Transactions of Nanjing University of Aeronautics & Astronautics
Issue 1,2022 Table of Contents
2022(1):1-11.
DOI: 10.16356/j.1005-1120.2022.01.001
Abstract:
The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes. The arbitrarily shaped membrane is firstly mapped into a regular domain using blending functions， and the displacement in the element is assumed as the trigonometric functions. Explicit formulations are worked out for nodes of any type and a varying number of nodes. For verifications， results are compared with exact solutions and data obtained by other numerical methods. It is demonstrated that highly accurate frequencies can be obtained with a small number of nodes by present method.
The aim of the present study is to develop an efficient weak form quadrature element for free vibration analysis of arbitrarily shaped membranes. The arbitrarily shaped membrane is firstly mapped into a regular domain using blending functions， and the displacement in the element is assumed as the trigonometric functions. Explicit formulations are worked out for nodes of any type and a varying number of nodes. For verifications， results are compared with exact solutions and data obtained by other numerical methods. It is demonstrated that highly accurate frequencies can be obtained with a small number of nodes by present method.
2022(1):12-22.
DOI: 10.16356/j.1005-1120.2022.01.002
Abstract:
The dynamics of an axially accelerating beam subjected to axial flow is studied. Based on the Floquet theory and the Runge-Kutta algorithm， the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed， flow velocity， axial added mass coefficient， mass ratio， slenderness ratio， tension and viscosity coefficient. Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first- and second-mode frequencies or twice the lowest two natural frequencies， instability with combination or subharmonic resonance would occur. It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance. With the change of system parameters， the stability boundary may be widened， narrowed or drifted. In addition， the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.
The dynamics of an axially accelerating beam subjected to axial flow is studied. Based on the Floquet theory and the Runge-Kutta algorithm， the stability and nonlinear vibration of the beam are analyzed by considering the effects of several system parameters such as the mean speed， flow velocity， axial added mass coefficient， mass ratio， slenderness ratio， tension and viscosity coefficient. Numerical results show that when the pulsation frequency of the axial speed is close to the sum of first- and second-mode frequencies or twice the lowest two natural frequencies， instability with combination or subharmonic resonance would occur. It is found that the beam can undergo the periodic-1 motion under subharmonic resonance and the quasi-periodic motion under combination resonance. With the change of system parameters， the stability boundary may be widened， narrowed or drifted. In addition， the vibration amplitude of the beam under resonance can also be affected by changing the values of system parameters.
2022(1):23-35.
DOI: 10.16356/j.1005-1120.2022.01.003
Abstract:
A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory. The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects. The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate. The differential quadrature method is used to solve the governing equation numerically， and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly. Two kinds of boundary conditions are commonly used in practical engineering， namely the fixed and simply supported constraints， and are considered in numerical examples. The variations of natural frequencies with respect to the thickness to radius ratio， the angular velocity， the nonlocal characteristic scale and the material characteristic scale are analyzed in detail. In particular， the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically. The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.
A rotating axisymmetric circular nanoplate is modeled by the Mindlin plate theory. The Mindlin plate theory incorporates the nonlocal scale and strain gradient effects. The shear deformation of the circular nanoplate is considered and the nonlocal strain gradient theory is utilized to derive the governing differential equation of motion that describes the out-of-plane free vibration behaviors of the nanoplate. The differential quadrature method is used to solve the governing equation numerically， and the natural frequencies of the out-of-plane vibration of rotating nanoplates are obtained accordingly. Two kinds of boundary conditions are commonly used in practical engineering， namely the fixed and simply supported constraints， and are considered in numerical examples. The variations of natural frequencies with respect to the thickness to radius ratio， the angular velocity， the nonlocal characteristic scale and the material characteristic scale are analyzed in detail. In particular， the critical angular velocity that measures whether the rotating circular nanoplate is stable or not is obtained numerically. The presented study has reference significance for the dynamic design and control of rotating circular nanostructures in current nano-technologies and nano-devices.
2022(1):36-46.
DOI: 10.16356/j.1005-1120.2022.01.004
Abstract:
The vibration control in the frequency domain is significant. Therefore， an active vibration control in frequency domain is studied in this paper. It is generally known that piezo-intelligent structures possess satisfactory performances in the area of vibration control， and macro-fiber composites （MFCs） with high sensitivity and deformability are widely applied in engineering. So， this paper uses the MFC patches and designs a control method based on the pole placement method， and the natural frequency of the beam can be artificially designed. MFC patches are bonded on the top and bottom surfaces of the beam structure to act as the actuators and sensors. Then， the finite element method （FEM） is used to formulate the equation of motion， and the pole placement based on the out-put feedback method is used to design the active controller. Finally， the effectiveness of the active control method is verified.
