Introduction
Flow microchannel systems are commonly used to transfer material and energy or momentum and are therefore used in a wide range of equipment. The pressure wave pulsation of the fluid and the pipe wall structure are easily coupled, which induces strong vibration and noise, and has a serious impact on the performance and utilization of the equipment. Therefore, the study of reducing the vibration of microchannels and ensuring the safety of pipeline transportation is of great significance in theory and practice1. Fluid-solid coupling dynamics is a study of solid-liquid interaction, its main research content is the deformation of the mechanical behavior of the solid under the action of the fluid flow field and the deformation of the solid morphology of the flow field of the interaction between the effects of the field2,3, with the rapid development of computational solid mechanics and computational fluid mechanics and a variety of commercial development and use of finite element software, the flow of solid-solid coupling analysis and research has been the rapid development of the results of the research The results of the research have played an increasingly important reference value for engineering applications and equipment design4, 5–6. In recent years, the continuous development and improvement of the phononic crystal band gap theory in the field of condensed matter physics provides new technical support for vibration propagation control7, 8, 9, 10–11, and the phononic crystal is a periodic structure or composite material composed of one or more materials. When the elastic wave propagates within the phononic crystal, the periodicity of the internal medium can generate an elastic wave bandgap, and thus, the bandgap characteristics of the phononic crystal can be utilized to effectively suppress the vibration and noise propagation within the frequency range of the bandgap. Lee and Messahel et al.12, 13–14 investigated the sandwich beam structure of the embedded internal resonator, which improves the performance of the bending vibration under the shock loading, and completed the experimental verification. Aliabadi15 realized the effective merging of two bandgap frequency regions to form a single broadband energy-absorbing region by combining damping elements into a multiresonator metamaterial beam. Gimperlein et al.16 proposed a microstructural design of dissipative metamaterials consisting of multilayered viscoelastic continuum media for effective attenuation of transient shock waves. Lige Chang17 introduced an On-demand tunable metamaterial structure with multiple Maxwell-type resonators for the development of dissipative elastic metamaterials, which can be applied to mitigate dynamic loads and blast wave attenuation. Fang et al.18 proposed a novel superlattice truss-core sandwich structure, which can be used to realize pulse-wave attenuation and dynamic load attenuation with shock moderating capability and kinetic energy absorption. Brown and Tseng19,20 proposed a three-resonator metamaterial to enhance the attenuation of shock stress waves and analyzed the multi-objective optimization of this metamaterial, while a novel multi-resonator metamaterial for attenuating shock stress waves was later proposed.
The above studies on the shock wave attenuation of phononic crystals have made a lot of progress and have gradually progressed from theoretical studies to practical applications. However, there is a relative lack of research on the phononic crystal properties of fluid-solid coupled systems, especially the typical fluid-solid coupled structures such as flow-conveying microchannels, under shock loading21.
The application of the bandgap properties of phononic crystals to the design of fluid-solid coupled microchannel systems (e.g., constructing periodic composite channels or attaching periodic local resonance structures) has attracted much attention in recent years as it provides a new technological idea and theoretical basis for suppressing the vibrational noise of the microchannels22,23. Song et al.24 took the lead in revealing the bandgap properties of the infusional microchannels with periodic elastic supports and validated them by experiments. Mamaghani et al.25, 26–27 systematically investigated the propagation of elastic waves in a fluid-filled periodic shell, the effect of fluid-solid coupling on the bandgap, and the coupled vibrational bandgap under an additional mass system. Some scholars28, 29–30 successfully realized the bending vibrational bandgap of a periodic composite microchannel by combining Bragg scattering and local resonance mechanisms and experimentally verified its wave attenuation capability. Henclik and Feng et al.7,31,32 applied periodic microchannels to hydraulic systems, proposed a frequency response calculation method considering fluid-solid coupling, and investigated the bandgap characteristics under high pressure. Although the above studies laid the foundation for phononic crystal microchannels in the field of fluid transport vibration analysis, there are two key limitations: first, the in-depth consideration of the fluid-solid coupling effect33,34 is insufficient, and most of the models are relatively simplified in their treatment of the complex mechanism of fluid-solid coupling interaction. Second, the research on the bandgap vibration isolation and attenuation characteristics of phononic crystal microchannels under shock excitation is not deep enough and systematic.
