Mechanical property of cylindrical sandwich shell with gradient core of entangled wire mesh

To explore the wide-frequency damping and vibration-attenuation performances in the application of aerospace components,the cylindrical sandwich shell structure with a gradient core of entangled wire mesh was proposed in this paper.Firstly,the gradient cores of entangled wire mesh in the axial and radial directions were prepared by using an in-house Numerical Control weaving machine,and the metallurgical connection between skin sheets and the gradient core was performed using vacuum brazing.Secondly,to investigate the mechanical properties of cylindrical sandwich shells with axial or radial gradient cores,quasi-static and dynamic mechanical experiments were carried out.The primary evaluations of mechanical properties include secant stiffness,natural frequency,Specific Energy Absorption(SEA),vibration acceleration level,and so on.The results suggest that the vibration-attenuation performance of the sandwich shell is remarkable when the high-density core layer is at the end of the shell or abuts the inner skin.The axial gradient material has almost no influence on the vibration frequencies of the shell,whereas the vibration frequencies increase dramatically when the high-density core layer approaches the skin.Moreover,compared to the conventional sandwich shells,the proposed functional grading cylindrical sandwich shell exhibits more potential in mass reduction,stiffness designing,and energy dissipation.

Vibration of black phosphorus nanotubes via orthotropic cylindrical shell model

Black phosphorus nanotubes(BPNTs)may have good properties and potential applications.Determining thevibration property of BPNTs is essential for gaining insight into the mechanical behaviour of BPNTs and designingoptimized nanodevices.In this paper,the mechanical behaviour and vibration property of BPNTs are studied viaorthotropic cylindrical shell model and molecular dynamics(MD)simulation.The vibration frequencies of twochiral BPNTs are analysed systematically.According to the results of MD calculations,it is revealed that thenatural frequencies of two BPNTs with approximately equal sizes are unequal at each order,and that the naturalfrequencies of armchair BPNTs are higher than those of zigzag BPNTs.In addition,an armchair BPNTs witha stable structure is considered as the object of research,and the vibration frequencies of BPNTs of differentsizes are analysed.When comparing the MD results,it is found that both the isotropic cylindrical shell modeland orthotropic cylindrical shell model can better predict the thermal vibration of the lower order modes of thelonger BPNTs better.However,for the vibration of shorter and thinner BPNTs,the prediction of the orthotropiccylindrical shell model is obviously superior to the isotropic shell model,thereby further proving the validity ofthe shell model that considers orthotropic for BPNTs.

Experimental Study on Full-Surface Buckling of Variable Curvature Cylindrical Shell Using Multi-camera 3D-DIC System

To achieve full-surface strain measurement of variable curvature objects,a 360°3D digital image correlation(DIC)system is proposed.The measurement system consists of four double-camera systems,which capture the object’s entire surface from multiple angles,enabling comprehensive full-surface measurement.To increase the stitching quality,a hierarchical coordinate matching method is proposed.Initially,a 3D rigid body calibration auxiliary block is employed to track motion trajectory,which enables preliminary matching of four 3D-DIC sub-systems.Subsequently,secondary precise matching is performed based on feature points on the test specimen’s surface.Through the hierarchical coordinate matching method,the local 3D coordinate systems of each double-camera system are unified into a global coordinate system,achieving 3D surface reconstruction of the variable curvature cylindrical shell,and error analysis is conducted on the results.Furthermore,axial compression buckling experiment is conducted to measure the displacement and strain fields on the cylindrical shell’s surface.The experimental results are compared with the finite element analysis,validating the accuracy and effectiveness of the proposed multi-camera 3D-DIC measuring system.

DYNAMICAL BEHAVIOR OF VISCOELASTIC CYLINDRICAL SHELLS UNDER AXIAL PRESSURES

The hypotheses of the Krmn_Donnell theory of thin shells with large deflections and the Boltzmann laws for isotropic linear, viscoelastic materials, the constitutive equations of shallow shells are first derived. Then the governing equations for the deflection and stress function are formulated by using the procedure similar to establishing the Krmn equations of elastic thin plates. Introducing proper assumptions, an approximate theory for viscoelastic cylindrical shells under axial pressures can be obtained. Finally, the dynamical behavior is studied in detail by using several numerical methods. Dynamical properties, such as, hyperchaos, chaos, strange attractor, limit cycle etc., are discovered.