The vibration control in the frequency domain is significant. Therefore， an active vibration control in frequency domain is studied in this paper. It is generally known that piezo-intelligent structures possess satisfactory performances in the area of vibration control， and macro-fiber composites （MFCs） with high sensitivity and deformability are widely applied in engineering. So， this paper uses the MFC patches and designs a control method based on the pole placement method， and the natural frequency of the beam can be artificially designed. MFC patches are bonded on the top and bottom surfaces of the beam structure to act as the actuators and sensors. Then， the finite element method （FEM） is used to formulate the equation of motion， and the pole placement based on the out-put feedback method is used to design the active controller. Finally， the effectiveness of the active control method is verified.
2022(1):47-57.
DOI: 10.16356/j.1005-1120.2022.01.005
Abstract:
The vibration and instability of functionally graded material （FGM） sandwich cylindrical shells conveying fluid are investigated. The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells. Based on the third-order shear deformation shell theory， the governing equations of the system are derived by using the Hamilton’s principle. To check the validity of the present analysis， the results are compared with those in previous studies for the special cases. Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent， while decreases with the rise of fluid density， radius-to-thickness ratio and length-to-radius ratio. The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1—2.5， which should be avoided in engineering application.
The vibration and instability of functionally graded material （FGM） sandwich cylindrical shells conveying fluid are investigated. The Navier-Stokes relation is used to describe the fluid pressure acting on the FGM sandwich shells. Based on the third-order shear deformation shell theory， the governing equations of the system are derived by using the Hamilton’s principle. To check the validity of the present analysis， the results are compared with those in previous studies for the special cases. Results manifest that the natural frequency of the fluid-conveying FGM sandwich shells increases with the rise of the core-to-thickness ratio and power-law exponent， while decreases with the rise of fluid density， radius-to-thickness ratio and length-to-radius ratio. The fluid-conveying FGM sandwich shells lose stability when the non-dimensional flow velocity falls in 2.1—2.5， which should be avoided in engineering application.
2022(1):58-65.
DOI: 10.16356/j.1005-1120.2022.01.006
Abstract:
The doubly curved shell （DCS） is a common structure in the engineering field. In a thermal environment， the vibration characteristics of the DCS will be affected by the thermal effect. The research on the vibration characteristics of DCS in thermal environment is relatively limited. In this paper， the thermal strain and the change of Young’s modulus caused by the changing of temperature are studied， and the DCS energy equation is established systematically. The displacement tolerance function of the DCS is constructed by the spectral geometry method， and the natural frequencies and mode shapes of the DCS with different structural parameters， such as thicknesses， ratios of Ra/Rb and a/b， at different temperatures are solved by the Rayleigh-Ritz method. The results show that the natural frequency of the DCS decreases with the increasing temperature， Ra/Rb and a/b ratios， and increases with the increasing thickness.
The doubly curved shell （DCS） is a common structure in the engineering field. In a thermal environment， the vibration characteristics of the DCS will be affected by the thermal effect. The research on the vibration characteristics of DCS in thermal environment is relatively limited. In this paper， the thermal strain and the change of Young’s modulus caused by the changing of temperature are studied， and the DCS energy equation is established systematically. The displacement tolerance function of the DCS is constructed by the spectral geometry method， and the natural frequencies and mode shapes of the DCS with different structural parameters， such as thicknesses， ratios of Ra/Rb and a/b， at different temperatures are solved by the Rayleigh-Ritz method. The results show that the natural frequency of the DCS decreases with the increasing temperature， Ra/Rb and a/b ratios， and increases with the increasing thickness.
2022(1):66-78.
