ACTIVE VIBRATION CONTROL OF A CAR BODY BASED ON EXPERIMENTALLY EVALUATED MODAL PARAMETERS

Active vibration control has been successfully tested for structures with simple geometry, such as beams and plates, by using modal controllers. Since the dynamical behaviour of a variety of mechanical structures can be expressed in terms of modal parameters, the application of modal control concepts can be extended to structures with more complex geometries. For such structures the evaluation of modal parameters from numerical calculations of local modes is complicated because the results strongly depend on proper boundary conditions of the truncated structure. Therefore, the modal data are identified by an experimental modal analysis. The transformation of the experimentally evaluated mode shapes into a closed analytical formulation and the extraction of modal input and output factors for sensors and actuators connect experimental modal analysis and modal control theory. The implementation of the input and output factors into a modal state-space formulation results in a modal filter for the point sensor array and a retransformation filter for the segmented actuator patches. In this study, PVDF foil is used for sensors and actuators. The modal controller is implemented on a digital controller board and experimental tests with the floor panel and centre panel of a car body are carried out to validate the proposed concept.     

阶梯变厚度齿轮的横向弯曲振动

针对含轮毂、腹板、轮缘的齿轮结构特点,将其简化为一阶梯变厚度环板,应用Mindlin中厚板理论推导了他横向弯曲振动的频率方程,求得了固有频率,计算结果与有限元模态分析结果非常吻合。并通过大量算例分析了影响计算精度的主要因素是齿轮的厚径比和轮毂与腹板的厚度之比,在中厚板理论适用范围内(厚径比小于0.5)及轮毂与腹板厚度比小于2的情况下,本文理论计算可以获得很高精度。     

Generic nonlinear behavior of antisymmetric angle-ply laminated plates

A generic presentation of the large deflection, postbuckling and nonlinear flexural vibration behavior of antisymmetric angle-ply laminated plates is investigated. A transformation between on-axis and off-axis stiffnesses is presented such that all the stiffnesses, including bending-stretching coupling, in the nonlinear governing equations of angle-ply laminates can be expressed in terms of bounded global constants in orthotropic plates. The results presented are applicable to a large variety of composite materials and show that a higher generalized rigidity ratio will lead to smaller deflection of plates, higher buckling loads and lower postbuckling deflection, and higher relative large-amplitude natural frequencies. The information presented should be helpful to anyone seeking a better understanding of the correlation between composite material properties and nonlinear behavior of laminated plates.     

Vibration of rectangular Mindlin plates resting on non-homogenous elastic foundations

This paper is concerned with the vibration behaviour of rectangular Mindlin plates resting on non-homogenous elastic foundations. A rectangular plate is assumed to rest on a non-homogenous elastic foundation that consists of multi-segment Winkler-type elastic foundations. Two parallel edges of the plate are assumed to be simply supported and the two remaining edges may have any combinations of free, simply supported or clamped conditions. The plate is first divided into subdomains along the interfaces of the multi-segment foundations. The Levy solution approach associated with the state space technique is employed to derive the analytical solutions for each subdomain. The domain decomposition method is used to cater for the continuity and equilibrium conditions at the interfaces of the subdomains. First-known exact solutions for vibration of rectangular Mindlin plates on a non-homogenous elastic foundation are obtained. The vibration of square Mindlin plates partially resting on an elastic foundation is studied in detail. The influence of the foundation stiffness parameter, the foundation length ratio and the plate thickness ratio on the frequency parameters of square Mindlin plates is discussed. The exact vibration solutions presented in this paper may be used as benchmarks for researchers to check their numerical methods for such a plate vibration problem. The results are also important for engineers to design plates supported by multi-segment elastic foundations.     

Blast response of corroded steel plates

Numerical results for one- and both-sided corroded steel plates subjected to blast loading are presented. Finite element analysis, with ABAQUS software, is employed to determine the deformation and stress distributions. The results for the case of triangular pulse pressure on un-corroded plates are validated against literature-based data and then, detailed parametric studies are carried-out. The effects of influential parameters including, plate aspect ratio, degree of pit and different ratio of pit depth at each sides of the plate are investigated. The results show that position of pitted surface in respect to applied pressure is the most influential parameter on reduction of dynamic load carrying capacity of pitted plates. By increasing degree of pitting, reduction of dynamic load carrying capacity decrease more.     

