Free vibration of formed sandwich panel

In this paper, the free vibration of prefabricated architectural sandwich panels is studied. The core of the sandwich panel is approximated by finite prisms and the thin faces are modelled by finite strips. The finite prism-strip method is simple to program and saves considerable computing effort when compared with the finite element method. In this paper, only the dynamic characteristics of flat faced homogeneous sandwich panels are compared with results obtained by other methods, and also with the analytical solutions. Several examples are also presented for the free vibration of prefabricated architectural sandwich panels.     

On the growth rate of bending induced edge cracks in acoustically excited panels

Parts of an aircraft structure may be made to vibrate as a result of acoustic waves generated by various aircraft noise sources impinging on the structure. The stresses associated with this acoustically induced vibration may be sufficiently large to result in fatigue failure of portions of the structure. If acoustically induced fatigue cracks occur in the stiffened skin structures widely used in aircraft construction they may initiate in the skin panels near the stiffener attachment points. The initiation and subsequent propagation of these cracks at the panel edges is primarily due to the bending stresses arising from the out-of-plane vibration of the individual skin panels.The emphasis of the work described in this paper is on examining the growth rate of edge cracks in acoustically excited panels. A single panel with an edge crack is considered and this structural element is modelled as a flat plate clamped on three edges and part of the fourth. The crack is represented by the unclamped part of the fourth edge. Fracture mechanics principles are used to predict the crack growth rates associated with the first two modes of vibration of the edge cracked panel. The crack tip stress intensity factors associated with these panel modes are estimated by a technique based on finding the nominal bending stresses at the crack tips. The nominal bending stresses are in turn found from mode shapes determined by the Rayleigh Principle. The validity of the various assumptions is assessed by comparing the predicted crack growth rates with measured growth rates in panels representative of those used in aircraft construction.     

Free vibration of non-circular cylindrical shell panels

In the free vibration analysis of clamped non-circular cylindrical shell panels, a matrix method has been used to solve the governing differential equations, which have variable coefficients. The effect of the curvature, thickness ratio and aspect ratio on the natural frequencies has been studied. The results obtained for circular cylindrical panels are compared with other available results. The convergence of the solution is found to be good.     

Passive and active interior noise control of box structures using the structural intensity method

This paper presents passive and active vibro-acoustic noise control methods for attenuating the interior noise level in box structures which can be an analogy of cabins of vehicle and aircraft. The structural intensity (SI) approach is adopted to identify the predominant vibration panels and interior noise sources for box structures. In the study, the finite element method is used to determine the structural vibration and structural intensity in the box surfaces. According to structural intensity vectors plot and structural intensity stream lines presentation, the possible effective control positions where the dampers may be attached and the active control forces may act to reduce vibration and interior noise, are identified. From the study, it can be demonstrated that the structural intensity approach and stream line presentation are possible methods for identifying the vibro-acoustic interior noise source and predominant panels which may be modified to reduce the interior noise level. The structural intensity methodology, passive and active noise control results can be extended to the further study of the vibration and interior noise control of actual cabins of vehicles and aircraft.     

Structural-acoustic finite element analysis of the automobile passenger compartment: A review of current practice

This paper contains a brief review of the formulation of the finite element method for structural-acoustic analysis of an enclosed cavity, and illustrations are given of the application of this analytical method at General Motors Corporation to investigate the acoustics of the automobile passenger compartment. Low frequency noise in the passenger compartment (in approximately the 20–200 Hz frequency range) is of primary interest, and particularly that noise which is generated by the structural vibration of the wall panels of the compartment. The topics which are covered in the paper include the computation of acoustic modes and resonant frequencies of the passenger compartment, the effect of flexible wall panels on the cavity acoustics, the methods of direct and modal coupling of the structural and acoustic vehicle systems, and forced vibration analysis illustrating the techniques for computing panel-excited noise and for identifying critical panels around the passenger compartment. The capabilities of the finite element method are illustrated by applications to the production automobile, and experimental verifications of the various techniques are presented to illustrate the accuracy of the method.     

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.     

Acoustic response behaviour of panels mounted with equipment and its prediction using statistical energy analysis

Responses of non-uniform panels, like equipment panels of spacecraft, are not presently estimated using Statistical Energy Analysis. It is demonstrated that by treating the equipment as separate subsystems, with appropriate coupling loss factors for their connectivity, the response levels of the equipment can be estimated. The coupling loss factors are determined by the wave attenuation caused by the changes in structural properties introduced by the equipment. The estimated responses are valid at locations away from the boundary, in this case interface of the equipment. Information on the vibration levels at the interface of the equipment is necessary, especially to arrive at the random vibration loads of the equipment. A technique is developed to predict the vibration levels at locations at any distance from the interface of the equipment and validated by experiments. The prediction model is based on the interference pattern of the bending waves due to the reflection at the boundaries. It is seen that the existing techniques are suitable in estimating the responses of equipment only if the equipment behaves like mass attached at a point. But the technique developed in this study predicts the responses of the equipment that have large interface area.     

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.     

