Vibration Of Panels Research Articles

Modified Elliptic Integral Approach for the Forced Vibration and Sound Transmission Analysis of a Nonlinear Panel Backed by a Partitioned Cavity

This article is the further work of previous papers and also the first study to adopt the elliptic integral approach to solve the forced nonlinear structural acoustic problem. A previous elliptic integral approach, which was only used for the free vibration analyses of various nonlinear structural acoustic problems, is modified and custom designed for conducting this forced vibration analysis. The main advantage of the proposed approach is that one elliptic cosine contains various harmonic components, while one simple cosine term only carries one particular harmonic component. That is why the proposed solution form can be more concise than those in the harmonic balance procedures. This is the first study to employ the proposed elliptic cosine solution form for the forced vibration and sound transmission of a nonlinear panel backed by a partitioned cavity. This study has two focuses: (1) the development of elliptic integral approach for solving the nonlinear structural acoustic governing equations, and (2) the effect of partitioned cavities on the forced vibration response and sound transmission loss. Moreover, a set of elliptic cosine solutions is verified by that from the modified residue harmonic balance method. A mode convergence study and a harmonic contribution analysis are also conducted.

Improvement on the passive method based on dampers for the vibration control of spacecraft solar panels

In this study, a passive vibration control method termed as translational root mounting method is proposed and investigated, for suppressing the low frequency vibrations of spacecraft solar panels. The translational root mounting method employs dampers installed at the roots of solar panels to dissipate the dynamic energy. The key of translational root mounting method is that translational root mounting method modifies the fundamental mode shape of the solar panel, by releasing the translation freedoms at its root. The root of the solar panel then has translational freedom instead of rotational freedom. As a result of mode shape modification, the translational root mounting method enables the root dampers to have sufficient working stroke, however without obviously reducing the solar panel’s fundamental frequency. Finite element model of a satellite solar panel with the length of 7 [Formula: see text] is established. Applying the finite element model, the limitation of a conventional passive vibration control method based on rotational root mounting is illustrated. To verify and illustrate the principle of translational root mounting method, the free vibration of the 7 [Formula: see text]-length satellite solar panel controlled by translational root mounting method is analyzed by finite element method. Finite element analysis (FEA) results indicate that the effect of a conventional passive control method is not obvious unless dampers with quite large damping coefficients are employed. In contrast, applying dampers with much smaller damping coefficients, the effect of translational root mounting method is fantastic comparing with the conventional passive method. To optimize the translational root mounting method and theoretically compare it to the conventional passive vibration control method, the solar panel is simplified into a non-linear one-degree of freedom system, and the analytical solution of its low frequency vibration is derived. Applying the analytical solution, it is found that damping ratio of the whole solar panel system does not increase with the damper’s damping coefficient, instead there are optimum values of damping coefficient. Applying the translational root mounting method, for the discussed 7 [Formula: see text]-length satellite solar panel, the damping ratio of which can be elevated from 0.0027 to 0.326.

Coupled structural resonance of elastic panels for suppression of airfoil tonal noise

In this paper the aeroacoustic characteristics of coupled flow-induced vibration of elastic panels mounted on an airfoil is numerically studied to uncover its potential for suppression of airfoil tonal noise. The proposed approach utilizes the inter-dynamical structural coupling between two elastic panels which maintain a synchronized flow-induced vibration pattern to weaken the flow fluctuations responsible for tonal noise generation. In the study, a NACA0012 airfoil at a low Reynolds number of 5×104 and an angle of attack of 5° is taken as the basic structure on which various panel configurations are attempted. The results of preliminary analysis of aeroacoustic-structural interactions of various panel configurations, using a reduced-order modeling approach, reveal that an airfoil-panel configuration with two elastic panels separated by approximately one convective wavelength and mounted in a region exposed to high boundary layer flow instabilities yields optimal noise suppression. Comprehensive aerodynamic and acoustic analyzes of airfoil-panel configurations, using the results of high fidelity direct aeroacoustic simulation, reveal that an average and maximum noise suppression up to 7.6 dB and 7.9 dB respectively can be achieved with negligible sacrifice on overall airfoil aerodynamics when strongly coupled structural resonance between the panels prevails. The magnitude of noise suppression is higher than twice of that from the configuration mounted with a single panel. This fact firmly illustrates the synergy of coupled flow-induced structural resonance of the panels prevailing in noise suppression. Nonlinear fluid–structure interactions of coupled resonant panels in airfoil-panel configuration are characterized by extensive spectral analyzes in frequency and wavenumber domains as well as correlation analyzes. The panels exhibit highly synchronized dynamic behaviors and run into limit cycle oscillations. Their strongly coherent structural responses are proven able to provide a more effective suppression of the boundary layer instabilities to be scattered at airfoil trailing edge as noise. The upstream propagating component of the generated noise does not interfere the coupled structural resonance of the panels as revealed from their weak correlations. Key characteristics required for the design of strongly coupled structural resonant panels for effective absorption of flow fluctuation energy are discerned and discussed.

Сравнительный анализ определения частот собственных колебаний прямоугольных панелей с защемленно-свободными краями

An iterative method for assessing the frequency spectrum of free vibrations of rectangular panels with different support conditions in combination with the parameter enumeration method is proposed. Two hyperbolo-trigonometric series on two coordinates with indeterminate coefficients containing the desired frequency of free vibrations as a parameter are taken as a basis. The obtained natural frequencies and waveforms are compared with the results provided by other authors, and are presented very fully in tabular form, the accuracy of calculations and methods are analyzed.