机载大长宽比风冷均温冷板优化设计

大长宽比冷板在机载电子设备中应用广泛。文中在现有风冷散热技术的基础上,同时采用均温板技术和非连续流道技术设计了一种全新的大长宽比机载风冷均温冷板。对该风冷均温冷板进行了数值仿真分析,并与普通的风冷散热冷板进行了对比。同时,对其进行了散热试验,并与数值仿真结果进行了进一步对比分析。结果表明,该风冷散热冷板具有2 个特点:对冷却风资源利用充分,因而散热效率较高;工作时表面的温度一致性较好。     

Natural frequencies of symmetrically laminated elliptical and circular plates

Elliptical and circular fibre reinforced composite plates are important structural elements in modern engineering structures. Vibration analysis of these elements are of interest to structural designers. The present paper deals with the free transverse vibration analysis of symmetrically laminated solid and annular elliptic and circular plates with several complicating effects.The approach developed is based on the Rayleigh–Ritz method where the deflection of the plate is approximated by a general shape function of polynomial type.The analysis includes several complicating effects, such as the presence of an internal hole, an internal ring support, several concentrated masses and the boundary elastically restrained against rotation and translation.Several examples are solved and some results which correspond to particular cases are compared with existing values in the literature. New results are also presented for cross-ply and angle-ply elliptical and circular laminates with different boundary conditions.The algorithm developed can be applied to a wide range of elastic restraint conditions, to any aspect ratio and to higher modes. The effect of the restraint parameters along the boundary on the natural frequencies for plates with these complicating effects is considered.     

Stress concentration in metallic plates with special shaped cutout

Panels and shells with variously shaped cutout are often used in both modern and classical aerospace, mechanical and civil engineering structures. The understanding of the effects of cutout on the load bearing capacity and stress concentration of such plates/shells is very important in designing of structures. An analytical investigation is undertaken to study the stress analysis of plates with different central cutouts. Particular emphasis is placed on flat infinite plates subjected to a uniaxial tension load. The results based on analytical solution are compared with the results obtained using finite element methods. The main objective of this study is to demonstrate the accuracy and simplicity of presented analytical solution for stress analysis of plates with central cutout. The varying parameters, such as cutout shape and bluntness, load direction or cutout orientations, which affect the stress distributions and SCF in the perforated plates, are considered. The results presented herein indicated that the stress concentration factor of perforated plates can be significantly changed by using proper cutout shape, bluntness and orientation.     

Vibration of stepped thickness plates

The vibration characteristics of stepped thickness plates of rectangular geometry with simply supported edges are investigated through an exact analysis. To illustrate the effect of sudden variation of thickness in the step form on the dynamic characteristics of plates, numerical calculations have been made for various combinations of thickness step, step-length ratio and side ratio. Natural frequencies for the first eight to nine modes are presented in the form of tables. Nodal lines are also plotted for a few selected cases. Several interesting features such as that of the thickness step splitting the degenerate frequencies of uniform rectangular plates into distinct ones, and the “frequency crossing” of some of the modes are observed.     

Analysis of sandwich plates with unbalanced cross-ply faces

The analysis of rectangular sandwich plates constructed of an orthotropic core and unbalanced cross-ply face plates is presented. A double Fourier series approach is used for simply supported sandwich plates under lateral loads. Results are compared to the corresponding sandwich plate results with orthotropic faces. The results indicate that the effect of bending-membrane coupling depends mainly upon the relative thicknesses of the core and faces; other factors include the shear stiffnesses of the core, the degree of anisotropy of the individual plies, the total number and lay-up of plies in the faces and the aspect ratio of the plate.     

The numerical simulation of a rectifying device with a perforated plate

The aim of this research is to verify a perforated plate design technique for generating a certain velocity and turbulence distribution by introducing the connection condition that demonstrates the disturbance attenuation characteristics of the plate. The application range on the downstream side of the perforated plate is studied based on a numerical simulation of the resistance characteristics of perforated plates. The optimum numerical simulations of turbulent flows through perforated plates are then clarified. The numerical simulation results and the experimental data for the disturbance attenuation are highly consistent with the numerical simulation and experimental data for the perforated plates with fixed opening ratios and pore diameters. In addition, the calculation results for the downstream disturbance distribution almost correspond with the experimental results when the opening ratio of the perforated plate is fixed but the pore diameter is variable. Consequently, the disturbance numerical simulation technique developed in this research by utilising the connection conditions for perforated plates clarifies the reliability of the rectifying device design method used to generate the velocity and turbulence distribution of perforated plates.     

Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM

The critical compressive load in the buckling of circular and annular composite plates reinforced with carbon nanotubes (CNTs) is calculated using finite element method. The developed model is based on the third-order shear deformation theory for moderately thick laminated plates. Effects of CNTs orientation angles and thickness-to-inner radius ratio on the buckling of composite plates are discussed. The results are compared with those obtained by analytical method based on classical plate theory. The finite element method shows lower values for critical buckling load because of the elimination of shear strain in the classical plate theory.     