The core innovation of this paper is that the transfer matrix method is used to analyze the bandgap vibration isolation characteristics of microchannels with unfilled and filled cycles in response to the shortcomings of the existing studies. At the same time, combined with the finite element method for secondary development to explore the influence of different impact excitation conditions on the vibration transmission characteristics of the liquid-filled periodic microchannel.
Fluid-solid coupling theory and transfer matrix method
The fluid-filled microchannel consists of tube A and tube B. Among them, the walls of tubes A and B are composed of three layers of composite plate structures, namely, the inner wall, the middle part, and the outer wall, respectively. The vibration modes of the liquid-filled microchannel are bending vibration, axial vibration, torsional vibration, and complex coupling vibration between them. The bending vibration refers to the vibration in the y-direction in Fig. 1, i.e., the vibration perpendicular to the direction of the microchannel axis; the axial vibration refers to the vibration in the x-direction in Fig. 1, i.e., the vibration along the direction of the microchannel axis. Torsional vibration refers to the torsional vibration of the microchannel around the axis, which is generally caused by the loss of equilibrium between the active moment of the rotating machinery and the load counter-moment. Microchannels may flex or vibrate strongly when internal fluids flow at higher or lower velocities. And under external excitation, the microchannel will mainly produce bending vibration, axial vibration, and torsional vibration are small and negligible. Therefore, microchannel bending vibration is the main vibration mode. Therefore, the study of bending vibration has important theoretical significance for microchannel vibration control. Most of the current theoretical studies on microchannel bending vibration are based on the beam model. In general, when the ratio of the microchannel length to the tube diameter is greater than 10, the microchannel can be considered as a Timoshenko model. To calculate the energy band structure, here we simplify the fluid-solid coupling microchannel by assuming that the liquid inside the tube is ideal (isotropic, homogeneous, incompressible, linear).
Fig. 1 [Images not available. See PDF.]
Structural-mechanical schematic model of the front-end frame.
Considering the bending vibration characteristics of the microchannel wall, Timoshenko beam theory is used to establish its dynamic equations35. And the transfer matrix method36,37 is applied to analyze the wave propagation characteristics of the periodic microchannel. The model takes into account the effects of shear deformation and rotational inertia, and its governing equations can be formulated as follows.
1
2
3
4
5
6
Where: is the transverse displacement of the microchannel; is the transverse bending angle; is the torsion angle of the microchannel; is the vertical displacement of the microchannel; is the vertical bending angle; is the axial displacement of the microchannel; P is the axial force of the microchannel, which is positive under pressure; z0 is the distance from the center of cross-section to the shear center; E is the Young’s modulus of the microchannel; ρ is the density of the microchannel; Ar is the area of microchannel cross-section; is the shear factor; G is the shear rigidity Iz and Iy are the moments of inertia of the microchannel around the z-axis and y-axis, respectively; is the rotational inertia of the microchannel;
Bringing in the above equation yields 12 wave numbers for the four characteristic waves in the microchannel, for the vertical bending wave, and the longitudinal wave characteristic equations:
7
8
The free beam wave number is found to be k1 ~ k6.
For transverse bending and torsion waves, there is bending-torsion coupling at this point:
9
And denote the above wave numbers as k7 ~ k12.
Thus, the transfer matrix[] between neighboring periodic cells can be obtained:
10
Where TA and the state vector transfer matrix of TB satisfy the following Eq.
11
12
By solving the above transfer matrix, the dispersion curves in the frequency wave number domain and the corresponding bandgap characteristics are obtained.