DOI: 10.16356/j.1005-1120.2022.01.007
Abstract:
As a miniaturized direct injection （DI） solution， a self-pressurized injector is of great significance for small aviation piston engines， such as spark-ignited two-stroke heavy-fuel engines. The spray characteristics of DI injectors are an important application prerequisite. In this paper， the computational fluid dynamics （CFD） software AVL Fire is employed to study the spray characteristics. Two types of spray models are established based on the Han Sheet model and the KH-RT model， and simulation works are carried out according to two types of spray tests in the literature. The comparison results show that in the constant volume bomb test， the spray patterns obtained by simulation under the two sets of environmental pressures are similar to those in the experiment， and the simulation spray using the KH-RT model can fit the spray contraction of the near nozzle field and the vortex of the far nozzle field better. In the tube test， the spray patterns obtained by simulation under the five sets of flow velocity are similar to those in the experiment， and the simulation spray using the KH-RT model can fit the spray expansion and the vortex of the far nozzle field better. The RP-3 kerosene spray characteristics of the self-pressurized injector are also experimentally studied， and the results demonstrate that due to the higher viscosity of kerosene， the spray shrinks more easily， resulting in a smaller spray cone angle and larger penetration. Therefore， changes in environmental pressure have greater impact on the kerosene spray pattern.
As a miniaturized direct injection （DI） solution， a self-pressurized injector is of great significance for small aviation piston engines， such as spark-ignited two-stroke heavy-fuel engines. The spray characteristics of DI injectors are an important application prerequisite. In this paper， the computational fluid dynamics （CFD） software AVL Fire is employed to study the spray characteristics. Two types of spray models are established based on the Han Sheet model and the KH-RT model， and simulation works are carried out according to two types of spray tests in the literature. The comparison results show that in the constant volume bomb test， the spray patterns obtained by simulation under the two sets of environmental pressures are similar to those in the experiment， and the simulation spray using the KH-RT model can fit the spray contraction of the near nozzle field and the vortex of the far nozzle field better. In the tube test， the spray patterns obtained by simulation under the five sets of flow velocity are similar to those in the experiment， and the simulation spray using the KH-RT model can fit the spray expansion and the vortex of the far nozzle field better. The RP-3 kerosene spray characteristics of the self-pressurized injector are also experimentally studied， and the results demonstrate that due to the higher viscosity of kerosene， the spray shrinks more easily， resulting in a smaller spray cone angle and larger penetration. Therefore， changes in environmental pressure have greater impact on the kerosene spray pattern.
2022(1):79-86.
DOI: 10.16356/j.1005-1120.2022.01.008
Abstract:
The modified couple stress theory （MCST） is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory. The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy， and expressed in nominal form with the introduced nominal variables. With the application of generalized differential quadrature method （GDQM）， both the differential governing equations and boundary conditions are expressed in discrete form， and a set of linear equations are obtained. The bending deflection can be obtained through solving the linear equations， while buckling loads can be determined through solving general eigenvalue problems. The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
The modified couple stress theory （MCST） is applied to analyze axisymmetric bending and buckling behaviors of circular microplates with sinusoidal shear deformation theory. The differential governing equations and boundary conditions are derived through the principle of minimum total potential energy， and expressed in nominal form with the introduced nominal variables. With the application of generalized differential quadrature method （GDQM）， both the differential governing equations and boundary conditions are expressed in discrete form， and a set of linear equations are obtained. The bending deflection can be obtained through solving the linear equations， while buckling loads can be determined through solving general eigenvalue problems. The influence of material length scale parameter and plate geometrical dimensions on the bending deflection and buckling loads of circular microplates is investigated numerically for different boundary conditions.
2022(1):87-97.
DOI: 10.16356/j.1005-1120.2022.01.009
Abstract:
In order to study the dynamic characteristics of multilayer fiber reinforced plastic （MFRP） shaft， the coupling model of three-dimensional equivalent bending stiffness theory and transfer matrix method is established， and the influence of thickness-radius ratio， length-radius ratio， layer angles， layer proportion， and stacked approaches on MFRP shaft dynamic characteristics is investigated. The result shows that the proposed coupling model has high accuracy in MFRP shaft dynamic performance prediction. The proportion of small-angle layers is the decisive factor of MFRP shaft natural frequency. With the increase of thickness-radius ratio and length-radius ratio， the natural frequency of MFRP shaft decreases. The natural frequency of MFRP shaft with the angle layers combination of ±45° and ±90° is smaller compared with the metal shaft no matter in simple/free boundary condition or simple/simple supported boundary condition.