Dynamic Buckling of Elasto-Plastic Cylindrical Shells Under Axial Fluid-Solid Impact Load

The dynamic buckling of elasto-plastic cylindrical shells under axial fluid-solid impact is investigated theoretically. A simplified liquid- gas- structure model is given to approximately imitate the problem. The basic equation of the structure is derived from a minimum principle in dynamics of elasto-plastic continua at finite deformation, and the flow theory of plasticity is employed. The liquid is incompressible and the gas is compressed adiabatically. A number of numerical results are presented and the characteristics of the buckling behavior under fluid-solid impact are illustrated.

Bending and vibration analyses of a rotating sandwich cylindrical shell considering nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields

The bending and free vibration of a rotating sandwich cylindrical shell are analyzed with the consideration of the nanocomposite core and piezoelectric layers subjected to thermal and magnetic fields by use of the first-order shear deformation theory （FSDT） of shells. The governing equations of motion and the corresponding boundary conditions are established through the variational method and the Maxwell equation. The closed-form solutions of the rotating sandwich cylindrical shell are obtained. The effects of geometrical parameters, volume fractions of carbon nanotubes, applied voltages on the inner and outer piezoelectric layers, and magnetic and thermal fields on the natural frequency, critical angular velocity, and deflection of the sandwich cylindrical shell are investigated. The critical angular velocity of the nanocomposite sandwich cylindrical shell is obtained. The results show that the mechanical properties, e.g., Young＇s modulus and thermal expansion coefficient, for the carbon nanotube and matrix are functions of temperature, and the magnitude of the critical angular velocity can be adjusted by changing the applied voltage.

Shaking table test and numerical simulation of an isolated cylindrical latticed shell under multiple-support excitations

In order to study the infl uence of the ground motion spatial eff ect on the seismic response of large span spatial structures with isolation bearings, a single-layer cylindrical latticed shell scale model with a similarity ratio of 1/10 was constructed. An earthquake simulation shaking table test on the response under multiple-support excitations was performed with the high-position seismic isolation method using high damping rubber (HDR) bearings. Small-amplitude sinusoidal waves and seismic wave records with various spectral characteristics were applied to the model. The dynamic characteristics of the model and the seismic isolation eff ect on it were analyzed at varying apparent wave velocities, namely infi nitely great, 1000 m/s, 500 m/s and 250 m/s. Besides, numerical simulations were carried out by Matlab software. According to the comparison results, the numerical results agreed well with the experimental data. Moreover, the results showed that the latticed shell roof exhibited a translational motion as a rigid body after the installation of the HDR bearings with a much lower natural frequency, higher damping ratio and only 1/2~1/8 of the acceleration response peak values. Meanwhile, the structural responses and the bearing deformations at the output end of the seismic waves were greatly increased under multiple-support excitations.

Parametric Analysis of A Submerged Cylindrical Shell Subjected to Shock Waves

In this study, an FEM-SBFEM （scaled boundary finite element method） coupling procedure proposed by Fan et al. （2005） is adopted to obtain the dynamic responses of a submerged cylindrical shell subjected to plane step or exponential acoustic shock waves. The coupling procedure can readily be applied to three-dimensional problem, however for clarity, the problems to be presented are hmited to two-dimeusional domain. In the analyses, the cylindrical shell is modeled by simple beam elements （using FEM）, while the effects of the surrounding infinite fluid is modeled by the SBFEM. In it, no free surface and seabed are involved. Compared with Fan and his co-authors＇ works, the FEM-SBFEM coupling procedure is further verified to be feasible for shock waves by benchmark examples. Furthermore, parametric studies are performed and presented to gain insight into effects of the geometric and material properties of the cylindrical shell on its dynamic responses.

Vibration and Acoustic Radiation from Orthogonally Stiffened Infinite Circular Cylindrical Shells in Water

Based on the motion differential equations of vibration and acoustic coupling system for thin elastic shells with ribs, by means of the Fourier integral transformation and the Fourier inverse transformation, as well as the stationary phase method, an analytic solution, which has satisfying computational effectiveness and precision, is derived for the solution to the vibration and acoustic radiation from a submerged stiffened infinite circular cylinder with both ring and axial ribs. It is easy to analyze the effect of stiffening supports in the acoustic radiation field by use of the formulas obtained by the presented method and corresponding numerical computation. It is shown that the axial-stiffeners can improve the mechanical and acoustical characteristics. Moreover, the present method can be used to study the acoustic radiation mechanism of the type of structure.

