Modeling and nonlinear vibration analysis method for cone-column combined shell connected by bolts and flanges

Abstract

The embodiment of the invention relates to a modeling and nonlinear vibration analysis method for a cone-column combined shell connected by a bolt and a flange. The method comprises the following steps: establishing a three-dimensional model of the bolt flange connection cone-column combined shell, performing simulation pretreatment on the model to obtain a finite element model of the bolt flange connection cone-column combined shell, setting parameters, applying acceleration excitation, and performing state setting; simulating calculation is conducted on the inherent frequency, the vibration mode and the structural vibration response under different excitation amplitudes under the set tightening torque, and a simulation result is verified through a modal test and a basic excitation response test; the dynamic softening phenomenon of an amplitude-frequency curve is explained from the two aspects of contact stress and contact state of a bolt flange connection interface; and analyzing the influence rule of the excitation amplitude, the bolt pre-tightening force and the flange thickness on the nonlinear vibration characteristic of the structure. According to the method, a finite element model is adopted and is combined with a test for comparative research, the modeling method is accurate in calculation result, and the modeling requirement of a complex actual structure can be met.

Description

Technical Field

[0001] The invention belongs to the technical field of mechanical dynamics, and in particular relates to a method for modeling and nonlinear vibration analysis of a cone-cylinder combined shell connected by bolt flanges. Background Art

[0002] Bolted flange connection structures are widely used in aerospace, machinery manufacturing, construction engineering and other fields due to their advantages such as detachability, easy assembly and strong load-bearing capacity. However, due to the complex and nonlinear mechanical characteristics of bolted flange connection structures, it is difficult to accurately predict their dynamic behavior through simplified theoretical analysis methods. This is particularly evident in the cone-cylinder combined shell structure. Due to the particularity of the geometric shape and the complex stress environment, the nonlinear dynamic characteristics of the bolted flange connection cone-cylinder combined shell are very significant.

[0003] Therefore, it is particularly important to establish a high-fidelity finite element model of the bolted flange-connected cone-cylinder composite shell and systematically carry out its nonlinear vibration analysis.

[0004] To date, given that the friction behavior at the interface of bolted connections has an important influence on the structural dynamics of bolted systems, many scholars have systematically studied and summarized the mechanical properties of bolted connections based on theoretical derivation combined with experimental fitting. Eriten et al. conducted tensile tests on aluminum and steel joints under different load conditions and proposed a mechanical model that considers the sliding behavior of the spherical contact part. Abad et al. conducted a series of transient nonlinear analyses, determined the Valanis model parameters of bolted lap joints, and studied their changes with bolt preload. Based on experimental results under torsional excitation, Liu et al. proposed a third-order modified Jenkins unit model. Song et al. proposed an Iwan beam unit consisting of a spring and a friction slider to analyze the dynamic response of bolted beam structures.

[0005] In addition, some researchers have used the finite element method to analyze the mechanical properties of bolted connections. Jamia et al. introduced an equivalent mechanical model of bolted connections that can predict micro-slip behavior and proposed a parameter identification scheme based on contact interface behavior. Zhao et al. developed a new probability density function to analyze the actual two-dimensional pressure distribution in bolted connections and proposed an improved tangential stiffness model based on the finite element method. Verwaerde proposed a nonlinear finite element model and its identification method to simulate the characteristics of single bolt connections. Liu et al. introduced an improved two-dimensional finite element model for predicting the load distribution in multi-bolt single lap joints of composite materials. Zhao et al. performed finite element analysis on the combined rotor structure and clarified the mechanism of the uneven slip phenomenon.

