Neural potentials and micro-signals of non-linear deep and shallow conical shells

Conventional sensors, such as proximeters and accelerometers, are add-on devices usually adding additional weights to structures and machines. Health monitoring of flexible structures by electroactive smart materials has been investigated over the years. Thin-film piezoelectric material, e.g. polyvinylidene fluoride (PVDF) polymeric material, is a lightweight and dynamic sensitive material appearing to be a perfect candidate in monitoring structure's dynamic state and health status of flexible shell structures with complex geometries. The complexity of shell structures has thwarted the progress in studying the distributed sensing of shell structures. Linear distributed sensing of various structures have been studied, e.g. beams, plates, cylindrical shells, conical shells, spherical shells, paraboloidal shells and toroidal shells. However, distributed microscopic neural signals of non-linear shell structures has not been carried out rigorously. This study is to evaluate microscopic signals, modal voltages and distributed micro-neural signal components of truncated non-linear conical shells laminated with distributed infinitesimal piezoelectric neurons. Signal generation of distributed neuron sensors laminated on conical shells is defined first. The dynamic neural signal of truncated non-linear conical shells consists of microscopic linear and non-linear membrane components and linear bending component based on the von Karman geometric non-linearity. Micro-signals, modal voltages and distributed neural signal components of two different truncated non-linear conical shells are investigated and their sensitivities discussed.     

Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness

The free vibration analysis of laminated conical shells with variable stiffness is presented using the method of differential quadrature (DQ). The stiffness coefficients are assumed to be functions of the circumferential coordinate that may be more close to the realistic applications. The first-order shear deformation shell theory is used to account for the effects of transverse shear deformations. In the DQ method, the governing equations and the corresponding boundary conditions are replaced by a system of simultaneously algebraic equations in terms of the function values of all the sampling points in the whole domain. These equations constitute a well-posed eigenvalue problem where the total number of equations is identical to that of unknowns and they can be solved readily. By vanishing the semivertex angle (α) of the conical shell, we can reduce the formulation of laminated conical shells to that of laminated cylindrical shells of which stiffness coefficients are the constants. Besides, the present formulation is also applicable to the analysis of annular plates by letting α=π/2. Illustrative examples are given to demonstrate the performance of the present DQ method for the analysis of various structures (annular plates, cylindrical shells and conical shells). The discrepancies between the analyses of laminated conical shells considering the constant stiffness and the variable stiffness are mainly concerned.     

Thermally induced vibration control of cylindrical shell using piezoelectric sensor and actuator

Shell type components and structures are very common in many mechanical and structural systems. Modeling and analysis of adaptive piezothermoelastic shell laminates represent a high level of sophistication and complexity. In this paper a finite element model is developed for the active control of thermally induced vibration of laminated composite shells with piezoelectric sensors and actuators. The present model takes into account the mass, stiffness and thermal expansion of the piezoelectric patches. A C_o continuous nine-node degenerated shell element is implemented to model the structure. The piezoelectric sensing layer senses the structural vibration and a suitable voltage applied in the piezoelectric actuator layer suppresses the oscillation. Actuator and sensor are coupled together with a control algorithm so as to actively control the dynamic response of the structure in a close loop. Numerical results are generated for a cylindrical shell and it is observed that thermally induced vibration of a laminated cylindrical shell can be suppressed through the application of piezoelectric sensor and actuator. Effects of variation in control gain and piezoelectric layer area coverage (PAC) have been studied. Higher control gain is more effective in damping out the vibration. Although the damping is enhanced by increase in PAC, increase beyond a certain level may not be useful in view of smaller efficacy and increased weight.     

