### As/Nzs 2327:2017  
As previously stated, EN 1994-1-1 has a significant impact on the design specifications of Australia and New Zealand. Still, AS/NZS 2327:2017 [13] has made greater progress towards perfection than EN 1994-1-1 because, in AS/NZS 2327:2017 clause 3.4.2, provisions of the effective width of concrete flange have three parts according to the type of slab. The first part is clause 3.4.2.1 for the solid slab, the second part is clause 3.4.2.2 for the composite slab, and the third part is clause 3.4.2.3 for the void slab. In clause 3.4.2.1, for the solid slab, the provisions of effective width are the same as in EN 1994-1-1 and use the same diagram as in Figure 4 to clarify the equivalent width. Still, it has a unique requirement--when a slab has pockets or a cut-out within its effective width, then, at the cross-section of concern, the effective width shall be reduced by the width they encroach into this region. In clause 3.4.2.2, for a composite slab in which the ribs are parallel to or within \(15^{\circ}\) of the steel beam axis, the effective width of the concrete flange shall be calculated by clause 3.4.2. For a composite slab in which the ribs form an angle greater than \(15^{\circ}\) from the axis of the steel beam, only the contribution of the concrete above the ribs shall be considered based on the effective width calculated by clause 3.4.2.1. In clause 3.4.2.3, where the concrete flange consists of the avoided slab, the effective width is reduced to account for the loss in compression transfer, which occurs as a consequence of the void slab units. However, the effective width determined by Equation (5) cannot exceed that determined by clause 3.4.2.1. Voided slab depths shall not exceed 260 mm, and the plastic neutral axis of the cross-section shall lie in the steel beam.  
\[b_{\text{eff}}=\left(\frac{\sqrt{1.2f_{c}^{\prime}}}{40}\frac{32d_{b}}{500} \frac{f_{sy}}{460}100\right)+2.5g \tag{5}\]  
where  
\(f_{\text{c}}^{\prime}\) is the characteristic compressive (cylinder) strength of concrete at 28 days, \(d_{\text{b}}\) is the diameter of the transverse reinforcement, \(f_{\text{sy}}\) is the characteristic strength of the reinforcement, and \(g\) is the gap between the ends of the precast units.
###### Abstract  
The application of \(\beta\)-glucosidase from non-_Saccharomyces_ yeasts to improve wine aroma has been widely explored. However, few enzymes are active under the severe conditions of wine aging (high ethanol concentration, low temperature, and low pH). Therefore, the application of \(\beta\)-glucosidase in wine aging needs further research. In this study, the \(\beta\)-glucosidaseages Mg-\(\beta\)gl and Hu-\(\beta\)gl extracted from _Mayerczyma guilliermondii_ NM218 and _Hansenisporn uwarum_ BF345 were purified and used in young Chardonnay wines aged for 50 days. The enzyme activity of the two enzymes was measured. The effects of the two enzymes and a commercial \(\beta\)-glucosidase (An-\(\beta\)gl) on the volatile composition and sensory quality of the wine were also determined. The results showed that Mg-\(\beta\)gl and Hu-\(\beta\)gl had high specific activity of 1.95 U/mg and 2.11 U/mg, respectively, maintaining the activity of 70-80% at 20 \({}^{\circ}\)C, pH of 3.0-4.0, and 15% ethanol, corresponding to wine aging conditions. Analysis of volatiles with GC-MS showed a 65-70% increase in total terpenids and new detection of C\({}_{13}\)-horisoprenoids when the wines were treated with the three \(\beta\)-glucosidase. In addition, wines treated with Mg-\(\beta\)gl and Hu-\(\beta\)gl had more hexanol, phenylethanolamine, ethyl octanoate, ethyl pentanoate, and ethyl caprate than wines treated without and with An-\(\beta\)gl. In sensory analysis, the judges showed a greater preference for Hu-\(\beta\)gl-treated wines, to which they attributed pleasant sweet, floral, honey, pomelo, and banana aromas. The results of this study not only offer a way to improve flavor complexity in wine but also provide a reference for the use of other edible sources of \(\beta\)-glucosidase in wine aging.  