[0006] Based on the above-mentioned mechanical model of bolted connection, many scholars have conducted extensive research on the vibration characteristics of bolted thin-walled structures. Pan et al. proposed a simplified dynamic model of bolted flange connection, focusing on the nonlinear modes of double joint systems with free boundary conditions. Liu et al. proposed a semi-analytical dynamic model of bolted composite plates, considering the viscosity, slip and separation behavior of bolted connections. Xing and Wang studied the nonlinear vibration characteristics of bolted flange connection plates by theoretical and experimental methods. Chai and Wang studied the nonlinear dynamic characteristics of bolted cone-cylinder composite shells and analyzed their dynamic responses under radial viscosity and slip contact states. It should be pointed out that these studies all belong to the category of semi-analytical methods.

[0007] In addition to the semi-analytical method, many researchers have also used the finite element method to establish a unified dynamic model of the bolted connection structure and carried out corresponding vibration analysis. Sun et al. developed a finite element model of an aero-engine high-pressure rotor system to analyze its dynamic characteristics under different preload conditions. Qin et al. constructed a finite element model of a bolted disk-drum structure and studied the effect of bolt loosening on steady-state response and time-varying stiffness. Zou et al. used the finite element method to establish a dynamic model of a multi-bolt flange-connected disk-drum rotor and evaluated the effect of the preload state of the mating surface on the vibration behavior.

[0008] Generally speaking, the methods for analyzing the dynamic response of bolted thin-walled structures are mainly semi-analytical methods and finite element methods. Compared with the semi-analytical method, modal tests and back-stepping identification are required to obtain the bolted joint stiffness before subsequent response analysis. The finite element method allows the direct construction of the structural dynamic model based on the actual boundary conditions and realizes the complete modal and response analysis process. In addition, the finite element method has a wider applicability and can meet the modeling requirements of complex bolted joint structures. Therefore, the dynamic analysis of bolted joint structures based on the finite element method has unique advantages.

[0009] The present invention first develops a comprehensive dynamic modeling and vibration analysis process for a cone-cylinder composite shell with bolted flange boundaries. The proposed model is then validated by modal tests and vibration response tests under foundation excitation. In addition, the dynamic softening phenomenon observed in the amplitude-frequency curve is revealed based on the contact stress and contact state at the bolted connection interface. Finally, the effects of excitation amplitude, preload, and flange thickness on the nonlinear vibration response of the structure are discussed. Summary of the invention

[0010] 1. Technical issues to be resolved

[0011] In order to solve the above problems in the prior art, the present invention provides a method for modeling and nonlinear vibration analysis of a cone-cylindrical composite shell connected by bolt flanges.

[0012] (II) Technical solution

[0013] In order to achieve the above object, the main technical solutions adopted by the present invention include:

[0014] A method for modeling and nonlinear vibration analysis of a bolted flange-connected cone-cylinder composite shell comprises the following steps:

[0015] Establish a three-dimensional model of a bolted flange-connected cone-cylinder composite shell and perform simulation pre-processing on the model to obtain a finite element model of a bolted flange-connected cone composite shell, set parameters, apply acceleration excitation, and perform state setting;

[0016] The natural frequency, vibration mode and structural vibration response under different excitation amplitudes are simulated and calculated under the set tightening torque, and the simulation results are verified by modal test and basic excitation response test.

[0017] The dynamic softening phenomenon of the amplitude-frequency curve is explained from the two aspects of contact stress and contact state of the bolt-flange connection interface; the influence of excitation amplitude, bolt preload and flange thickness on the nonlinear vibration characteristics of the structure is analyzed.

[0018] Preferably, a bolt flange boundary cone-cylinder combined shell model is established based on SOLIDWORKS three-dimensional mechanical design software;

[0019] Based on ANSYS Workbench finite element analysis software, complete finite element simulation pre-processing;

[0020] In the Static Structural module, set parameters such as friction contact, step size, and convergence residual value to calculate the contact stress and contact state. In the Harmonic Response module, apply horizontal foundation acceleration excitation to the clamping position of the bolt hole at the bottom of the base to extract the displacement response at the vibration pickup point.