Free vibration of a laminated composite shell of revolution: Effects of shear non-linearity

Effects of shear non-linearity on free vibration of a laminated composite shell of revolution are investigated using a semi-analytical method based on the Reissner–Mindlin shell theory. The coupling between symmetric and anti-symmetric vibration modes of the shell is considered in the shear deformable shell element employed in this study. The Hahn–Tsai non-linearly elastic shear stress–shear strain relation is adopted. Numerical examples are given for laminated composite circular cylindrical and conical shells with various boundary conditions. The numerical results indicate that shear non-linearity may reduce significantly the fundamental frequencies of cross-ply composite shells of revolution.     

Postbuckling of cross-ply laminated cylindrical shells with piezoelectric actuators under complex loading conditions

A postbuckling analysis is presented for a cross-ply laminated cylindrical shell with piezoelectric actuators subjected to the combined action of mechanical, electric and thermal loads. The temperature field considered is assumed to be a uniform distribution over the shell surface and through the shell thickness and the electric field is assumed to be the transverse component E_z only. The material properties are assumed to be independent of the temperature and the electric field. The governing equations are based on the classical shell theory with a von Kármán–Donnell-type of kinematic nonlinearity. The nonlinear prebuckling deformations and initial geometric imperfections of the shell are both taken into account. A boundary layer theory of shell buckling, which includes the effects of nonlinear prebuckling deformations, large deflections in the postbuckling range, and initial geometric imperfections of the shell, is extended to the case of hybrid laminated cylindrical shells. A singular perturbation technique is employed to determine the buckling loads and postbuckling equilibrium paths. The numerical illustrations concern the postbuckling behavior of perfect and imperfect, cross-ply laminated cylindrical thin shells with fully covered or embedded piezoelectric actuators subjected to combined mechanical loading of external pressure and axial compression, and under different sets of thermal and electric loading conditions. The effects played by temperature rise, applied voltage, shell geometric parameter, stacking sequence, as well as initial geometric imperfections are studied.     

PIEZOELECTRIC ACTUATOR AND SENSOR MODELS FOR AN INFLATED TOROIDAL SHELL

Due to their low mass and conformability, actuators and sensors made of active materials can be used in the vibration control of inflatable structures. In this study, we model piezoelectric patches attached to an inflated toroidal shell as actuators and sensors. Using Sanders' shell theory in the presence of initial stresses, the generalised forces due to the piezoelectric actuators are derived for the inflated toroidal shell assuming quasi-static conditions. The derivations are given for both unimorph and bimorph configurations. Effects of the mass and stiffness of the patches are incorporated in the equations of motion. Thereafter, a sensor equation is presented. Within linear shell theory, the methodology is quite general in nature and can be applied easily to other types of shells and membranes. To demonstrate this, we specialise the actuator and sensor equations for a circular cylinder. Using the formulations for the inflated toroidal shell, the modal forces and modal sensing constants are calculated for different sizes and locations of the piezoelectric patches. Along with this, controllability and observability indices are calculated to quantify the performance of the actuators and sensors. A study of the stiffness and mass effects of the piezoelectric patches is performed using frequency response function.     

Postbuckling of symmetrically laminated, moderately thick, axisymmetric shallow spherical shells

The paper deals with the buckling and postbuckling behaviour of cylindrically orthotropic, axisymmetric laminated, moderately thick shallow spherical shells under uniformly distributed normal loading. Considering the effects of transverse shear, the governing equations of equilibrium for the shells are derived and expressed in terms of normal deflection , slope qf and stress function gy. An iterative Chebyshev series solution technique is employed for the buckling and postbuckling analyses. Critical loads are estimated and the effects of boundary conditions, material properties, shell parameter, base radius to thickness ratio and number of layers on the postbuckling behaviour are shown.     