In order to study the dynamic characteristics of multilayer fiber reinforced plastic （MFRP） shaft， the coupling model of three-dimensional equivalent bending stiffness theory and transfer matrix method is established， and the influence of thickness-radius ratio， length-radius ratio， layer angles， layer proportion， and stacked approaches on MFRP shaft dynamic characteristics is investigated. The result shows that the proposed coupling model has high accuracy in MFRP shaft dynamic performance prediction. The proportion of small-angle layers is the decisive factor of MFRP shaft natural frequency. With the increase of thickness-radius ratio and length-radius ratio， the natural frequency of MFRP shaft decreases. The natural frequency of MFRP shaft with the angle layers combination of ±45° and ±90° is smaller compared with the metal shaft no matter in simple/free boundary condition or simple/simple supported boundary condition.
2022(1):98-107.
DOI: 10.16356/j.1005-1120.2022.01.010
Abstract:
Crack monitoring at the bolt hole edge is one of the important focuses of aircraft structural health monitoring. In this study， a novel eddy current sensing film based on a parallelogram coil array is developed to quantitatively monitor the crack characteristics near the bolt hole with fewer layers and coils， compared with the existing methods. The parallelogram coil array configuration is designed and optimized to improve the quantitative monitoring ability of the crack. A 3×3 parallelogram coil array is used to quantify the crack parameters of aluminum bolted joints. Finite element simulation and experiments show that the proposed parallelogram coil array could not only accurately and quantitatively identify the crack angle at the edge of the bolt hole， but also track the crack length along the radial direction of the bolt hole and the depth along the axial direction.
Crack monitoring at the bolt hole edge is one of the important focuses of aircraft structural health monitoring. In this study， a novel eddy current sensing film based on a parallelogram coil array is developed to quantitatively monitor the crack characteristics near the bolt hole with fewer layers and coils， compared with the existing methods. The parallelogram coil array configuration is designed and optimized to improve the quantitative monitoring ability of the crack. A 3×3 parallelogram coil array is used to quantify the crack parameters of aluminum bolted joints. Finite element simulation and experiments show that the proposed parallelogram coil array could not only accurately and quantitatively identify the crack angle at the edge of the bolt hole， but also track the crack length along the radial direction of the bolt hole and the depth along the axial direction.
11 Computational Study on Interaction Between Swimming Fish and Drifting Vortices Behind the Cylinder
2022(1):108-120.
DOI: 10.16356/j.1005-1120.2022.01.011
Abstract:
To predict the flow evolution of fish swimming problems， a flow solver based on the immersed boundary lattice Boltzmann method is developed. A flexible iterative algorithm based on the framework of implicit boundary force correction is used to save the computational cost and memory， and the momentum forcing is described by a simple direct force formula without complicated integral calculation when the velocity correction at the boundary node is determined. With the presented flow solver， the hydrodynamic interaction between the fish-induced dynamic stall vortices and the incoming vortices in unsteady flow is analyzed. Numerical simulation results unveil the mechanism of fish exploiting vortices to enhance their own hydrodynamic performances. The superior swimming performances originate from the relative movement between the “merged vortex” and the locomotion of the fishtail， which is controlled by the phase difference. Formation conditions of the “merged vortex” become the key factor for fish to exploit vortices to improve their swimming performance. We further discuss the effect of the principal components of locomotion. From the results， we conclude that lateral translation plays a crucial role in propulsion while body undulation in tandem with rotation and head motion reduce the locomotor cost.
To predict the flow evolution of fish swimming problems， a flow solver based on the immersed boundary lattice Boltzmann method is developed. A flexible iterative algorithm based on the framework of implicit boundary force correction is used to save the computational cost and memory， and the momentum forcing is described by a simple direct force formula without complicated integral calculation when the velocity correction at the boundary node is determined. With the presented flow solver， the hydrodynamic interaction between the fish-induced dynamic stall vortices and the incoming vortices in unsteady flow is analyzed. Numerical simulation results unveil the mechanism of fish exploiting vortices to enhance their own hydrodynamic performances. The superior swimming performances originate from the relative movement between the “merged vortex” and the locomotion of the fishtail， which is controlled by the phase difference. Formation conditions of the “merged vortex” become the key factor for fish to exploit vortices to improve their swimming performance. We further discuss the effect of the principal components of locomotion. From the results， we conclude that lateral translation plays a crucial role in propulsion while body undulation in tandem with rotation and head motion reduce the locomotor cost.
CHINA AERO-SCIENCES
Mobile website
Transactions of Nanjing University of Aeronautics & Astronautics ® 2024 All Rights Reserved