Dispersion characteristics of liquid-filled phononic crystals
Based on the theory in Sect. “Fluid-solid coupling theory and transfer matrix method”, we can perform the dispersion curve solution of the phononic crystal microchannel structure to obtain the bandgap. The structure is schematically shown in Fig. 1, and Fig. 1(a) is the infinite periodic unit. Figure 1(b) is the fundamental periodic unit. The Bragg phononic crystal microchannel is a periodic microchannel formed by two different tube wall materials A and B arranged in alternating cycles along the z-axis.
The lattice constant of the periodic microchannel is a0 = La+Lb. Where La and Lb are the lengths of pipe A and pipe B, respectively. The radius of the microchannel is R, and the thickness of the wall is d.
In this paper, a seawater microchannel system is investigated, and the pulsation source is assumed to be a six-vane centrifugal pump with a rotational speed of 2500 r/min.The peak frequency of vibration and the peak frequency of second-order vibration are 250 Hz and 500 Hz, respectively. The dimensions of the microchannel inner diameter, R, and the wall thickness, d, are required for the project application. Therefore, the microchannel bandgap is changed by varying the lattice constant a and the length of the tube section A, and the length of the tube section B. The bandgap of the microchannel is calculated as follows. To make the calculated microchannel bandgap satisfy the vibration control requirements of lobe frequency and sub-frequency, structural steel and epoxy resin are used for tube segments A and B, respectively, in the calculation. The material parameters are shown in Table 1, taking the length of tube section A as l = 0.25 m, the length of tube section B as l = 0.25 m, the inner diameter of the microchannel as R = 0.01 m, the thickness of the tube wall as d = 0.001 m, the medium inside the tube as water with a density of 1000 kg/m3, and the speed of sound inside the medium as 1400 m/s. The rest of the relevant material parameters can be referred to the parameters in the built-in material library of COMSOL. The other relevant material parameters can be found in COMSOL’s built-in material library. The transfer matrix T is solved from Eqs. (7)-(9) in Sect. 2.1, and the energy band structure and frequency response of the infinite-period unit with the above parameters are calculated.
Table 1. Microchannel material parameters.
Makings | Modulus/GPa | Density/(kg/m³) | Poisson’s ratio |
|---|---|---|---|
Structural steel | 200 | 7850 | 0.3 |
Resinous | 4.4 | 1180 | 0.37 |
Figure 2 shows the energy band structure and frequency response curves of the bending vibration of the unfilled Bragg phononic crystal microchannel calculated using the transfer matrix method. The medium inside the “unfilled” microchannel is air by default. The density of air is taken as 1.205 kg/m3, and the speed of sound of air is 343 m/s. Since the density of air is small compared with that of liquid and solid pipelines, and the effect of air gas on the vibration of the bending wave is very small, no special analysis is needed.
Figure 2 illustrates the energy band structure (Fig. 2a) and the finite-structure frequency response curve (Fig. 2b) of the bending vibration of an unfilled Bragg phononic crystal microchannel calculated based on the transfer matrix method with five periods. The frequency range corresponding to the real part of the wave vector in the energy band structure (Fig. 2a) reveals the existence of a band gap. The analysis shows that there are two significant attenuation bandgaps in the frequency range of 0–800 Hz: 70–90 Hz and 280–690 Hz. The corresponding frequency response curves (Fig. 2b) show that the peak region of vibration transmission loss (i.e., attenuation) of the finite-period structure is highly coincident with the frequency range of the bandgap of the infinite-period structure, which verifies the vibration suppression effect of the bandgap. Notably, the attenuation intensity of the second bandgap (280–690 Hz) is much larger than that of the first bandgap (70–90 Hz), with the maximum attenuation value up to −60 dB.
Figure 3 illustrates the corresponding bending vibration energy band structure (Fig. 3a) and frequency response curves (Fig. 3b) of the fluid-filled Bragg period microchannel. In contrast to the unfilled case (Fig. 2), the fluid-filled microchannel produces three attenuation bandgaps in the range of 0–800 Hz: 40–65 Hz, 180–340 Hz, and 485–735 Hz. This change suggests that the presence of the fluid significantly alters the dynamics of the system, leading to a reorganization of the bandgap structure and a shift to lower frequencies (e.g., the original 70–90 Hz bandgap shifts to 40–65 Hz, and a new one emerges). Hz, and a new 180–340 Hz bandgap appears. The frequency response curves (Fig. 3b) reconfirm the effective suppression of vibration propagation by the bandgap, with the three bandgaps corresponding to three distinct peaks of transmission loss with peak attenuation of −20 dB, −46 dB, and − 52 dB, respectively.
