Anti-vibration Design of the Civil Aircraft’s Horizontal Tail Trailing Edge Compartment

The horizontal tail trailing edge compartment is a vital component of civil aircraft, situated between the horizontal tail beam and elevator. Its primary function is to connect the elevator and meet the aerodynamic sealing requirements of the unflapped elevator, and to transfer the aerodynamic and inertial load of the elevator to the outboard wing box of the horizontal tail in concentrated form. Under aerodynamic or other excitation, the horizontal tail trailing edge compartment may experience vibration, increasing the risk of structural damage. This study aims to enhance the anti-vibration capability of the horizontal tail trailing edge compartment via parametric finite element analysis. This analysis examines various design elements of the horizontal tail end cabin and compares the first-order modal frequency to deduce the influence of factors on the stiffness. The results provide a reference for the anti-vibration design of the horizontal tail trailing edge compartment in civil aircraft.


Introduction
The main function of the civil aircraft's horizontal tail is to ensure the longitudinal stability and pitch control of the aircraft [1] .In actual flight, the horizontal tail is subjected to aerodynamic loads caused by various factors, such as the deflection of the control surfaces, downwash of the wing-body combination, and jet exhaust from the aircraft engine [2] .These can cause vibration phenomena on the horizontal tail.
In practical situations, excessive vibration may lead to serious fatigue issues.According to statistics from the US in the last century, accidents caused by fatigue fracture due to alternating dynamic loads accounted for 95% of the total number of failures in mechanical structures.To avoid such fatigue problems, anti-vibration design has become one of the key considerations in the aircraft design process [3]   .Relevant design specifications have also been made to regulate the strength and stiffness of aircraft [4]   .
Increasing structural stiffness as one of the commonly used methods for anti-vibration design can effectively increase the low-order modal frequency of the structure, reduce vibration response, and greatly reduce the risk of structural damage caused by severe vibration.
To improve the anti-vibration capability of the horizontal tail of civil aircraft, finite element simulation was used to optimize the local first-order modal frequency of the cabin after comparing various design elements.The research was conducted on the anti-vibration design of the horizontal tail trailing edge compartment.

Anti-vibration design process
The vibration-resistant design and analysis process of the horizontal tail trailing edge compartment is illustrated in Figure 1.First, it is necessary to determine the geometric structure of the horizontal tail trailing edge compartment, and propose parameters that can be optimized for design based on the structural characteristics of the trailing edge compartment, such as rib thickness and stringer thickness [5]   .Then we choose appropriate modeling criteria, establish a dynamic finite element model of the horizontal tail trailing edge compartment, define material parameters and boundary conditions, and use them for variational modal analysis.After solving, the optimization effect is determined by comparing the local first-order modal frequencies of the trailing edge compartment under different values of a single variable.Finally, the analysis results are verified through experimental comparison to determine the best anti-vibration design optimization scheme.Its main structure includes ribs, suspension joints, actuator supports, upper and lower skin panels, reinforced profiles, and seal components [6] .Figure 2 shows more information about the structure of the rear airframe.

Optimization parameters of vibration resistance for the horizontal tail trailing edge compartment
The stiffness of the horizontal tail trailing edge compartment was analyzed to select several parameters that have a significant impact on it.These parameters include the thickness of the stringer and rib, the number of ribs, as well as the length of the free end of the sealing strip [7] .The impact of these variables on stiffness was obtained through a variable analysis.

Structural Dynamics Modeling
According to the dynamic modeling method of large civil aircraft structures [8][9] , HyperMesh is used for pre-processing the finite element model, with a mesh base size of 10 mm.In the model shown in Figure 3, the upper and lower unidirectional laminated strips of the panels are modeled using Shell elements, and the QUAD4 four-sided single-element form is preferred.The honeycomb structure is modeled using Solid elements, and the Hex8 hexahedral element is preferred.The stringers, ribs, sealing strips and other structures are modeled using Shell elements, and the QUAD4 four-sided single-element form is preferred.The fasteners are modeled using Cweld elements.The boundary conditions are that six degrees of freedom are restricted for the part connected to the horizontal tail rear beam by applying fixed supports.
The model consists of 131, 801 nodes and 147, 645 elements.According to the optimization parameters selected in the previous stage, the ribs are first added in the outermost compartment section.The calculation results of the local first-order mode frequency in the outermost compartment section are shown in Table 1.
Based on the configuration with added ribs, variational analysis is conducted on the thickness of stringers and ribs, and the local first-order mode frequency at the outermost compartment section is calculated between 2.0 mm and 3.0 mm.The calculation results are shown in Table 2 and Table 3, respectively.
Finally, a variable parameter analysis is conducted on the length of the sealing strips' free section, and the calculated results are shown in Table 4.

Experimental Verification
In order to verify the validity of the analysis results [10] , modal experiments are performed on the horizontal tail trailing edge compartment under the original configuration and the horizontal tail trailing edge compartment with two additional ribs [11] .The modal test models are shown in Figures 5  and 6, respectively.Comparing the test results with the analysis results, the error of the local first-order modal frequency is only 7 Hz, and the increase of the local first-order modal frequency after the configuration change is 30 Hz in both cases.

Conclusions
This paper investigates the anti-vibration design of the horizontal tail trailing edge compartment of civil aircraft and draws the following conclusions: 1) By comparing the results of the modal test with the finite element analysis, the error of the local first-order modal frequency analysis result is only 7 Hz, the modal frequency increase is completely consistent, so the analysis result is accurate and reliable.
2) The anti-vibration design of the horizontal tail trailing edge compartment is carried out.The results show that increasing the thickness of the ribs and stringers in the horizontal tail trailing edge compartment structure has an insignificant effect on improving stiffness; increasing the rib partitions and shortening the length of the free end of the sealing strip have a significant effect on improving stiffness and can be used to guide the design of the horizontal tail trailing edge compartment.

Figure 2 .
Figure 2. Structure of the horizontal tail trailing edge compartment

Figure 3 .
Figure 3. Finite element model of the horizontal tail trailing edge compartment 3.4.Variational analysis Under the condition of the original configuration, the local first-order mode of the horizontal tail trailing edge compartment appeared in the outermost compartment section, with a frequency of 60.20 Hz and a mode shown in Figure 4.The thickness of the stringers and ribs in the original configuration was 2 mm, and the sealing strips extended to 45 mm.According to the optimization parameters selected in the previous stage, the ribs are first added in the outermost compartment section.The calculation results of the local first-order mode frequency in the outermost compartment section are shown in Table1.Based on the configuration with added ribs, variational analysis is conducted on the thickness of stringers and ribs, and the local first-order mode frequency at the outermost compartment section is calculated between 2.0 mm and 3.0 mm.The calculation results are shown in Table2 and Table 3, respectively.Finally, a variable parameter analysis is conducted on the length of the sealing strips' free section, and the calculated results are shown in Table4.

Figure 4 .
Figure 4.The local first-order mode of the horizontal tail trailing edge compartment

Figure 5 .Figure 6 .
Figure 5. Mode experiment model of the original configuration

Figure 7 .Figure 8 .
Figure 7.The local first-order mode of the original configuration

Table 1 .
Analysis results of variable rib quantity

Table 2 .
Analysis results of variable rib thickness

Table 3 .
Analysis results of variable stringer thickness

Table 4 .
Analysis results of variable sealing strip free section length