Free vibration analysis of functionally graded laminated sandwich cylindrical shells integrated with piezoelectric layer

An analytical method for the three-dimensional vibration analysis of a functionally graded cylindrical shell integrated by two thin functionally graded piezoelectric （FGP） layers is presented. The first-order shear deformation theory is used to model the electromechanical system. Nonlinear equations of motion are derived by considering the von Karman nonlinear strain-displacement relations using Hamilton＇s principle. The piezoelectric layers on the inner and outer surfaces of the core can be considered as a sensor and an actuator for controlling characteristic vibration of the system. The equations of motion are derived as partial differential equations and then discretized by the Navier method. Numerical simulation is performed to investigate the effect of different para- meters of material and geometry on characteristic vibration of the cylinder. The results of this study show that the natural frequency of the system decreases by increasing the non-homogeneous index of FGP layers and decreases by increasing the non-homogeneous index of the functionally graded core. Furthermore, it is concluded that by increasing the ratio of core thickness to cylinder length, the natural frequencies of the cylinder increase considerably.

BUCKLING AND POSTBUCKLING OF LAMINATED THIN CYLINDRICAL SHELLS UNDER HYGROTHERMAL ENVIRONMENTS

The influence of hygrothermal effects on the buckling and postbuckling of composite laminated cylindrical shells subjected to axial compression is investigated using a micro-to-macro-mechanical analytical model. The material properties of the composite are affected hy the variation of temperature and moisture, and are hosed on a micromechanical model of a laminate. The governing equations are based on the classical laminated shell theory, and including hygrothermal effects. The nonlinear prebuckling deformations and initial geometric imperfections of the shell were both taken into account. A boundary layer theory of shell buckling was extended to the case of laminated cylindrical shells under hygrothermal environments, and a singular peturbation technique was employed to determine buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical shells under different sets of environmental conditions. The influences played by temperature rise, the degree of moisture concentration, fiber volume fraction, shell geometric parameter, total number of plies, stacking sequences and initial geometric imperfections are studied.

FREE VIBRATION OF PIEZOELECTRIC CYLINDRICAL SHELLS

Three displacement functions are introduced to represent each mechanical displacement according to the 3-D theory in this paper. By expanding the displacement functions and the electric potential in orthogonal series, the free vibration equation of piezoelectric cylindrical shells satisfying SS3 boundary conditions can be obtained. The equation was solved by utilizing Bessel functions with complex arguments. Results are presented graphically as well as in table, and compared with those of other references. Some frequencies that were missing in Ref. [9] are discovered.

Acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials

Using the multilayered cylinder model, we study acoustic scattering from a submerged cylindrical shell coated with locally resonant acoustic metamaterials, which exhibit locally negative effective mass densities. A spring model is introduced to replace the traditional transfer matrix, which may be singular in the negative mass region. The backscattering form function and the scattering cross section are calculated to discuss the acoustic properties of the coated submerged cylindrical shell.

Identifying the temperature effect on the vibrations of functionally graded cylindrical shells with porosities

The free thermal vibration of functionally graded material(FGM) cylindrical shells containing porosities is investigated. Both even distribution and uneven distribution are taken into account. In addition, three thermal load types, i.e., uniform temperature rise(UTR), nonlinear temperature rise(NLTR), and linear temperature rise(LTR), are researched to explore their effects on the vibration characteristics of porous FGM cylindrical shells. A modified power-law formulation is used to describe the material properties of FGM shells in the thickness direction. Love’s shell theory is used to formulate the straindisplacement equations, and the Rayleigh-Ritz method is utilized to calculate the natural frequencies of the system. The results show that the natural frequencies are affected by the porosity volume fraction, constituent volume fraction, and thermal load. Moreover,the natural frequencies obtained from the LTR have insignificant differences compared with those from the NLTR. Due to the calculation complexity of the NLTR, we propose that it is reasonable to replace it by its linear counterpart for the analysis of thin porous FGM cylindrical shells. The present results are verified in comparison with the published ones in the literature.

Experimental study of wind loads on cylindrical reticulated shells

The cylindrical reticulated shell structures without side walls, which are normally arranged in pairs, are usually used as dry-coal sheds in a thermal power plant. The wind loads of these shells do not exist in standards or codes. Therefore, this study investigates the mean and fluctuating wind loads on a cylindrical reticulated shell with a rise-to-span ratio of 0.39 through a series of wind tunnel tests. The characteristics of the wind pressures on the upper and lower surfaces and the net pressures are presented. The results show that the wind direction and another shell structure significantly affect the wind loads on the principal shell. The most unfavorable wind direction is around 30~, whereas the effects of the wind field and the height of the coal stack are small. The surfaces of the shells are divided into nine blocks, and the block mean and fluctuating （rms） pressure coefficients suitable for engineering applications are given as references for wind load codes.