[0021] In terms of the connection interface contact settings, the bolt and nut and the base and nut are set to binding, the bolt head and the cone-column combined shell are set to friction, the bolt and the base are set to friction, and the cone-column combined shell and the base are set to friction;

[0022] The whole structure is meshed with Solid 185 entity elements. The number of elements after meshing is 360546 and the number of nodes is 794998. The cone-cylinder composite shell adopts tetrahedral mesh with an element size of 5mm.

[0023] The base uses a hexahedral grid with a cell size of 2 mm;

[0024] The bolt and nut structure uses hexahedral mesh and multi-region meshing methods, and the unit size is 3mm;

[0025] The mesh of the bolt and nut contact surface is refined to a size of 1 mm;

[0026] The natural frequency, vibration mode and resonance displacement are simulated and calculated under the set tightening torque, and the simulation results are verified by modal test and basic excitation response test.

[0027] The dynamic softening phenomenon of the amplitude-frequency curve is explained from the aspects of contact stress and contact state of the bolt-flange connection interface.

[0028] Analyze the influence of bolt preload and flange thickness on the nonlinear vibration characteristics of the structure.

[0029] Preferably, the modal test is to obtain the natural frequency and vibration mode of the bolted flange-connected cone-column composite shell by a hammer method, and to obtain the vibration response of the bolted cone-column composite shell by a vibration table test, so as to effectively verify the accuracy of the finite element results.

[0030] Preferably, the nonlinear structural analysis and the harmonic response sweep frequency analysis are combined to directly provide the amplitude-frequency curve of the structure in a finite element simulation manner.

[0031] Preferably, the dynamic softening phenomenon of the amplitude-frequency curve of the component under different excitation amplitudes is explained from the perspective of contact stress and contact state.

[0032] Preferably, the influence of the preload force on the nonlinear vibration response (including frequency and amplitude) of the structure under different acceleration excitation amplitudes is analyzed.

[0033] Preferably, the influence of different flange thicknesses on the structural resonant frequency and nonlinear vibration response is analyzed.

[0034] Beneficial Effects

[0035] The beneficial effects of the present invention are as follows: the method for modeling and nonlinear vibration analysis of a cone-cylinder combined shell with bolt flange connection provided by the present invention takes a solid bolt-connected cone-cylinder combined shell model as a research object, and adopts a method combining simulation and experiment to conduct comparative research. This modeling method has accurate calculation results and can meet the modeling requirements of complex actual structures. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A schematic flow chart of a method for modeling and nonlinear vibration analysis of a cone-cylinder composite shell connected by bolted flanges provided in a specific embodiment of the present invention;

[0037] Figure 2 A schematic diagram of a cone-cylinder composite shell with bolt connections provided in a specific embodiment of the present invention;

[0038] Figure 3The matching interface between the finite element model of the cone-cylinder composite shell and the bolt flange boundary provided in the specific embodiment of the present invention;

[0039] Figure 4 A schematic diagram of a modal test device provided for a specific embodiment of the present invention;

[0040] Figure 5 A schematic diagram of a basic stimulus response test device provided for a specific embodiment of the present invention;

[0041] Figure 6 Comparison of simulation and test amplitude-frequency curves provided for specific implementations of the present invention;

[0042] Figure 7 The amplitude-frequency curves under different tightening torques provided in the specific embodiments of the present invention show different degrees of dynamic softening phenomenon, among which Figure 7 a. Figure 7 b. Figure 7 The tightening torques of c are 8N·m, 12N·m and 16N·m respectively;

[0043] Figure 8 A schematic diagram of the contact stress of the connection interface under different excitation amplitudes provided in a specific embodiment of the present invention, wherein Figure 8 a. Figure 8 b. Figure 8 The excitation amplitudes of c are 1g, 2g, and 3g;

[0044] Fig. 9 A schematic diagram of the contact state of the connection interface under different excitation amplitudes provided by a specific embodiment of the present invention, wherein Fig. 9 a. Fig. 9 b. Fig. 9 The excitation amplitudes of c are 1g, 2g, and 3g;