Performance evaluation of piezoelectric and differential pressure sensor for vortex flowmeters

Piezoelectric and transient differential pressure sensors are two among the most widely employed sensors for vortex flowmeter application. The present study evaluates the performance of these two techniques under fully developed and disturbed flow conditions. Firstly, the location of the transient differential pressure sensor is optimized to obtain high amplitude signals and good linearity in Strouhal number. Empirical mode decomposition method in combination with autocorrelation decay is successfully employed at high Reynolds numbers to identify the vortex shedding frequency in presence of hydrodynamic noise. The performance of the differential pressure sensor deteriorates significantly under disturbed flow conditions at low Reynolds number due to the presence of low frequency components. This deterioration in the signal quality limits the lower operating range of the flowmeter with differential pressure sensor. The output signals of the piezoelectric sensor and differential pressure sensor under no flow condition are compared to obtain the background noise due to piping vibrations and electrical interferences. These results will help a designer to suggest robust signal processing algorithms for vortex frequency detection.     

Effect of transverse shear on nonlinear vibration and postbuckling of anti-symmetric cross-ply imperfect cylindrical shells

Based on the Timoshenko-Mindlin kinematic hypothesis, the Donnell-type shell theory is extended to include transverse shear and rotary inertia for the nonlinear analysis of an anti-symmetrically laminated cross-ply circular cylindrical shell. The resulting governing equations are expressed in terms of a stress function, two rotations and transverse displacement. The shell is assumed to be all-simply-supported and all-clamped. A solution is formulated by a multi-mode approach and the method of harmonic balance for nonlinear vibrations. The corresponding postbuckling problem is treated as a special case. The results are compared with available data.     

On the inextensional axial collapse of thin PVC conical shells

Inextensional collapse mechanisms are presented for the axial crumpling of thin-walled circular cones and frusta (truncated circular cones). Shortening of the (thin) shell height is achieved by folding in a non-symmetric diamond mode about stationary circumferential and inclined plastic hinges; collapse proceeds progressively from the narrower end of the conical shell during the passage of a travelling hinge. Expressions for the various mean crushing loads, when collapsing frusta of rigid-perfectly-plastic material, are developed. Theoretical collapse modes and predicted loads are compared with those obtained experimentally by collapsing rigid PVC conical shells of constant axial length, of various wall-thicknesses and semi-apical angles, as well as metal (aluminium alloy and low-carbon steel) conical shells of similar geometry; agreement is found to be good.     

脱层复合材料圆柱壳屈曲的实验研究

脱层的存在将会大大降低层台结构的屈曲载荷。本文首先针对在轴压载荷作用下含脱层的复合材料层合圆柱壳，设计了测试其稳定性的实验方案。然后利用位移传感器、应变传感器、声发射仪器和红外热像仪等实验仪器，对含任意位置脱层与不含脱层的圆柱壳的屈曲载荷进行了实验测试，并对实验进行了精度分析。最后给出了实验结果并进行了讨论。     

Thermoelastic damping in cylindrical shells with application to tubular oscillator structures

Thermoelastic vibration and damping of cylindrical shell structures is studied in this paper. The general thermoelastic coupled equations for cylindrical thin shells are presented first. Since the general governing equations are quite complicated, they are then simplified with Donnell–Mushtari–Vlasov approaches for the cylindrical shells under transverse deflection-dominated vibrations. By solving the simplified thermoelastic equations with Galerkin method, the approximate solutions for thermoelastic damping in a cylindrical shell structure are obtained. The solutions are suitable for the predictions of thermoelastic damping of tubular oscillator structures. Some numerical examples for micro- or nano-tube resonators are provided to illustrate the results.     

Nonlinear finite element analysis of composite shell under impact

Large deflection dynamic responses of laminated composite cylindrical shells under impact are analyzed by the geometrically nonlinear finite element method based on a generalized Sander’s shell theory with the first order transverse shear deformation and the von-Karman large deflection assumption. A modified indentation law with inelastic indentation is employed for the contact force. The nonlinear finite element equations of motion of shell and an impactor along with the contact laws are solved numerically using Newmark’s time marching integration scheme in conjunction with Akay type successive iteration in each step. The ply failure region of the laminated shell is estimated using the Tsai-Wu quadratic interaction criteria. Numerical results, including the contact force histories, deflections and strains are presented and compared with the ones by linear analysis. The effect of the radius of curvature on the composite shell behaviors is investigated and discussed.     