According to the phononic crystal theory, the change in bandgap frequency mainly originates from the following two interrelated fluid effects: (1) the presence of fluid in the channel significantly increases the equivalent mass density of the system. According to the fundamental wave propagation theory, an increase in mass usually decreases the intrinsic frequency of the structure, as shown in Eq. (13). This explains the phenomenon that part of the bandgap (e.g., the original 70–90 Hz bandgap decreases to 40–65 Hz) shifts to lower frequencies. (2) There is a dynamic coupling between fluid pressure pulsation and pipe wall deformation, and this coupling changes the equivalent stiffness distribution of the system, affects the phase and group velocities of wave propagation, and thus leads to the deformation of the dispersion curve. Specifically manifested as a certain band gap (such as the new 485–735 Hz band gap and the evolution of high frequency band), not only positional movement, its width and depth will be accompanied by nonlinear changes.
13
Where ke is the equivalent stiffness and me is the equivalent mass.
Fig. 2 [Images not available. See PDF.]
The liquid-unfilled Bragg phononic crystal (a) Dispersion curve (b) Transmission loss.
Fig. 3 [Images not available. See PDF.]
The liquid-filled Bragg phononic crystal (a) Dispersion curve (b) Transmission loss.
Characteristics of fluid-solid coupled phononic crystals
Finite element modeling and algorithm validation
Based on the bandgap characteristics studied above, we need to go further to investigate the effect of the bandgap on the vibration law under different excitation conditions. Without considering the fluid-structure coupling effect, based on the COMSOL platform, the harmonic response module is utilized to apply a velocity signal of amplitude 1, denoted as vin, at the excitation end and pick up the velocity signal, denoted as Vout, at the response end. The frequency response is calculated by the equation TL 20 log (Uout/Uin), and the vibrational frequency response curves of the acoustic sub-crystal microchannel for 5 periodicities are obtained. Comparison with the vibrational transfer response calculated by the transfer matrix method yields Fig. 4. Figure 4 shows the bending vibrational transfer loss curves of the unfilled and filled Bragg microchannels for 5 periodicities. The blue dashed line and the black solid line are the calculation results of the finite element method and the transfer matrix method, respectively. From the figure, it can be seen that the calculation results of the transfer matrix method and the finite element method are in good agreement, which strongly proves the accuracy and effectiveness of the transfer matrix method.
Figure 5 shows the displacement amplitudes of the unfilled and filled Bragg phononic crystal microchannels at different frequencies. Where Fig. 5(a) represents the displacement amplitude of the microchannel of the liquid-unfilled phononic crystal. It can be found that the bending vibration of the microchannel at f = 500 Hz has been greatly attenuated in the first two cycles, and the microchannel in the latter half of the period has almost no vibration. It shows that the Bragg phononic crystal microchannel can suppress the vibration in the bandgap better, and the vibration attenuation effect is obvious. f 750 Hz are the frequency points outside the bandgap. The displacement amplitude at this frequency is much larger than that inside the bandgap, and the whole microchannel is in vibration. At this time, the bending vibration can be effectively transmitted to the end of the tube. Figure 5(b) represents the displacement amplitude of the microchannel of the liquid-filled phononic crystal. It can be found that the bending vibration of the microchannel at f = 750 Hz has been greatly attenuated in the first two cycles, and the microchannel in the latter half is almost not vibrated. This indicates that the liquid-filled Bragg phononic crystal microchannel can be better suppressed for the vibration within the bandgap, and the vibration attenuation effect is obvious. f = 800 Hz are all the frequency points outside the bandgap, and the displacement amplitude at the frequency is much larger than that within the bandgap, and the whole microchannel is in a vibration state. At this point, the bending vibration can be effectively transmitted to the end of the tube. The above results correspond to the bandgap in the vibration frequency response curve of the phononic crystal microchannel in Fig. 4.
