VIBRATION OF TWISTED AND CURVED CYLINDRICAL PANELS WITH VARIABLE THICKNESS

A numerical procedure, with an exact strain-displacement relationship of twisted and curved cylindrical panels having variable thickness derived by considering the Green strain tensor on general shell theory, is presented using the principle of virtual work and the Rayleigh-Ritz method with algebraic polynomials as in-plane and transverse displacement functions. The accuracy and applicability of the procedure are verified by comparing the present results with previous experimental and theoretical results for several panels. The effects of variation ratio of thickness in chordwise and lengthwise directions, twist, and curvature both in two directions aforementioned on vibrations of cylindrical panels are studied in detail, and typical vibration mode shapes are plotted to demonstrate the effects.     

STRUCTURAL RESPONSE OF LAMINATED COMPOSITE SHELLS SUBJECTED TO BLAST LOADING: COMPARISON OF EXPERIMENTAL AND THEORETICAL METHODS

The results from a theoretical and experimental investigation of the dynamic response of cylindrically curved laminated composite shells subjected to normal blast loading are presented. The dynamic equations of motion for cylindrical laminated shells are derived using the assumptions of Love's theory of thin elastic shells. Kinematically admissible displacement functions are chosen to represent the motion of the clamped cylindrical shell and the governing equations are obtained in the time domain using the Galerkin method. The time-dependent equations of the cylindrically curved laminated shell are then solved by the Runge-Kutta-Verner method. Finite element modelling and analysis for the blast-loaded cylindrical shell are also presented. Experimental results for cylindrically curved laminated composite shells with clamped edges and subjected to blast loading are presented. The blast pressure and strain measurements are performed on the shell panels. The strain response frequencies of the clamped cylindrical shells subjected to blast load are obtained using the fast Fourier transformation technique. In addition, the effects of material properties on the dynamic behaviour are examined. The strain-time history curves show agreement between the experimental and analysis results in the longitudinal direction of the cylindrical panels. However, there is a discrepancy between the experimental and analysis results in the circumferential direction of the cylindrical panels. A good prediction is obtained for the response frequency of the cylindrical shell panels.     

Vibrations of axially loaded stiffened cylindrical panels with elastic restraints

A method has been developed for analysis of the vibration and buckling of preloaded stiffened cylindrical panels with different boundary conditions along the straight edges, including elastic restraints. In the analysis linear, “smeared” stiffener, Flügge type theory is used. A computer program VIBUPAL has been developed. The method has been verified by comparison with results available for limited cases and very good agreement has been obtained.     

Mathematical Modeling of Complex Oscillations of Flexible Micropolar Mesh Cylindrical Panels

Russian Physics Journal - A new mathematical model of oscillations of mesh micropolar geometrically nonlinear cylindrical panels under the action of a normal alternating distributed load has been...     

Dynamic behaviour of a simply supported circular cylindrical panel subjected to an initial bending moment

The vibration of cylindrical panels with simply supported boundary conditions in the presence of an initial bending moment is investigated. The analysis is based on the theory of Herrmann and Armenàkas. The results for the stability and free vibration of the panels are obtained as special cases.     

FREQUENCY RESPONSE OF A MODERATELY THICK ANTISYMMETRIC CROSS-PLY CYLINDRICAL PANEL USING MIXED TYPE OF FOURIER SOLUTION FUNCTIONS

A hitherto unavailable analytical solution to the boundary-value problem of the free vibration response of shear-flexible antisymmetric cross-ply laminated cylindrical panels is presented. The laminated shell theory formulation is based on the first order shear deformation theory (FSDT) including rotatory and surface-parallel inertias. The governing equations of the panel are defined by five highly coupled partial differential equations in five unknowns—three displacements, and two rotations. The assumed solution functions for the eigen/boundary-value problem are selected in terms of mixed-type double Fourier series. Numerical results presented for parametric effects, such as length-to-thickness ratio and radius-to-thickness ratio, should serve as a bench mark for future comparison. A four-node shear-flexible finite element is selected to compare the results with the present solution.     

Noise transmission from a curved panel into a cylindrical enclosure: analysis of structural acoustic coupling

Much of the research on sound transmission through the aircraft fuselage into the interior of aircraft has considered coupling of the entire cylinder to the acoustic modes of the enclosure. Yet, much of the work on structural acoustic control of sound radiation has focused on reducing sound radiation from individual panels into an acoustic space. Research by the authors seeks to bridge this gap by considering the transmission of sound from individual panels on the fuselage to the interior of the aircraft. As part of this research, an analytical model of a curved panel, with attached piezoelectric actuators, subjected to a static pressure load was previously developed. In the present work, the analytical model is extended to consider the coupling of a curved panel to the interior acoustics of a rigid-walled cylinder. Insight gained from an accurate analytical model of the dynamics of the noise transmission from the curved panels of the fuselage into the cylindrical enclosure of an aircraft is essential to the development of feedback control systems for the control of stochastic inputs, such as turbulent boundary layer excitation. The criteria for maximal structural acoustic coupling between the modes of the curved panel and the modes of the cylindrical enclosure are studied. For panels with aspect ratios typical of those found in aircraft, results indicate that predominately axial structural modes couple most efficiently to the acoustic modes of the enclosure. The effects of the position of the curved panel on the cylinder are also studied. Structural acoustic coupling is found to not be significantly affected by varying panel position. The impact of the findings of this study on structural acoustic control design is discussed.     