[0045] Fig.10 The influence of preload force on structural vibration response (including frequency and amplitude) under different acceleration excitation amplitudes provided by the specific implementation method of the present invention is as follows: Fig.10 a. Fig.10 b. Fig.10 The excitation amplitudes of c are 1g, 2g, and 3g;

[0046] Fig.11 Schematic diagram of contact stress of connection interface under different preload forces provided in a specific embodiment of the present invention, wherein 11a, Fig.11 b. Fig.11 c. Fig.11 The preload torques of d are 8N·m, 10N·m, 18N·m and 20N·m respectively;

[0047] Fig.12A schematic diagram of the contact state of the connection interface under different preload forces provided by a specific embodiment of the present invention, wherein Fig.12 a. Fig.12 b. Fig.12 c. Fig.12 The tightening torques of d are 8N·m, 10N·m, 18N·m and 20N·m respectively;

[0048] Fig.13 The effect of the excitation amplitude on the nonlinear vibration characteristics of the structure under different flange thickness conditions provided by the specific implementation method of the present invention, wherein Fig.13 a. Fig.13 b. Fig.13 The flange thicknesses of c are 4mm, 6mm and 8mm respectively;

[0049] Fig.14 A schematic diagram of the contact stress of the connection interface under different flange thicknesses provided for a specific embodiment of the present invention, wherein Fig.14 a. Fig.14 b. Fig.14 The flange thicknesses of c are 4mm, 6mm and 8mm respectively;

[0050] Fig.15 A schematic diagram of the contact state of the connection interface under different flange thicknesses provided for a specific embodiment of the present invention, wherein Fig.15 a. Fig.15 b. Fig.15 The flange thicknesses of c are 4mm, 6mm and 8mm respectively. DETAILED DESCRIPTION

[0051] In order to better explain the present invention and facilitate understanding, the present invention is described in detail below through specific implementation modes in conjunction with the accompanying drawings.

[0052] like Figure 1 As shown, the present invention discloses a method for modeling and nonlinear vibration analysis of a cone-cylinder composite shell connected by bolt flanges, comprising the following steps:

[0053] A three-dimensional model of a bolted flange-connected cone-cylinder composite shell is established, and the model is pre-processed for simulation to obtain a finite element model of a bolted flange-connected cone composite shell. Parameters are set, acceleration excitation is applied, and state settings are performed.

[0054] The natural frequency, vibration mode and structural vibration response under different excitation amplitudes are simulated under the set tightening torque, and the simulation results are verified by modal test and basic excitation response test.

[0055] The dynamic softening phenomenon of the amplitude-frequency curve is explained from the aspects of contact stress and contact state of the bolt flange connection interface.

[0056] Analyze the influence of excitation amplitude, bolt preload and flange thickness on the nonlinear vibration characteristics of the structure.

[0057] The method is specifically described as follows:

[0058] 1. Model building

[0059] The 3D mechanical design software SOLIDWORKS is used to establish a bolt flange boundary cone-cylinder combined shell model. Based on the built-in Toolbox standard parts bolt and nut design library of SOLIDWORKS, hexagonal head bolts and nuts are selected, and the model is GB / T5781-2000.

[0060] Figure 2 A schematic diagram of a cone-cylinder composite shell with bolted connections is shown, where the cone angle of the structure is represented by α. The cone end is free and the cylinder end is fixed by evenly distributed bolts. The thickness of the cone and cylinder sections is equal, represented by h. The lengths of the cone and cylinder sections are represented by L o and L y The minimum and maximum radii of the conical segment are represented by R o and R. Flange thickness is h f .