The vibration transfer characteristics of the phononic crystal microchannel under the fluid-solid coupling condition are further considered. Based on the COMSOL platform, the flow-solid coupling analysis of the microchannel under different impact excitations is carried out, and the basic flow of the two-way flow-solid coupling analysis is established as shown in Fig. 6. Concerning the parameters of the phonon crystal microchannel in Fig. 1, a five-cycle phonon crystal microchannel model is established, as shown in Fig. 7. The model is selected as a transient structure and a hydrodynamic module. The length of the microchannel is 2.5 m, the inner diameter of the microchannel is 0.02 m, and the thickness of the pipe wall is 0.001 m. The elastic pipe wall is used, and the effect of pipe damping is ignored. The fluid part is water, an incompressible fluid with a density of 1000 kg/m³, the temperature is set to 25 °C, and the coefficient of dynamic viscosity is selected as the default value of 0.001003 kg/(m·s). Due to the COMSOL calculation of two-way fluid-solid coupling, the fluid through the fluid-solid coupling face microchannel structure transfers only the turbulent movement generated by the fluid Reynolds stress, viscous stress, and pulsating shear stress of the fluid force, not including the fluid mass. Therefore, the results are more accurate in the simulation calculation of lightweight fluid, but when the fluid in the tube is heavy, the simulation results will produce a large error. Therefore, it is necessary to introduce additional mass Am pπr2 in the microchannel. The fluid in this paper is water, which belongs to heavy fluid, so it is necessary to set the equivalent density of the microchannel material when modeling the microchannel, i.e.
1
Where is the density of the microchannel material, is the fluid density, rin is the inner diameter of the microchannel, and rout is the outer diameter of the microchannel. The microchannel materials are selected as structural steel and epoxy resin in Table 1, then the equivalent densities of structural steel and epoxy resin, which are set as the microchannel materials in the simulation analysis, are 12,612 kg/m3 and 5941.9 kg/m3. Respectively.
Fig. 4 [Images not available. See PDF.]
Transfer Curve (a) Liquid-unfilled (b) Liquid-filled.
Fig. 5 [Images not available. See PDF.]
Amplitude of vibration displacements under the theoretical model (a) Liquid-unfilled (b) Liquid-filled.
Fig. 6 [Images not available. See PDF.]
Bidirectional fluid-solid coupling modeling schematic.
Fig. 7 [Images not available. See PDF.]
Mechanical Modeling of Fluid-Solid Coupling Pipelines.
In this example, we mainly set the inner wall surface of the pipe in contact with the fluid and the liquid as the fluid-solid coupling surface, and set the limitations on the displacement of the two end surfaces in the X, Y and Z directions as the support boundary conditions, i.e., the fixed constraints (solidly supported structure). We set the different inlet velocities in m/s and the outlet pressure to zero in the interface of COMSOL-Fluent; we set the coupling time in the interface of the coupling analysis of the system to 0.0512 s and the coupling time step to 0.0001 s, and choose the two-way coupling; the initial conditions are regarded as smooth pipe walls. The coupling time step is 0.0001 s, and the two-way coupling is selected; the initial condition is regarded as a smooth pipe wall.
Microchannel vibration characterisation
Assuming that a shock load is applied at a distance from the inlet at the left end of the microchannel, the form of the shock wave satisfies the following equation:
1
The parameters in the simulation are set as follows. Amplitude of force Fmax = 200 N, initial moment setting t0 = 0.0005 s, setting of event interval td = 0.0001 s. Impact time t is set to 0.0005 s.