_Hansenisporn uwarum; Meyerczyma guilliermondii; \(\beta\)-glucosidase; enzymatic characterization; aging; volatiles_
# A Comprehensive Survey on Real-Time Applications of WSN
## 2 Types and Requirements of WSN
### Underwater Wireless Sensor Network  
An underwater WSN includes very expensive sensor nodes, which are placed under the water for collecting data and information about underground ambiance. Some limitations or challenges of wireless communication underground include the delay of the network, limited bandwidth, and poor network signal. The aforesaid problem has been recognized by investigators, and in order to eradicate the problem, they proposed a solution via a suitable routing algorithm [18]. [PERSON] et al. (2009) proposed an underwater wireless sensor network based on optical communication between nodes. Radio frequencies and acoustic waves are profoundly attenuated in water. To overcome this problem, optical communication can be considered. In order to increase the efficiency of the system, the authors designed a user interface for managing the optical Physical (PHY) layer implementation on a Digilent Spartan 3 Board [19]. [PERSON] et al. (2017) have assembled a review for prevalent approaches and issues relating to a certain parameter of research. They have presented a paper based on a survey of the underwater wireless sensor network with data aggregation to highlight its advantages and disadvantages. The authors implemented different clustering techniques for performing data aggregation as a result to demonstrate the impact of data aggregation [20].
## 3 Results and Discussion
### Binding Properties  
The isothermal adsorption capacities of the MDMIPs and MDNIPs for melamine are shown in Figure 4C. The amounts of melamine adsorbed on the MDMIPs and MDNIPs increased with increasing initial melamine concentration. The binding capacity of the MDMIPs was higher than that of the MDNIPs. The reason might be that the MDMIPs have specific binding sites that match the size and structure of melamine, whereas the MDNIPs have only non-specific binding sites. Scatchard analysis was used to investigate the adsorption site heterogeneities of the MDMIPs and MDNIPs. Figure 4D shows that the Scatchard plot for melamine adsorption on the MDMIPs was not a single linear plot but two linear plots with different slopes. The slopes and intercepts of the two linear regression curves can be used to calculate \(K_{\rm D}\) and \(Q_{\rm max}\). The linear regression equation for low initial concentrations was \(y=-2.8043x+2400.1\); the \(K_{\rm D}\) and \(Q_{\rm max}\) values were 0.36 ug/mL and 855.8 ug/g, respectively.  
Figure 4: **(A)** FT-IR spectra of Fe\({}_{3}\)O\({}_{4}\) (a), Fe\({}_{3}\)O\({}_{4}\)@SiO\({}_{2}\) (b) and MDMIPs (c); **(B)** Magnetization curves for Fe\({}_{3}\)O\({}_{4}\) (a), Fe\({}_{3}\)O\({}_{4}\)@SiO\({}_{2}\) (b), and MDMIPs (c); **(C)** Melamine adsorption isotherms of MDMIPs (a) and MDMIPs (b); **(D)** Scatchard analysis of melamine adsorption by MDMIPs.  
The linear regression equation for high initial concentrations was \(y=-0.5702x+833.8\); the \(K_{\rm D}\) and \(Q_{\rm max}\) values were 1.75 \(\mu\)g/mL and 1.46 mg/g, respectively. As shown in Figure 4D, two parts of the Scatchard plot curve indicated there were two types of binding sites, nonspecific and specific binding sites. At the low initial concentration of melamine, MIP showed nonspecific adsorption. However, specific recognition binding sites will be activated at the relative high melamine concentrations.
# Performance Analysis of Ground Target Detection Utilizing Beidou Satellite Reflected Signals
## 1 Introduction
Up until now, sea ice detection, sea breeze monitoring, soil moisture, and other research areas have been based on extracting effective information from reflected signals, such as phase information, interference signals, and the polarization ratio to invert different media on the Earth's surface. Because of the difference in the reflection medium between the target and the ground, the target on the ground can be effectively detected by using the reflected signal. The principle of using phase difference information in the tracking loop of GPS-reflected signals to detect ground targets was introduced in detail in [28]. The paper further proposes the use of the reflected signal of the BeiDou satellite to detect ground targets, and carries out the relevant experiment. Section 2 briefly describes the principle of ground detection based on the phase difference information in the tracking loop. Additionally, the relationship between the carrier-to-noise ratio (CNR) information and the target presence is presented. In Section 3, two experiments that were conducted in the suburban area of Beijing city are introduced, including the instruments used, the target movement, and the data collection. Section 4 presents the data processing results of the two experiments in detail, and the results are analyzed based on the geometric relationships among the specular points and the reflection mechanism of the signals. Finally, the conclusions are presented.