[0061] Import the established 3D model into the finite element analysis software ANSYS Workbench, define the geometry and material parameters in turn, establish contact, divide the mesh, set constraints, and complete the finite element simulation pre-processing; set the friction contact, step size, convergence residual value and other parameters in the Static Structural module, calculate the Mise equivalent stress and contact state, and in the harmonic response module, apply horizontal foundation acceleration excitation to the clamping position of the bolt hole at the bottom of the base to extract the displacement response at the vibration pickup point; Figure 3 The matching modes of different structural surfaces in the bolt flange connection area are given. In terms of the connection interface contact settings, the bolt and nut and the base and nut are set to be bound, the bolt head and the cone-cylinder combined shell are set to be friction (friction coefficient 0.15); the bolt and the base are set to be friction (friction coefficient 0.15); the cone-cylinder combined shell and the base are set to be friction (friction coefficient 0.1).

[0062] The entire structure is meshed using Solid 185 solid elements, where the cone-cylinder combined shell uses tetrahedral meshes with a unit size of 5 mm, and the base uses hexahedral meshes with a unit size of 2 mm. The bolt and nut structure uses hexahedral meshes and multi-zone meshing methods (MultiZone), with a unit size of 3 mm. Since the bolts and nuts are smaller than the overall cone shell structure, and the simulation results focus on the contact surface, the mesh of the bolt and nut contact surface is refined to 1 mm. The number of units after final meshing is 360,546, and the number of nodes is 794,998.

[0063] 2. Experimental Verification

[0064] 2.1 Modal test verification

[0065] The homogeneous cone-cylinder composite shell specimen made of Q235 is used as the test object, and the corresponding parameters are shown in Table 1. Figure 4 As shown in the figure, the cone-cylinder composite shell specimen is installed in the fixture by 32 M12 bolts, and the tightening torque is 12N·m. The test facilities required for the modal experiment include a three-axis acceleration sensor (PCB 356A01), a force hammer (PCB 086C01) and a 12-channel LMS data acquisition system (SC-XS12-a).

[0066] Table 1 Materials and geometric parameters of cone-cylinder composite shell specimens

[0067]

[0068] In the modal test, a multi-input single-output analysis method was used to evenly arrange 128 hammer points in the cone-cylinder composite shell. The hammer was used to vertically hit the 128 points on the outer surface of the cone-cylinder composite shell in sequence, and the test data collected by the acceleration sensor was transmitted to the LMS data acquisition front end.

[0069] Tables 2 and 3 list the natural frequencies and vibration modes obtained from the experiment and simulation, respectively. The maximum error between the natural frequencies of the experiment and simulation is less than 5.6%, which occurs at f n2 In addition, the vibration modes of the simulation and the experiment are very consistent. The above comparison verifies the accuracy of the current simulation results and shows that the vibration characteristics of the bolted flange-connected cone-cylinder composite shell can be effectively estimated by the current simulation model.

[0070] Table 2 Comparison of natural frequency simulation and test results

[0071]

[0072] Table 3 Comparison of vibration mode simulation and test results

[0073]

[0074]

[0075] 2.2 Basic stimulus response test verification

[0076] Figure 5The response test system of the bolted flange-connected cone-cylinder composite shell is shown, in which the bolted cone-cylinder composite shell with a fixture is installed on a vibration table (DONGLING LTT1212). Then, a series of frequency sweep tests with different excitation levels were carried out. To ensure the accuracy of the measurement results, the sweep speed of each event of the sweep frequency test was set to 1Hz / 4sec. The frequency sweep interval was determined by the hammer test. Considering the importance of the fundamental frequency, the f n1 Therefore, the modal damping ratio related to the first two natural frequencies is introduced in the theoretical calculation. According to the modal test results, the modal f n1 and f n2 The modal damping ratios are 1.24% and 0.10% respectively.

[0077] The vibration response of the bolted cone-cylinder composite shell obtained by experiment and simulation is shown in Figure 6 As shown in Figure 1, the amplitude-frequency curves under different excitation levels are analyzed. Figure 6 As shown in the figure, the overall trend of the simulated amplitude-frequency curve is roughly the same as the experimental results. When the excitation amplitude is 1g, the maximum error of the resonance displacement does not exceed 7.8%. The above comparison results show that the developed model can effectively predict the dynamic characteristics of bolted cone-cylinder composite shells.