Postbuckling analysis of functionally graded graphene platelet-reinforced polymer composite cylindrical shells using an analytical solution approach

An analytical approach is proposed to study the postbuckling of circular cylindrical shells subject to axial compression and lateral pressure made of functionally graded graphene platelet-reinforced polymer composite (FG-GPL-RPC). The governing equations are obtained in the context of the classical Donnell shell theory by the von K′arm′an nonlinear relations. Then, based on the Ritz energy method, an analytical solution approach is used to trace the nonlinear postbuckling path of the shell. The effects of several parameters such as the weight fraction of the graphene platelet (GPL), the geometrical properties, and distribution patterns of the GPL on the postbuckling characteristics of the FG-GPL-RPC shell are analyzed.

Dynamic behavior of single-layer latticed cylindrical shells subjected to seismic loading

The single-layer latticed cylindrical shell is one of the most widely adopted space-fl'amed structures.In this paper,free vibration properties and dynamic response to horizontal and vertical seismic waves of single-layer latticed cylindrical shells are analyzed by the finite element method using ANSYS software.In the numerical study,where hundreds of cases were analyzed,the parameters considered included rise-span ratio,length-span ratio,surface load and member section size.Moreover,to better define the actual behavior of single-layer latticed shells,the study is focused on the dynamic stress response to both axial forces and bending moments.Based on the numerical results,the effects of the parameters considered on the stresses are discussed and a modified seismic force coefficient method is suggested.In addition,some advice based on these research results is presented to help in the future design of such structures.

Free vibration of circular cylindrical shell with constrained layer damping

Free vibration characteristics of circular cylindrical shell with passive constrained layer damping （PCLD）are presented. Wave propagation approach rather than finite element method, transfer matrix method, and Rayleigh-Ritz method is used to solve the problem of vibration of PCLD circular cylindrical shell under a simply supported boundary condition at two ends. The governing equations of motion for the orthotropic cylindrical shell with PCLD are derived on the base of Sanders＇ thin shell theory. Nu- merical results show that the present method is more effective in comparison with other methods. The effects of the thickness of viscoelastic core and constrained layer, the elastic modulus ratio of orthotropic constrained layer, the complex shear modulus of viscoelastic core on frequency parameter, and the loss factor are discussed.

A NOVEL SEMI-ANALYTICAL METHOD FOR SOLVING ACOUSTIC RADIATION FROM LONGITUDINALLY STIFFENED INFINITE NON-CIRCULAR CYLINDRICAL SHELLS IN WATER

Based on the extended homogeneous capacity high precision integration method and the spectrum method of virtual boundary with a complex radius vector, a novel semi-analytical method, which has satisfactory computation efectiveness and precision, is presented for solving the acoustic radiation from a submerged infnite non-circular cylindrical shell stifened by longitudinal ribs by means of the Fourier integral transformation and stationary phase method. In this work, besides the normal interacting force, which is commonly adopted by some researchers, the other interacting forces and moments between the longitudinal ribs and the non-circular cylindrical shell are considered at the same time. The efects of the number and the size of the cross-section of longitudinal ribs on the characteristics of acoustic radiation are investigated. Numerical results show that the method proposed is more efcient than the existing mixed FE-BE method.

Sanders＇ Mid-long Cylindrical Shell Theory and its Application to Ocean Engineering Structures

The cylindrical shell is one of the main structural parts in ocean engineering structures.These cylinders are mostly of medium length,which means that the radius of the cross section is significantly smaller than the length of the cylindrical shell.From the viewpoint of the shell theory,they belong to the mid-long cylindrical shell category.To solve mechanical problems on this kind of structure,especially a cracked cylindrical shell,analysis based on shell theory is necessary.At present the generally used solving system for the mid-long cylindrical shell is too complicated,difficult to solve,and inapplicable to engineering.This paper introduced the Sanders' mid-long cylindrical shell theory which reduces the difficulty of the solution process,and will be suitable for solving problems with complicated boundary conditions.On this basis,the engineering applications of this theory were discussed in conjunction with the problem of a mid-long cylindrical shell having a circumferential crack.The solution process is simple,and the closed form solution can usually be found.In practical engineering applications,it gives satisfactory precision.