Influence of the initial imperfection on the non-linear buckling response of FGM truncated conical shells

Non-linear buckling analyses of imperfect functionally graded truncated conical shells with simply supported boundary conditions and subjected to an axial compressive load have been presented in this work. The material properties of functionally graded shells are assumed to vary continuously through the thickness of the shell. The non-linear prebuckling deformations and initial geometric imperfections of an FGM truncated conical shell are both taken into account. The fundamental relations, modified Donnell type non-linear stability and compatibility equations of an imperfect FGM truncated conical shell are obtained and are solved by superposition and Galerkin methods, and the upper and lower critical axial loads has been found analytically. The numerical illustrations concern the non-linear buckling response of FGM truncated conical shells with different values of truncated conical shell parameters, initial imperfections and compositional profiles. Comparing the results of this study with those in the literature validates the present analysis.     

Vibration and buckling of cross-ply laminated composite circular cylindrical shells according to a global higher-order theory

Natural frequencies and buckling stresses of cross-ply laminated composite circular cylindrical shells are analyzed by taking into account the effects of higher-order deformations such as transverse shear and normal deformations, and rotatory inertia. By using the method of power series expansion of displacement components, a set of fundamental dynamic equations of a two-dimensional higher-order theory for laminated composite circular cylindrical shells made of elastic and orthotropic materials is derived through Hamilton's principle. Several sets of truncated approximate higher-order theories are applied to solve the vibration and buckling problems of laminated composite circular cylindrical shells subjected to axial stresses. The total number of unknowns does not depend on the number of layers in any multilayered shells. In order to assure the accuracy of the present theory, convergence properties of the first natural frequency and corresponding buckling stress for the fundamental mode r=s=1 are examined in detail. The internal and external works are calculated and compared to prove the numerical accuracy of solutions. Modal transverse shear and normal stresses can be calculated by integrating the three-dimensional equations of equilibrium in the thickness direction, and satisfying the continuity conditions at the interface between layers and stress boundary conditions at the external surfaces. It is noticed that the present global higher-order approximate theories can predict accurately the natural frequencies and buckling stresses of simply supported laminated composite circular cylindrical shells within small number of unknowns.     

光纤光栅传感网络的冲击定位方法

针对航空航天层合板结构冲击与振动监测的需求,提出一种基于小波包分解方法和分布式光纤光栅传感网络的板状结构低速冲击辨识方法。根据四边固支板结构的承载形式与光纤光栅传感器的感知特性,设计合理的传感器网络布局,再利用快速傅里叶变换(fast Fourier transformation,简称FFT)与小波包分解对光纤光栅传感网络监测到的冲击响应信号进行时频域分析,获取能表征冲击特性的时域特征分解信号。在此基础上,分别计算出每一个特征分解信号与其对应的时域原始信号之间的互相关系数,并将其做为相似度分配权值,分解出所有样本冲击点对应冲击响应信号的特征分解信号,构建样本信息库。利用Haudorff距离计算测试信号与样本信息库各个信号之间的相似度,并根据相似度来确定冲击点的位置坐标。研究表明,该方法能够实现对航空航天层合板结构低速冲击位置的辨识。     

Design and implementation of a versatile and variable-frequency piezoelectric coefficient measurement system

We present a simple but versatile piezoelectric coefficient measurement system, which can measure the longitudinal and transverse piezoelectric coefficients in the pressing and bending modes, respectively, at different applied forces and a wide range of frequencies. The functionality of this measurement system has been demonstrated on three samples, including a PbZr(0.52)Ti(0.48)O(3) (PZT) piezoelectric ceramic bulk, a ZnO thin film, and a laminated piezoelectric film sensor. The static longitudinal piezoelectric coefficients of the PZT bulk and the ZnO film are estimated to be around 210 and 8.1 pC∕N, respectively. The static transverse piezoelectric coefficients of the ZnO film and the piezoelectric film sensor are determined to be, respectively, -0.284 and -0.031 C∕m(2).     