[0078] 3. Parameter influence and discussion

[0079] 3.1 Effect of excitation amplitude

[0080] Firstly, the influence of excitation amplitude on the nonlinear vibration characteristics of bolted flange boundary cone-cylinder composite shell under different tightening torques is analyzed, and the frequency sweep range is 330-380Hz. Figure 7 As shown in the figure, with the increase of the basic excitation amplitude, the amplitude-frequency curves under different tightening torques show different degrees of dynamic softening. As the excitation amplitude increases from 1g to 3g, under the tightening torque of 8N·m, the resonance frequency decreases from 358.5Hz to 348.0Hz, a decrease of 10.5Hz, and the displacement amplitudes are 1.62×10 -5 and 6.10×10 -7 m, the resonance displacement increases by 3.77 times. Under a tightening torque of 12 N·m, the frequency attenuates by 5.0 Hz and the displacement increases by 3.20 times. Under a tightening torque of 16 N·m, the frequency attenuates by 4.0 Hz and the displacement increases by 3.01 times. It can be seen that the dynamic softening effect caused by the increase in the excitation level decreases with the increase in the tightening torque. In addition, for the resonant response of high tightening torque (such as Figure 7 (c)), a linear increase in the excitation level can cause an approximately linear increase in the resonant displacement, and as the tightening torque decreases, the increase in the resonant displacement caused by the same excitation level will gradually increase.

[0081] To explain Figure 6 and Figure 7 The contact stress and contact state in the bolt flange connection interface under different excitation levels when the tightening torque is 12N·m are studied by considering the dynamic softening phenomenon in the bolt flange connection interface. Firstly, the Mise stress at the bolt flange connection interface under different excitation levels is analyzed, and the unit is MPa, such as Figure 8 It is not difficult to see that the increase in the acceleration excitation level leads to an increase in the contact stress at the connection interface and also leads to an uneven distribution of the contact stress. Fig. 9 The change of contact state at the connection interface under different excitation levels is shown. According to different constraint positions and states, the contact state is divided into the following five categories: "overconstraint" represents the overconstraint state, "separation" represents the separation state, "contact" represents contact but not fully bonded, "sliding" represents relative sliding, and "stickiness" represents full bonding. It can be clearly seen that the increase in the excitation level leads to a significant change in the contact state at the bolt flange connection interface. When the excitation level is 1g, the contact state is mainly a sticky state. However, as the excitation level increases, the adhesion area at the connection interface gradually decreases and the sliding area gradually increases. When the acceleration excitation level reaches 3g, the contact state is mainly slip. The slip at the contact surface directly leads to a decrease in the local stiffness of the structure, which reduces the resonant frequency.

[0082] 3.2 Influence of bolt preload

[0083] The influence of preload (tightening torque) on the nonlinear vibration characteristics of the structure under different acceleration excitation amplitudes (such as Fig.10 ). In general, under different excitation amplitudes, the structural resonance frequency increases with the increase of preload, and the resonance response decreases first and then increases with the increase of preload. When the tightening torque exceeds 18N·m, the resonance frequency and resonance response tend to be stable.

[0084] Take the 2g incentive level as an example (such as Fig.10 (b) The influence of preload on the nonlinear vibration characteristics of the structure is analyzed from two aspects: contact stress and contact state of the bolt connection interface. Under low preload conditions (unfastened stage), as the preload increases from 2N·m to 12N·m, the resonant frequency of the structure gradually increases and the resonant response gradually decreases. Fig.11 In (a) and (b), the contact stress between the bolted joint interfaces increases significantly with the increase of preload. The contact stiffness (normal and tangential stiffness) increases with the increase of contact stress, which in turn increases the vibration frequency of the structure. In addition, the increase of contact stiffness improves the overall stiffness of the system and reduces the structural deformation caused by external excitation. Fig.12As shown in (a) and (b), the sliding area of ​​the bolted connection interface decreases with the increase of preload, resulting in a reduction in friction energy consumption, but at this stage, the damping effect of the structural vibration response caused by the increase in bolted connection stiffness is dominant.