## 4 Results and Discussion
### Discussion  
#### 4.2.1 Effect of Gas Pressure  
This section analyzes the influence of gas pressure increases from 10 MPa to 100 MPa at 15 \({}^{\circ}\)C on O-ring performance. Figure 15a shows the maximum von Mises stress curves of the O-ring under various gas pressures. When the gas pressure is below 33 MPa, the inflation-state O-ring endures greater stress and is more susceptible to damage. Conversely, when the gas pressure surpasses 33 MPa, the deflation-state O-ring endures greater stress and is more susceptible to damage. As the gas pressure increases, the von Mises stress of the O-ring experiences a significant rise in both the inflation and deflation states, indicating that higher gas pressure accelerates the damage of the O-ring. Notably, the maximum von Mises stress increases at a faster rate in the deflation state, indicating a higher damage rate in this state.  
Figure 15b shows the maximum contact pressure curve of the O-ring under various gas pressures. The maximum contact pressures of contact surfaces I and II are greater than the corresponding gas pressure, indicating that the O-ring effectively realizes the sealing function within the pressure range of 10-100 MPa. With the gas pressure increases  
Figure 14: The O–ring in the deflation state at \(-60\)\({}^{\circ}\)C and 56 MPa: (**a**) the contact area of contact surface I and contact surface II; (**b**) the inner diameters of contact surface I and contact surface II; (**c**) the effective sealing lengths of contact surface I and contact surface II.  
Figure 15: Influence of gas pressure on O–ring performance: (**a**) max von Mises stress; (**b**) max contact pressure.  
from 10 MPa to 100 MPa at 15 \({}^{\circ}\)C, the contact pressure of contact surface I in the deflation state remains consistently lower than the other three situations (contact surface I inflation, contact surface II inflation, and contact surface II deflation), indicating relatively poorer sealing performance in this situation. Furthermore, the maximum contact pressure of the three situations increases approximately linearly, aligning with the experimental results of [PERSON], [PERSON] et al. [32]. The maximum contact pressure of contact surface I in the deflation state experiences minor fluctuations around 10%. In summary, the increase in gas pressure (10-100 MPa) has a negligible influence on the sealing performance of contact surface I in the deflation state, while significantly improving the sealing performance of the other three conditions.
## 4 The Digital-Twin-Based Detection and Protection Framework
### The Detection and Protection Method in the Framework
#### 4.3.1 Overall Workflow  
Two assumptions are made in this paper: (1) the sensor equipment of the satellite is reliable; and (2) the credibility of the interaction information between the satellite and ground can be guaranteed through the secure communication protocol. The overall workflow of the detection and protection framework proposed in this paper is shown in Figure 15 and is divided into the following main steps.  
Step 1. When the satellite network starts the routing update process, the satellite nodes obtain the current position information (Pos) and link-state advertisements (LSAs) through  
Figure 15: The overall workflow of the detection and protection framework.  
the sensor and send them to the ground station. The ground station updates the digital simulation scenario according to the information received.  
Step 2. After receiving the LSAs, the ground station detects whether the LSA has errors. If an LSA has errors, the ground station will further determine which satellite has errors, send commands to the satellite to rebuild the LSA, and let the satellite return the new LSA to the ground station.  
Step 3. After routing discovery, the satellite network sends the RIBs to the ground station. Based on the digital-twin routing data, the ground station detects whether the RIB has a false link and further determines whether the false link can generate a SH node. If a SH node can be generated, the ground station will rebuild the RIB for the satellite, generate a routing table, and upload the routing table to the satellite.  