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。     

Sound insulation provided by single and double panel walls—a comparison of analytical solutions versus experimental results

The predicted values for acoustic insulation of single and double panel walls, using analytical models previously developed by the authors, are compared with experimental findings. The analytical method used fully takes into account the coupling between the air and the solid panels, and there is no restriction on their thickness, as the Kirchhoff or Mindlin approaches require. The laboratory experiments involved placing test specimens between standard chambers. Results are presented for panels made of glass, concrete and steel. From the results we can conclude that the predictive analytical solutions are in good agreement with the experimental results, except when the area of the panels is very small and the frequencies are very low. At low frequencies, the experimental results appear to be significantly affected by the resonance effects associated with the creation of stationary waves within the acoustic chambers, and the vibration modes introduced into the dynamic system by the restriction on the movement of the panel along its boundary.     

Non-ambiguous recovery of Biot poroelastic parameters of cellular panels using ultrasonicwaves

The inverse problem of the recovery of the poroelastic parameters of open-cell soft plastic foam panels is solved by employing transmitted ultrasonic waves (USW) and the Biot-Johnson-Koplik-Champoux-Allard (BJKCA) model. It is shown by constructing the objective functional given by the total square of the difference between predictions from the BJKCA interaction model and experimental data obtained with transmitted USW that the inverse problem is ill-posed, since the functional exhibits several local minima and maxima. In order to solve this problem, which is beyond the capability of most off-the-shelf iterative nonlinear least squares optimization algorithms (such as the Levenberg Marquadt or Nelder-Mead simplex methods), simple strategies are developed. The recovered acoustic parameters are compared with those obtained using simpler interaction models and a method employing asymptotic phase velocity of the transmitted USW. The retrieved elastic moduli are validated by solving an inverse vibration spectroscopy problem with data obtained from beam-like specimens cut from the panels using an equivalent solid elastodynamic model as estimator. The phase velocities are reconstructed using computed, measured resonance frequencies and a time-frequency decomposition of transient waves induced in the beam specimen. These confirm that the elastic parameters recovered using vibration are valid over the frequency range ofstudy.     

自由阻尼复合板的模态密度研究

模态密度是统计能量分析（SEA）的一个重要参数,尽管有关阻尼复合板振动特性的文献很多,便至今为止,研究其模态密度及变化规律的论文尚未见到,为此本文利用弹性最小势能原理和变分法,并考虑振动阻尼的影响,导出了自由阻尼复合板的弯曲振动模态密度计算公式,系统地分析了模态密度随阻尼层厚度、温度和频率而变化的规律。     

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.     

GENERALIZED DIFFERENTIAL QUADRATURE METHOD FOR THE FREE VIBRATION OF TRUNCATED CONICAL PANELS

This paper presents an improved generalized differential quadrature (GDQ) method for the investigation of the effects of boundary conditions on the free vibration characteristics of truncated conical panels. The truncated conical panel is an important geometrical shape in the fields of aerospace, marine and structural engineering. However, despite this importance, few works in free vibration analysis have dealt with this particular geometry. In this work, the vibration characteristics of clamped and simply supported truncated conical shells are obtained for various circumferential wave numbers. Further, the effects of the vertex and subtended angles on the frequency parameters are also examined in detail. Due to limited published results in the open literature, results for a range of cases are compared with those generated from the commercial finite element solver McNeal-Schwendler Corporation Nastran, and excellent agreement is observed.     

IS A SIMPLE SUPPORT REALLY THAT SIMPLE?

A very frequently applied boundary condition in problems involving modelling the dynamic behaviour of beams and panels is a simple support. This type of boundary condition is particularly used in the research area of active control of vibrations on panels. However, the practical implementation of this boundary condition in the laboratory is not at all trivial, especially when high accuracy is required.In this paper, various possible practical implementations of a simply supported panel are considered. A suitable method is selected and investigated experimentally. The results from a forced vibration test are compared with those obtained from theory in order to verify the relative accuracy of the approach.The effect of the relative distance between the panel surface and a solid boundary on the fundamental resonant response frequency is experimentally investigated, as well as changes produced by fluctuations in the laboratory temperature.     

Investigation of cross-polarized heterodyne technique for measuring refractive index and thickness of glass panels

A new mathematical model of cross-polarized heterodyning is proposed for measuring glass panels. An optical system is presented for obtaining relative thickness variation and difference distribution of refractive indices simultaneously, and the dual-balanced coherent demodulation technique is used. The experiment results show that the transmittance of light beam can be less than 0.5% when the vibration amplitude of the glass panels is equal to 5 mm. It takes about 200 s to scan the whole glass sample with size of 1430 × 1360 mm². The resolution of the thickness variation is 0.3 μm, and the lateral sampling resolution is 1 mm.     

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.     

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.     

Aero-thermo-mechanical characteristics of imperfect shape memory alloy hybrid composite panels

A nonlinear finite element model is provided to predict the static aero-thermal deflection and the vibration behavior of geometrically imperfect shape memory alloy hybrid composite panels under the combined effect of thermal and aerodynamic loads. The nonlinear governing equations are obtained using Marguerre curved plate theory and the principle of virtual work taking into account the temperature-dependence of material properties. The effect of large deflection is included in the formulation through the von Karman nonlinear strain-displacement relations. The thermal load is assumed to be a steady-state constant-temperature distribution, whereas the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The Newton-Raphson iteration method is employed to obtain the nonlinear aero-thermal deflections, while an eigenvalue problem is solved at each temperature step and static aerodynamic load to predict the free vibration frequencies about the deflected equilibrium position. Finally, the nonlinear deflection and free vibration characteristics of a composite panel are presented, illustrating the effects of geometric imperfection, temperature rise, aerodynamic pressure, boundary conditions and shape memory alloy fiber embeddings on the panel response.