Natural frequencies of shallow cylindrically curved panels

The natural frequencies of cylindrically curved panels are available in closed form for only two boundary condition sets. This paper demonstrates how Sewall's shallow shell formation can be recast in a relatively simple form to allow direct computation of the natural frequencies and mode shapes of cylindrical panels with a wide range of boundary conditions.     

Free vibration and parametric resonance of shear deformable functionally graded cylindrical panels

This paper investigates free vibration and dynamic instability of functionally graded cylindrical panels subjected to combined static and periodic axial forces and in thermal environment. Theoretical formulations are based on Reddy's higher order shear deformation shell theory to account for rotary inertia and the parabolic distribution of the transverse shear strains through the panel thickness. Thermal effects due to steady temperature change are included in the analysis. Material properties are assumed to be temperature dependent and graded in the thickness direction according to a power-law distribution in terms of the volume fractions of the constituents. The panel under current consideration is clamped or simply supported on two straight edges and may be either free, simply supported or clamped on the curved edges. A semi-analytical approach, which takes the advantages of one-dimensional differential quadrature approximation, Galerkin technique and Bolotin's method, is employed to determine the natural frequencies and the unstable regions of the panel. Numerical results for silicon nitride/stainless-steel cylindrical panels are given in both dimensionless tabular and graphical forms. Effects of material composition, temperature rise, panel geometry parameters, and boundary conditions on free vibration and the parametric resonance are also studied.     

Natural frequencies of cylindrical shells and panels in vacuum and in a fluid

A unified formula for estimating the natural frequencies of circular cylindrical shells and panels in vacuum as well as in a fluid is presented. Boundary conditions considered include both simply supported and clamped. In the latter case, tables of constants are included to facilitate application of the formula. Extension of the method to estimate the frequencies of a system of cylindrical shells coupled by fluid gaps is also discussed. The methodology is particularly suitable for digital computer implementation.     

Numerical study of homogeneous dynamo based on experimental von Kármán type flows

A numerical study of the magnetic induction equation has been performed on von Kármán type flows. These flows are generated by two co-axial counter-rotating propellers in cylindrical containers. Such devices are currently used in the von Kármán sodium (VKS) experiment designed to study dynamo action in an unconstrained flow. The mean velocity fields have been measured for different configurations and are introduced in a periodic cylindrical kinematic dynamo code. Depending on the driving configuration, on the poloidal to toroidal flow ratio and on the conductivity of boundaries, some flows are observed to sustain growing magnetic fields for magnetic Reynolds numbers accessible to a sodium experiment. The response of the flow to an external magnetic field has also been studied: The results are in excellent agreement with experimental results in the single propeller case but can differ in the two propellers case.     

用于汽车低频振动控制的局域共振声子晶体*

低频振动的控制是评估汽车舒适性的重要指标。针对汽车板件结构的低频振动控制问题,提出了一种基于局域共振机理的新型准二维声子晶体板。其结构由单侧复合圆柱共振单元周期排布在基板上构成。通过有限元方法得到了该结构的带隙特性,并结合其振型和传输谱分析了低频完全带隙的形成机理。研究表明,不同形式的板振动模式与圆柱共振单元的局域共振模式相互耦合形成面内带隙与面外带隙,两者叠加形成完全带隙。进一步研究发现,通过改变结构的材料和尺寸参数可以将共振带隙调节到满足实际应用要求的极低频范围,可在低于100 Hz的频段形成完全带隙,并可在更宽的频带内抑制z方向振动的弯曲波,为声子晶体在车身板件减振中的实际应用提供了依据。     

Coaxial (tubular) glow discharge in electronegative gases

The positive-column plasma of a low- and medium-pressure electronegative glow discharge initiated in the gap between two coaxial cylindrical tubes has been considered (the current is directed along the tube axis). It is assumed that the gas mixture contains halogens, and ion diffusion is not negligibly weak. It is found that the coaxial discharge is characterized by plasma separation into three coaxial regions with different compositions in the direction transverse to the current. It has been shown that the ionization and excitation frequencies of atoms are higher than in the purely cylindrical case, even for a small (0.05–0.15) ratio of the radii of the inner and outer walls. An asymptotic analysis of the continuity equations yields analytic expressions that make it possible to rapidly and easily estimate the geometrical parameters of the spatial distributions of charge particle concentrations, as well as energy parameters of the plasma for the radii ratio that exceed 0.3. The conditions for the applicability of analytic relations and their accuracy are established from a comparison of the results of analytic and numerical calculations.     