Step 4. When sending RIBs, the satellite network does not need to wait for the detection results of the ground station and directly calculates the routing tables. Then, the satellite network will send the generated routing tables to the ground station for detection. If there is a routing table that can trigger a GH node, the ground station will regenerate the routing table for the satellite and upload it to the satellite.
###### Abstract  
Earthmoving is an integral civil engineering operation of significance, and tracking its productivity requires the statistics of loads moved by dump trucks. Since current truck loads' statistics methods are laborious, costly, and limited in application, this paper presents the framework of a novel, automated, non-contact field earthmoving quantity statistics (FEQS) for projects with large earthmoving demands that use uniform and uncovered trucks. The proposed FEQS framework utilizes field surveillance systems and adopts vision-based deep learning for full/empty-load truck classification as the core work. Since convolutional neural network (CNN) and its transfer learning (TL) forms are popular vision-based deep learning models and numerous in type, a comparison study is conducted to test the framework's core work feasibility and evaluate the performance of different deep learning models in implementation. The comparison study involved 12 CNN or CNN-TL models in full/empty-load truck classification, and the results revealed that while several provided satisfactory performance, the VGG16-FineTune provided the optimal performance. This proved the core work feasibility of the proposed FEQS framework. Further discussion provides model choice suggestions that CNN-TL models are more feasible than CNN prototypes, and models that adopt different TL methods have advantages in either working accuracy or speed for different tasks.  
vision-based deep learning; earthmoving operation; dump truck; model comparing; convolutional neural network; transfer learning +
Footnote †: journal: Applied Sciences
## 2 Review of Cryogenic-Cooling Benefits
### Spectroscopic, Lasing, Linear and Nonlinear Optical Parameters
#### 2.7.4 Spectral and Laser Properties of Traditional and New Laser Materials
\) & \(\Delta\lambda_{\text{An}}\textbf{(FWHM)}\) & \(\alpha_{\text{An}}^{P}\textbf{(cm^{2})}\textbf{(10-2)}\) & \(\lambda_{\text{An}}^{P}\textbf{(nm)}\) & \(\Delta\lambda_{\text{An}}\textbf{(FWHM)}\) & \(\alpha_{\text{An}}^{P}\textbf{(cm^{2})}\textbf{(10-2)}\) & **Temp (G)** & **Refs** \\ \hline T3B+ALO3 & & 455-580 & & & & & & & \\ E1 Ic(s) & U & 493 & 120.0 & 6.45 & 790 & 225.0 & 3.0 & 3.2 & 300 & [6,101] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & \\ \hline T3B+ALO3 & & 455-575 & & & & & & & & & \\ E1 Ia(s) & U & 493 & 122.0 & 2.79 & 800 & 236.0 & 1.5 & 3.2 & 300 & [6,101] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & \\ \hline C3B+ALSAF & & 60-703 & & & & & & & & & \\ E1 Ic & U & 637 & 97.7 & 5.4 & 850 & 192.0 & 4.8 & 67 & 300 & [102] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline C3B+ALSAF & & 593-693 & & & & & & & & & \\ E1 Ia & U & 637 & 102.3 & 2.6 & 850 & 171.4 & 1.6 & 67 & 300 & [102] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline C3B+ALCAF & & 585-680 & & & & & & & & & \\ E1 Ic & U & 647 & 85.8 & 2.95 & 763 & 127.0 & 1.3 & 175 & 300 & [102] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline C3B+ALSAF & & 580-680 & & & & & & & & & \\ E1 Ia & U & 647 & 92.7 & 2.00 & 763 & 127.0 & 0.9 & 175 & 300 & [102] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline Yb3+CaF2 & A & 915-970 & 53.3 & 0.83 & 1000 & 26.7 & 0.25 & 1900 & 300 & [103] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline Yb3+CaF2 & A & 915-970 & 53.3 & 0.88 & 1033 & 43.3 & 0.50 & 1900 & 77 & [103] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline Yb3+CaF2 & A & 980 & 2.93 & 1.57 & 990 & 10.7 & 0.83 & 1900 & 77 & [103] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline Yb3+CaF2 & A & 900-953 & 11.04 & 0.80 & 1033 & 13.2 & 1.89 & 820 & 300 & [104] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & & \\ \hline Yb3+LaAG & A & 978 & 3.49 & 3.81 & 1078 & 14.3 & 0.89 & 820 & 300 & [106] \\ \hline Yb3+LaAG & A & 915-945 & 30.0 & 0.94 & 1030 & 3.4 & 2.50 & 950 & 295 & [104] \\  & \multicolumn{4}{c}{Peak} & & & & & & & & \\ \hline Yb3+LaAG & A & 915-945 & 27.0 & 1.73 & & & & & & \\ \hline Yb3+LaAG & A & 970 & 1.10 & 2.47 & 1030 & 1.1 & 13.90 & 950 & 100 & [100] \\ \hline Yb3+Sc203 & A & 942 & 26.2 & 0.87 & 1041 & 13.4 & 1.44 & 1.44 & 1.44 & \\  & \multicolumn{4}{c}{Peak} & & & & & & & & \\ \hline Yb3+Y203 & A & 957 & 2.4 & 4.40 & 1095 & 10.7 & 0.33 & 800 & [107] \\ \hline Yb3+Y203 & A & 990 & 5.96 & 0.87 & 1031 & 14.3 & 1.06 & & & \\ \hline Yb3+Y203 & A & 977 & 3.97 & 2.40 & 1076 & 15.6 & 0.42 &
# Geophysical Study of a Large Landslide Affecting the Urban Area of Albuuuelas (S Spain)
## 3 Geophysical Methods  
### H/V Method  
The HVSR or H/V technique is broadly employed for the rapid detection and assessment of seismic amplification effects by measuring ambient vibrations (or seismic noise) with just a single three-component station. This technique requires the acquisition of three components of the ground motion and consists of obtaining the ratio between the horizontal and vertical Fourier spectrum. This ratio, which is expressed as a function of the frequency, is called the H/V (or HVSR) curve (or function). The frequency peaks (or H/V peaks) found in this spectral ratio provide a direct estimation of the seismic resonant effects of the soil under study (e.g., [15; 44; 45; 46; 47; 48; 49; 50; 51]). The resonant frequencies reflect impedance contrasts found between sedimentary layers and especially between the sedimentary cover and the bedrock.  
This method was first introduced by [52], and then revised by [16]. These authors highlighted the correlation between the frequency value of the H/V peak and the fundamental resonance frequency of the site (\(f_{0}\)), suggesting the ability of this technique to provide information on the dynamic characteristics of the subsoil. From these considerations, the well-known Equation (1) is derived [44],  
Figure 3: Geological map of the Alburuelas area showing the location of the measurement sites. (1) Red salts (Serravallian); (2) reef sandstone and calcarenite (Lower Tortonian); (3) red–orange conglomerates and silt (Upper Tortonian); (4) conglomerates (Pliocene–Quaternary); (5) alluvial sediments (Quaternary); (6) slope debris (Quaternary); (7) landslide (Quaternary); (8) landslide scarp; (9) strike and dip of beds; (10) single station measurements (HVSR); (11) array measurements; (12) borehole drilled + HVSR + Array; (13) blocks of houses.  
\[f_{0}=\frac{V_{\rm S}}{4\cdot h} \tag{1}\]  
relating the resonant frequency (\(f_{0}\)) with the average shear-wave velocity (\(V_{\rm S}\)) and the thickness (\(h\)) of the sedimentary layer.  
According to [53], the H/V analysis can be used for estimating the possible seismic impedance contrasts, taking into account the frequency peaks; defining the lithological and geological formations constituting the sedimentary cover and the bedrock; and creating a map of the resonance frequency along an urban area, which defines the limits of the more dangerous areas in terms of soil-building structure resonance.