Analysis of nonlinear vibration response of a functionally graded truncated conical shell with piezoelectric layers

The nonlinear vibration response of a functionally graded materials (FGMs) truncated conical shell with piezoelectric layers is analyzed. The vibration amplitude is suppressed by the positive and inverse piezoelectric effects. And the bifurcation phenomenon is described to reveal the motion state of the conical shell. Firstly, a truncated conical shell composed of three layers is described. And the effective material properties of the FG layer are defined by the Voigt model and the power law distribution. Next, the electric potentials of piezoelectric layers are defined as cosine distribution along the thickness direction. Meanwhile, the constant gain negative velocity feedback algorithm is used to suppress the vibration amplitude by the electric potential produced by the sensor layer. Thereafter, considering the first-order shear deformation theory and the von Karman nonlinearity, the relationship between the strain and displacement is defined. And the corresponding energy of the conical shell is calculated. After that, the motion equations of the conical shell are derived based on the Hamilton principle. Again, the nonlinear single degree of freedom equation is derived by the Galerkin method and the static condensation method. In the end, the nonlinear vibration response of FGMs truncated conical shell with piezoelectric layers under the external excitation is analyzed via using the harmonic balance method and the Runge-Kutta method. The effects of various parameters, such as ceramic volume fraction exponent, external excitation’s amplitude, control gain and geometric parameters on the nonlinear vibration response of the system are evaluated by case studies. Results indicate that the control gain plays an important role on the suppression of the vibration amplitude. The ceramic volume fraction exponents are not sensitive to the nonlinear vibration response compared with other parameters. The bifurcation behavior is observed under different parameters. The FGMs truncated conical shell with piezoelectric layers has three types of motion state, such as periodic motion, multi-periodic motion, and chaos motion.

     

Design, calibration and error analysis of a piezoelectric thrust dynamometer for small thrust liquid pulsed rocket engines

Small thrust liquid pulsed rocket engines operating in pulsed mode have gained a good reputation in attitude control applications for their potential reliability and efficiency. However, the pulsed characteristic creates a difficult measurement problem. In this paper, a novel thrust dynamometer with high natural frequency is developed for accurately measuring the pulsed thrust. It consists of two shear mode piezoelectric quartz crystal sensors and an integral shell. The sensors are inserted into unique double-elastic-half-ring grooves with an interference fit. Stiffness equations of the shell which are used to estimate the amount of interference are derived. The thrust dynamometer is calibrated both statically and dynamically. Static calibration uncertainty is evaluated. A trapezoidal impulse force is used to simulate the pulsed thrust for further characterizing the dynamic measurement performance of the thrust dynamometer. An evaluation algorithm of dynamic error is presented and used to evaluate the results of the dynamic simulation. The results show the thrust dynamometer has high sensitivity and natural frequency, good linearity and repeatability, and excellent dynamic performance. It can accurately trace trapezoidal thrust signal of 50 Hz without waveform distortion.     

Multidisciplinary optimization of a stiffened shell by genetic algorithm

Vibration analysis of simply supported rotating cross-ply laminated stiffened cylindrical shell is performed using an energy approach which includes variational and averaging method. The stiffeners include rings and stringers. The equations are obtained by Rayleigh-Ritz method and Sander’s relations. To validate the present method, the results are compared to the results available in other literatures. A good adoption is observed in different type of results including isotropic shells, rotating laminated shells, stiffened isotropic shells and stiffened laminated shells. Then, the optimization of parameters due to shell and stiffeners is conducted by genetic algorithm (GA) method under weight and frequency constraints. Stiffener shape, material properties and dimensions are also optimized.