[0085] As the preload increases, for example, when the preload increases from 12 N·m to Fig.10 When the stress on the contact surface is 18 N·m in (b), the resonant frequency and resonant response of the structure gradually increase. Fig.11 (b) and Fig.11 (c) shows that the change in contact stress begins to decrease, indicating that the contact stiffness begins to saturate. This means that the further increase in preload has a gradually decreasing effect on the overall stiffness. Fig.12 (b) and Fig.12 (c) It can be observed that at this stage, the friction energy dissipation effect of the interface has a greater impact on the structural resonance response. Specifically, as the preload force increases, the slip area on the contact surface decreases, while the viscosity area increases, resulting in a decrease in friction energy consumption, and thus the resonance amplitude gradually increases.

[0086] When the tightening torque reaches a higher level, the critical value of the structure studied in this paper is 18N·m. That is, as the preload increases from 18N·m to 40N·m, the structural resonant frequency and resonant response remain basically unchanged. Fig.11 (c) and Fig.11 The contact stress in (d) also remains constant, which means that the contact stiffness is stable and the resonant frequency does not increase any more. Fig.12 (c) and Fig.12 In (d), there is no significant slip between the contact surfaces and the nonlinear effects of the system are suppressed to a minimum. The dynamic characteristics of the structure are stable, and the resonant frequency and resonance peak do not change further.

[0087] 3.3 Influence of flange thickness

[0088] The influence of excitation amplitude on the nonlinear vibration characteristics of the structure under different flange thickness conditions is as follows Fig.13 As shown, the tightening torque is 12N·m. Obviously, the flange thickness has an important influence on the structural resonant frequency and vibration response. Increasing the flange thickness will lead to a significant increase in the resonant frequency and a significant attenuation of the resonant response. As the excitation amplitude increases from 1g to 3g, the resonant frequency decreases by 5.5Hz when the flange thickness is 4mm, 5.0Hz when the thickness is 6mm, and 3.5Hz when the thickness is 8mm. As the flange thickness increases from 4mm to 8mm, the resonant response amplitude increases from 10 -5 m is reduced to 10 -7This means that with the increase of flange thickness, the dynamic softening effect caused by the excitation amplitude is attenuated.

[0089] Fig.14 and Fig.15 This dynamic softening mechanism is explained from the perspective of contact stress and contact state. Fig.14 As shown in the figure, as the flange thickness increases, the local stress concentration phenomenon gradually weakens and the contact pressure distribution becomes more uniform. This is mainly because increasing the flange thickness improves the structural rigidity, allowing the bolt preload to be more evenly transmitted to the contact surface, thereby increasing the effective contact area between the surfaces and resulting in a more uniform distribution of contact pressure. Fig.15 As shown in the figure, with the increase of flange thickness, the viscosity area of ​​the contact interface increases significantly, while the slip area decreases, indicating that the increase of flange thickness significantly suppresses the dynamic softening effect of the structure.

[0090] 4. Conclusion

[0091] (1) The increase in excitation amplitude is the most direct factor causing the dynamic softening of the bolted flange boundary cone-cylinder composite shell structure, which also causes the increase of contact stress at the connection interface and the increase of the proportion of sliding contact state.

[0092] (2) Under the condition of constant excitation amplitude, as the preload increases, the resonant frequency gradually increases, while the resonant peak shows a trend of first decreasing and then increasing. The change of resonant frequency is related to the global stiffness, while the change of resonant peak is affected by the combined effect of structural stiffness and interface friction slip.