# Frequency Sensitivity and Mode Characteristics of Body Structure for a Piezoelectric-Based UUV
## 3 Dynamic Model and Equations
\begin{array}{l}\Delta u=\frac{\left[C_{13}(\Omega_{2 nm}^{2}-C_{22})- G_{12}G_{23}\right]}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^{2}-G_{22} \right)-G_{12}G_{21}}\sin(\lambda x)\sin(n\theta)\\ \Delta v=\frac{\left[C_{23}(\Omega_{2 nm}^{2}-G_{11})-G_{21}G_{13}\right]}{\left( \Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^{2}-G_{12}G_{21}\right)}\cos (\lambda x)\cos(n\theta)\\ \Delta w=\cos(\lambda x)\sin(n\theta)\end{array} \right. \tag{12}\]  
From Equations (12) and (5), the vibration mode of the UUV body can be obtained. Thus, the shear modes can be given as follows:  
\[\left\{ \begin{array}{l}F_{Sx}=K\bigg{[}\frac{G_{13}(\Omega_{2 nm}^{2}-G_{12}) -G_{12}G_{23}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^{2}-G_{ 21}\right)-G_{12}G_{21}}\lambda+\frac{\mu}{R_{m}}(1-B_{imn}n)\bigg{]}\cos( \lambda x)\sin(n\theta)\\ F_{S\theta}=K\bigg{[}\frac{G_{13}(\Omega_{2 nm}^{2}-G_{22})-G_{12}G_{23}}{\left( \Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^{2}-G_{22}\right)-G_{12}G_{ 12}}\lambda\mu+\frac{1}{R_{m}}-\frac{\mu}{R_{m}}-\frac{G_{22}(\Omega_{2 nm}^{2} -G_{11})-G_{21}G_{13}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^ {2}-G_{22}\right)-G_{12}G_{12}}\bigg{]}\cos(\lambda x)\sin(n\theta)\\ F_{Sx\theta}=K\frac{1-\mu}{2}\bigg{[}\frac{1}{R_{m}}\frac{G_{13}(\Omega_{2 nm}^ {2}-G_{22})-G_{12}G_{23}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{ 2 nm}^{2}-G_{22}\right)-G_{12}G_{12}}n-\frac{G_{22}(\Omega_{2 nm}^{2}-G_{11})-G _{11}G_{13}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm}^{2}-G_{22} \right)-G_{12}G_{21}}\lambda\bigg{]}\sin(\lambda x)\cos(n\theta)\\ \end{array} \right. \tag{13}\]  
where, \(F_{Sx}\) and \(F_{S\theta}\) are thin film force modes along \(x\) and \(\theta\) directions, while \(F_{Sx\theta}\) is thin film shear force mode. And the torsional moment modes can be expressed by:  
\[\left\{ \begin{array}{l}M_{x}=D\bigg{[}\lambda^{2}+\frac{\mu n}{R_{m}}\bigg{(} \frac{G_{23}(\Omega_{2 nm}^{2}-G_{11})-G_{21}G_{13}}{\left(\Omega_{2 nm}^{2}-G_{11 }\right)\left(\Omega_{2 nm}^{2}-G_{22}\right)-G_{12}G_{21}}-n\bigg{)}\bigg{]} \cos(\lambda x)\sin(n\theta)\\ M_{\theta}=D\bigg{[}\mu\lambda^{2}+\frac{n}{R_{m}}\bigg{(}\frac{G_{23}(\Omega_{ 2 nm}^{2}-G_{11})-G_{21}G_{13}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left( \Omega_{2 nm}^{2}-G_{22}\right)-G_{12}G_{21}}-n\bigg{)}\bigg{]}\cos(\lambda x) \sin(n\theta)\\ M_{x\theta}=D\lambda\frac{1-\mu}{2R_{m}}\bigg{(}2n-\frac{G_{23}(\Omega_{2 nm}^{2} -G_{11})-G_{21}G_{13}}{\left(\Omega_{2 nm}^{2}-G_{11}\right)\left(\Omega_{2 nm} ^{2}-G_{22}\right)-G_{12}G_{21}}\bigg{)}\sin(\lambda x)\cos(n\theta)\\ \end{array} \right. \tag{14}\]  
where, \(M_{x}\) and \(M_{\theta}\) are torsional moment modes along \(x\) and \(\theta\) directions, while \(M_{x\theta}\) is torsional moment mode.