The response signal was picked up at the inlet and outlet of the microchannel. The bending vibration response of the non-fluid-filled and fluid-filled microchannels is simulated separately. Liquid-filled microchannel simulation analysis using fluid-solid coupling simulation analysis, set the flow rate to 0. The impulse response of the pipe wall impact excitation is shown in Fig. 8 (a), and the frequency domain distribution is obtained using the fast Fourier transform as in Fig. 8 (b). It can be seen that the stress wave generated in the model has a wide bandwidth of 0–5000 Hz due to the pipe wall impact excitation.
Figure 9 shows the shock vibration characteristics of the 5-cycle phononic crystal microchannel when it is not filled with liquid and when it is filled with liquid. The shaded part in the frequency domain plot indicates that the velocity peak at the exit is smaller than that at the entrance, indicating that the phononic crystal microchannel has a better attenuation effect in this frequency range. Comparing Fig. 9(a) and Fig. 9(b), it can be found that when the microchannel is filled with liquid, the microchannel vibration amplitude is attenuated in both time and frequency domains. This indicates that when the microchannel is filled with fluid, the microchannel vibration induced by the external shock is weakened due to the fluid quality. In the comprehensive analysis, the unfilled phononic crystal microchannels have better attenuation in the range of 270–625 Hz, and the fluid-filled phononic crystal microchannels have better attenuation in the range of 175–332 Hz and 488–725 Hz. This agrees with the bandgap of 280–690 Hz for the unfilled microchannels and 180–340 Hz and 485–735 Hz for the liquid-filled microchannels calculated by the transfer matrix in Sect. 3. This suggests that the unfilled and liquid-filled Bragg phononic crystal microchannels have better suppression of external shocks to the microchannels.
Fig. 8 [Images not available. See PDF.]
Input Load Schematic (a) Time Domain (b) Frequency Domain.
Fig. 9 [Images not available. See PDF.]
Acoustic crystal microchannel shock response (a) unflushed liquid (b) filled liquid.
Figure 10 represents the velocity amplitude plots of the unfilled and filled phononic crystal microchannels at different moments. Figure 10(a) represents the velocity amplitude of the unfilled phononic crystal microchannel at t of 0.001, 0.0025, 0.005, 0.01 s. The velocity amplitudes of the liquid-filled phonon crystal microchannels are shown in Fig. 10(b). It can be found that the vibration at the exit of the phononic crystal microchannel lags and has a smaller vibration amplitude than that at the entrance, regardless of whether the microchannel is liquid-filled or not. This is because the shock response at the inlet of the microchannel takes some time to propagate along the wall of the tube, and the vibration amplitude at the outlet reaches its maximum at about 0.01 s. The vibration amplitude at the outlet is the largest. This is consistent with the vibration response curve at the exit in the time-domain plot in Fig. 9(a) and Fig. 9(b).
Fig. 10 [Images not available. See PDF.]
Fluctuation patterns inside and outside the band gap (a) unflushed fluid (b) flushed fluid.
Next, the effect of flow velocity on the impact response of the tube wall is considered, and the flow velocities are set to be 0 m/s and 10 m/s, respectively. The impact vibration response of the fluid-solid coupled phononic crystal microchannel at different flow velocities is obtained by simulation analysis. At the same time, a joint analysis is carried out by combining the vibration transmission modes in the previous section. The results are shown in Fig. 11, which shows the significant effects of 0 m/s and 10 m/s flow velocities on the exit vibration response of the flow-solid coupled phononic crystal microchannel under shock excitation. Although the bandgap frequency range remains relatively stable as the flow velocity varies, the key phenomenon is that the attenuation intensity decreases with the increase of flow velocity, and the vibration response of the exit section is significantly enhanced. This reveals a central mechanism by which the flow velocity affects the dynamics of the system through the fluid-solid coupled energy transfer path: at higher flow velocities (10 m/s), the kinetic energy carried by the fluid increases significantly. When the wall vibration is excited by an external shock, the fluid is not a passive medium, and its force on the wall is strongly and dynamically coupled to the structural vibration. This coupling effect allows the kinetic energy of the fluid flow to be continuously fed into the structural vibration system through the fluid-solid coupling interface, which partially offsets the intrinsic attenuation ability of the phonon crystal band gap. At the same time, the fluid medium in the pipe acts as a “carrier” or “transmission channel” for the vibration energy. The vibrational energy that would otherwise be induced by the shock at the front end or in a localized area is more effectively transported convectively to the outlet section. This directional transfer and diffusion of energy driven by the fluid flow is the main reason for the increased vibration response at the end of the microchannel and the overall attenuation effect (especially at the exit). Therefore, the increased flow velocity essentially enhances the two-way coupling strength and energy transfer efficiency between the fluid kinetic energy and the structural vibration energy, and weakens the localized suppression effect of the periodic structure on the shock vibration energy.