Self-Induction of a Fine Cylindrical Metallic Wire Versus a Mechanism of Electron Surface Scattering

Technical Physics - The self-induction of a thin cylindrical metallic wire has been calculated. A general case when the ratio of the electron free path to the wire radius may take an arbitrary...     

A comparison of some shell theories used for the dynamic analysis of cross-ply laminated circular cylindrical panels

The free vibration problem of thin elastic cross-ply laminated circular cylindrical panels is considered. For this problem, a theoretical unification as well as a numerical comparison of the thin shell theories most commonly used (in engineering applications) is presented. In more detail, the problem is formulated in such a way that by using some tracers, which have the form of Kronecker's deltas, the stress-strain relations, constitutive equations and equations of motion obtained produce, as special cases, the corresponding relations and equations of Donnell's, Love's, Sanders' and Flugge's theories. By using a closed form solution, obtained for simply supported panels, a comparison of corresponding numerical results obtained on the basis of all of the aforementioned shell theories is attempted.     

Improved sound absorption performance of three-dimensional MPP space sound absorbers by filling with porous materials

Because microperforated panels (MPPs), which can be made from various materials, provide wide-band sound absorption, they are recognized as one of the next-generation absorption materials. Although MPPs are typically placed in front of rigid walls, MPP space sound absorbers without a backing structure, including three-dimensional cylindrical MPP space absorbers (CMSAs) and rectangular MPP space absorbers (RMSAs), are proposed to extend their design flexibility and easy-to-use properties. On the other hand, improving the absorption performance by filling the back cavity of typical MPP absorbers with porous materials has been shown theoretically, and three-dimensional MPP space absorbers should display similar improvements. Herein the effects of porous materials inserted into the cavities of CMSAs and RMSAs are experimentally investigated and a numerical prediction method using the two-dimensional boundary element method is proposed. Consequently, CMSAs and RMSAs with improved absorption performances are illustrated based on the experimental results, and the applicability of the proposed prediction method as a design tool is confirmed by comparing the experimental and numerical results.     

Low frequency sound insulation using stiffness control with honeycomb panels

A new honeycomb core design has been used to increase the stiffness of the panel and applied to improve the noise transmission loss at frequencies between 100 and 200 Hz. A model is presented to predict the transmission loss of the honeycomb panels based on the structural modal parameters. A new test specimen with fiber reinforced plastic cores and face sheets had been used to investigate the effect of stiffness and damping on noise transmission loss. The measurements of noise transmission loss have been compared with data for common structural panels. The results show that the new core fabrication techniques using moulding to improve the noise transmission are effective. In comparison to a cement panel of the same mass, the honeycomb panels have higher TL at low frequencies between 100 and 200 Hz due to higher stiffness and damping. The honeycomb panels have more significant vibration responses above 500 Hz but these are limited by damping.     

The stability of cantilever panels in uniform incompressible flow

The stability of large aspect ratio cantilever panels in uniform incompressible flow is studied by employing linearized plate and potential flow theories together with asymptotic expressions for the generalized pressures. It is assumed that if the downstream wake effects on the panel stability are insignificant then the results will be almost independent of where these effects are neglected in the analysis. Accordingly two approximations for the pressure, corresponding to different ways of neglecting the wake effects, are compared, and it is concluded that such effects cannot be ignored when the mass ratio is large. The results also demonstrate that a two-dimensional analysis (infinite aspect ratio) may yield an overestimate of the critical flow velocity for finite width panels.     

Numerical analyses of the sound absorption of three-dimensional MPP space sound absorbers

Because microperforated panels (MPPs) can provide wide-band sound absorption without fibrous and porous materials, they are recognized as next-generation absorption materials. The fundamental absorbing mechanism is Helmholtz-resonance absorption due to the perforations and air-back cavity. Consequently, MPPs are usually placed in front of rigid-back walls. However, one of the authors has proposed MPP space sound absorbers without backing structures. Among these space absorbers, cylindrical MPP space absorbers and rectangular MPP space absorbers are advantageous due to their design flexibility and easy-to-use properties. Although their performances have been investigated experimentally, it is necessary to predict their absorption characteristics to develop improved shapes and efficient designs. Herein their absorption characteristics are numerically predicted using the two-dimensional boundary element method, and the applicability of a numerical method as a design tool to sufficiently predict the performance of MPP space absorbers is discussed.     

An investigation into the acoustic insulation of triple-layered panels containing Newtonian fluids: Theory and experiment

Sound insulation of triple-layered panels consisting of two impervious layers with the middle layer being a Newtonian fluid is studied here both theoretically and experimentally. The progressive impedance model is used to predict the transmission loss (TL) provided by the panel in a normal incidence field. Corrections are then made to obtain the TL values of such panels in random incidence field. A modified B&K impedance tube was constructed for experimental evaluation. Results are presented for a Pyrex glass cylindrical tube containing motor oil, a ferromagnetic nanoparticles fluid (in the absence of a magnetic field) and air. Good agreement is obtained between the measured and analytical results for a wide range of frequencies. Also, a significant difference in TL values, particularly at low frequencies (f ? 4 kHz), is observed once the air is replaced by the fluid layer.