Vibrational characteristics of annular plates and rings of radially varying thinkness

In this paper, annular plates having thickness variation are studied by deriving the equations of motion on the basis of the Mindlin plate theory. The Chebyshev collocation method is employed to solve the differential equation governing the transverse motion of such plates. The dimensionless frequencies are evaluated for different values of taper constant (α), thickness ratio (h _u). radii ratio (ε) and power (n). The results of an experimental investigation are also presented, and the agreement between these findings and the predicted values in theory is remarkably good. As a result of this study, it is found that the effects of rotatory inertia and transverse shear deformation reduce the natural frequencies for all boundary conditions and for all values ofn. h _o, ∈, a ands (mode number). This study also showed that the natural frequencies of annular plates with thickness expressed by the nth power function are higher than those by the (n?1)th power function for positive values of α, and vice versa for negative values ofe for all three boundary conditions. Moreover, there is a proof that the natural frequencies of annular plates tend to be higher as the taper constant decrease and/or as the radii ratio increase for all three boundary conditions and for all values ofn, s andh _o.     

The deflection coefficient of a rectangular plate reinforced in the middle

In this paper, we investigated the deflection coefficients of rectangular plates that are reinforced in the middle. For reinforced plates with three different aspect ratios and two types of boundary conditions (simply supported and clamped), we derived the deflection coefficients with respect to the elastic modulus ratio and the relative length of the inner plate using the least-squares method. We performed a finite element analysis of the models, and calculated the deflection coefficients of reinforced plates in terms of the deflection coefficients of simple (nonreinforced) plates. The results can be extended to various types of reinforced rectangular plates.     

Thermally induced buckling of functionally graded hybrid composite plates

In this paper, thermal buckling analysis is performed on hybrid functionally graded plates (FGPs) with an arbitrary initial stress. The governing equations are derived using the average stress method, including the effect of transverse shear deformation. Then, an eigenvalue problem is formed to evaluate thermal buckling temperatures for simple supported initially stressed ceramic-FGM-metal plates. The effects of functionally graded material (FGM) layer thickness, volume fraction index, layer thickness ratio, thickness ratio, aspect ratio and initial stress on the thermal buckling temperature of hybrid FGPs are investigated. The results reveal that the volume fraction index, initial stresses and FGM layer thickness have significant influence on the thermal buckling of hybrid FGPs.     

Analytical solution of a two variable refined plate theory for bending analysis of orthotropic Levy-type plates

This paper presents analytical solutions of deflection and stress for orthotropic plates using a two variable refined plate theory. The theory accounts for parabolic variation of transverse shear stress through the thickness, and satisfies the zero traction boundary conditions on the top and bottom surfaces of the plate without using shear correction factor. Additional features of the theory are that it has strong similarity with classical plate theory in many aspects, and the number of involved variables is only two as against three in case of other shear deformation theories. The Levy-type solution procedure in conjunction with the state space concept is used to determine the closed-form solutions for orthotropic rectangular plates with two opposite edges simply supported and the other two edges having arbitrary boundary conditions. Comparison studies are performed to verify the validity of the present results. Finally, the effects of thickness ratio, modulus ratio and aspect ratio on the deflection and stress of orthotropic plates are investigated and discussed.     

Thermal buckling behavior of laminated composite plates: a finite-element study

In this paper, the thermal buckling behavior of composite laminated plates under a uniform temperature distribution is studied. A finite element of four nodes and 32 degrees of freedom (DOF), previously developed for the bending and mechanical buckling of laminated composite plates, is extended to investigate the thermal buckling behavior of laminated composite plates. Based upon the classical plate theory, the present finite element is a combination of a linear isoparametric membrane element and a high precision rectangular Hermitian element. The numerical implementation of the present finite element allowed the comparison of the numerical obtained results with results obtained from the literature: 1) with element of the same order, 2) the first order shear deformation theory, 3) the high order shear deformation theory and 4) the three-dimensional solution. It was found that the obtained results were very close to the reference results and the proposed element offers a good convergence speed. Furthermore, a parametrical study was also conducted to investigate the effect of the anisotropy of composite materials on the critical buckling temperature of laminated plates. The study showed that: 1) the critical buckling temperature generally decreases with the increasing of the modulus ratio E _L/E _T and thermal expansion ratio α _T/α _L, and 2) the boundary conditions and the orientation angles significantly affect the critical buckling temperature of laminated plates.     

Thermal buckling of functionally graded rectangular plates subjected to partial heating

We present the thermal buckling analysis of functionally graded rectangular plates subjected to partial heating in a plane and uniform temperature rise through its thickness. The plate is simply supported for out-of-plane deformation and perfectly clamped for in-plane deformation. It is assumed that the functionally graded material properties such as the coefficient of linear thermal expansion and Young's modulus are changed individually in the thickness direction of the plate with the power law, while Poisson's ratio is assumed to be constant. Analytical developments consist of two stages. First, the nonuniform in-plane resultant forces are determined by solving a plane thermoelastic problem. Then the critical buckling temperatures of the plates with the predetermined resultant forces are calculated as the generalized eigenvalue problem which is constructed by using the Galerkin method. Finally, the effects of material inhomogeneity, aspect ratio, and heated region on the critical buckling temperatures are examined.