Fig. 11 [Images not available. See PDF.]
Shock Vibration Response at Velocities 0 and 10 m/s.
Conclusion and discussion
The vibrational characteristics of fluid-solid coupled phononic crystal microchannels under impact conditions are analyzed. The following conclusions are drawn from the study of this paper.
(1) Based on the transfer matrix method and the finite element method, a mathematical model of the bandgap characteristics of the fluid-solid coupled phononic crystal microchannel system has been established, which provides an effective tool for the analysis of the impact response of the fluid-solid coupled phononic crystal microchannel.
(2) When the flow velocity in the fluid-solid coupling microchannel system is small, the excitation response of the wall shock in the range of the phononic crystal bandgap frequency has a significant suppression effect. However, when the flow velocity increases, the fluid-solid coupling effect increases, and the vibration suppression effect is weakened.
(3) Under the excitation of fluid impact, the phononic crystal microchannels also have a better suppression effect on the vibration caused by the fluid impact. It is shown that the phononic crystal microchannels have better suppression of microchannel vibration in the bandgap frequency range when the fluid-solid coupling effect is taken into account.
The bandgap properties of phononic crystal microchannels are expected to provide new ideas for vibration and noise reduction in the field of precision instruments. Future vibration control applications in aerospace, medical, and other high-end fields can be combined with light-curing 3D-printing, micro and nano manufacturing technology for practical production and improve scalability.
Author contributions
Linlin Wang wrote the main manuscript text and reviewed the manuscript.
Data availability
The datasets used and/or analysed during the current study available from the corresponding author on reasonable reques.
Declarations
Competing interests
The authors declare no competing interests.
Publisher’s note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
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Abstract
The fluid solid coupling effect in the flow microchannel system can easily induce severe vibration and noise, which seriously affects the performance and safety of the equipment. By its bandgap characteristics, the phononic crystal provides a new way to suppress the propagation of elastic waves in specific frequency bands. In this study, the vibration suppression of fluid-solid coupled phononic crystal microchannels under shock excitation is addressed. Compared with the inadequacy of the existing bandgap calculation methods in fluid computation, this study innovatively combines the transfer matrix method with the wave-finite element method to establish a fluid-solid coupled dynamics model and perform a systematic analysis. The significant effects of fluid filling on the bandgap characteristics are revealed: the unfilled microchannels show two bandgaps (70–90 Hz, 280–690 Hz) in 0–800 Hz; the bandgaps evolve to three (40–65 Hz, 180–340 Hz, 485–735 Hz) after fluid filling. At the same time, the transient vibration propagation and attenuation mechanisms of the system under different fluid shock excitations are deeply investigated. It is shown that the flow velocity is the key parameter affecting the shock vibration suppression effect: at 0 m/s flow velocity, the phonon crystal bandgap can effectively attenuate the shock response; as the flow velocity increases to 10 m/s, the fluid-solid coupling effect is enhanced, and the attenuation intensity is weakened. This study elucidates the quantitative relationship between key parameters such as flow velocity, structural periodicity, and resonant unit characteristics and shock vibration attenuation performance. It is expected to provide an important theoretical foundation and design basis for the design of flow microchannel systems with excellent shock resistance.
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Details
1 School of Information Engineering, Xi’an University, 710065, Xi’an, China (ROR: https://ror.org/01zzmf129) (GRID: grid.440733.7) (ISNI: 0000 0000 8854 4301)