[0093] (3) Flange thickness directly affects the strength and stiffness of the structure. Appropriately increasing the flange thickness can usually improve the stiffness and stability of the connection and reduce dynamic softening and nonlinear effects.

[0094] The technical principles of the present invention are described above in conjunction with specific embodiments. These descriptions are only for explaining the principles of the present invention and cannot be interpreted in any way as limiting the scope of protection of the present invention. Based on the explanations here, those skilled in the art can associate other specific implementations of the present invention without creative work, and these methods will fall within the scope of protection of the present invention.

Claims

1. A method for modeling and nonlinear vibration analysis of a cone-cylinder composite shell connected by bolted flanges. It is characterized by: The following steps are involved: Based on the built-in Toolbox standard parts bolt and nut design library in SOLIDWORKS, hexagonal bolts and nuts are selected to establish a bolt-flange boundary cone-cylinder composite shell model; Import the established 3D model into the finite element analysis software ANSYS Workbench, define the geometry and material parameters in sequence, establish contact, divide the mesh, set constraints, and complete the finite element simulation pre-processing; In the Static Structural module, set parameters such as friction contact, step size, and convergence residual value to analyze the contact stress and contact state. In the Harmonic Response module, apply horizontal foundation acceleration excitation to the clamping position of the bolt hole at the bottom of the base to extract the displacement response at the vibration pickup point. In terms of the connection interface contact settings, the bolt and nut and the base and nut are set to binding, the bolt head and the cone-column combined shell are set to friction, the bolt and the base are set to friction, and the cone-column combined shell and the base are set to friction; The entire structure is meshed using Solid 185 solid elements. The number of elements after meshing is 360,546 and the number of nodes is 794,998. The cone-cylinder composite shell uses a tetrahedral grid with a unit size of 5 mm; The base uses a hexahedral grid with a cell size of 2 mm; The bolt and nut structure uses hexahedral mesh and multi-region meshing methods, and the unit size is 3mm; The mesh of the bolt and nut contact surface is refined to a size of 1 mm; The natural frequency, vibration mode and resonance displacement are simulated and calculated under the set tightening torque, and the simulation results are verified by modal test and basic excitation response test. The dynamic softening phenomenon of the amplitude-frequency curve is explained from the aspects of contact stress and contact state of the bolt-flange connection interface. Analyze the influence of excitation amplitude, bolt preload and flange thickness on the nonlinear vibration characteristics of the structure.

2. The method for modeling and nonlinear vibration analysis of bolted flange-connected conical-cylindrical composite shell according to claim 1 is characterized in that: The modal test is to obtain the natural frequency and vibration mode of the bolted flange-connected cone-cylinder composite shell through the hammer method, and the vibration response of the bolted flange-connected cone-cylinder composite shell is obtained through the vibration table test, which effectively verifies the accuracy of the simulation results.

3. The method for modeling and nonlinear vibration analysis of bolted flange-connected conical-cylindrical composite shell according to claim 1 is characterized in that: Combining nonlinear structural analysis with harmonic response sweep frequency analysis, the amplitude-frequency curve of the structure is directly given by finite element simulation.

4. The method for modeling and nonlinear vibration analysis of bolted flange-connected conical-cylindrical composite shell according to claim 1 is characterized in that: From the perspective of contact stress and contact state, the dynamic softening phenomenon of the amplitude-frequency curve of the component under different excitation amplitudes is explained.

5. The bolted flange-connected cone-cylinder composite shell modeling and nonlinear vibration analysis method according to claim 1 is characterized in that: The influence of preload on the nonlinear vibration response (including frequency and amplitude) of the structure under different acceleration excitation amplitudes is analyzed.

6. The method for modeling and nonlinear vibration analysis of bolted flange-connected conical-cylindrical composite shell according to claim 1 is characterized in that: Analyze the influence of different flange thicknesses on the structural resonant frequency and nonlinear vibration response.

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