Fluid–structural coupling of an impinging shock–turbulent boundary layer interaction at Mach 3 over a flexible panel

We present high-fidelity numerical simulations of the interaction of an oblique shock impinging on the turbulent boundary layer developed over a rectangular flexible panel, replicating wind tunnel experiments by Daub et al. (AIAA Journal, vol. 54, 2016, pp. 670–678). The incoming free-stream Mach and unit Reynolds numbers are $M_{\infty } = 3$ and $Re_{\infty }=49.4\times 10^6 {\rm m}^{-1}$ , respectively. The reference boundary layer thickness upstream of the interaction with the shock is $\delta _0 = 4$ mm. The oblique shock is generated with a rotating wedge initially parallel to the flow that increases the deflection angle up to $\theta _{{max}} = 17.5^{\circ }$ within approximately $15$ ms. A loosely coupled partitioned flow–structure interaction simulation methodology is used, combining a finite-volume flow solver of the compressible wall-modelled large-eddy simulation equations, an isoparametric finite-element solid mechanics solver and a spring-system-based mesh deformation solver. Simulations are conducted with rigid and flexible panels, and the results compared to elucidate the effects of panel flexibility on the interaction. Three-dimensional effects are evaluated by conducting simulations with both full ( $50 \delta _0$ ) and reduced ( $5\delta _0$ ) spanwise panel width, the latter enforcing spanwise periodicity. Panel flexibility is found to increase the separation bubble size and modify its spectral dynamics. Time- and spanwise-averaged streamwise profiles of the wall pressure exhibit a drop over the flexible panel prior to the interaction and a reduced peak pressure in comparison with the rigid case. Spectral analyses of wall pressure data indicate that the low-frequency motions have a similar spectral distribution for the rigid and flexible cases, but the flexible case shows a wider region dominated by low-frequency motions and traces of the panel vibration on the wall pressure signal. The sensitivity of the interaction to small variations in the wedge extent and incoming boundary layer thickness is evaluated. Predictions obtained from lower-fidelity modelling simplifications are also assessed.

Comparative Analysis of Surface Pressure Fluctuations of High-Speed Train Running in Open-Field and Tunnel Using LES and Wavenumber-Frequency Analysis

The interior noise of a high-speed train due to the external flow disturbance is more than ever a major problem for product developers to consider during a design state. Since the external surface pressure field induces wall panel vibration of a high-speed train, which in turn generates the interior sound, the first step for low interior noise design is to characterize the surface pressure fluctuations due to external disturbance. In this study, the external flow field of a high-speed train cruising at a speed of 300 km/h in open-field and tunnel are numerically investigated using high-resolution compressible LES (large eddy simulation) techniques, with a focus on characterizing fluctuating surface pressure field according to surrounding conditions of the cruising train, i.e., open-field and tunnel. First, compressible LES schemes with high-resolution grids were employed to accurately predict the exterior flow and acoustic fields around a high-speed train simultaneously. Then, the predicted fluctuating pressure field on the wall panel surface of a train was decomposed into incompressible and compressible ones using the wavenumber-frequency transform, given that the incompressible pressure wave induced by the turbulent eddies within the boundary layer is transported approximately at the mean flow and the compressible pressure wave propagated at the vector sum of the sound speed and the mean flow velocity. Lastly, the power levels due to each pressure field were computed and compared between open-field and tunnel. It was found that there is no significant difference in the power levels of incompressible surface pressure fluctuations between the two cases. However, the decomposed compressible one in the tunnel case is higher by about 2~10 dB than in the open-field case. This result reveals that the increased interior sound of the high-speed train running in a tunnel is due to the compressible surface pressure field.

각종 주름판 코어 샌드위치 패널의 강성 및 진동 해석

Corrugated core sandwich panels are relatively lightweight structure components compared to their large flexural rigidity, and are widely used in automotive, aerospace, ship, and plant industries. However, research on rigidity and vibration for these sandwich panels remains fairly poor. In this study, the optimal sandwich panel is determined by presenting the rigidities of corrugated core sandwich panels with sinusoidal, triangular, trapezoidal, and rectangular waves. Furthermore, by analyzing the vibration of the sandwich panels for arbitrary boundary conditions, a basic visual program for practical and efficient static and dynamic design data extraction of the sandwich panels is completed.

Parametric vibrations of piezoelectric viscoelastic cylindrical panels taking into account transverse shear deformations

The paper presents a numerical-analytical approach to solving problems of parametric vibrations of layered hinged piezoelectric viscoelastic cylindrical panels under electromechanical harmonic loading. The mathematical model is constructed using mechanical hypotheses about layer-by-layer approximation of shear deformations by quadratic functions on the thickness of panel, which are supplemented by adequate hypotheses on the distribution of electric field quantities when the components of the electric field strength vector and the normal component of the electric induction vector are different from zero. The dissipative properties of materials are taken into account on the basis of the theory of linear viscoelectric elasticity. To solve the problems, a technique based on the use of the variation principle and the representation of the required quantities in the form of decomposition into double trigonometric series has been developed. This makes it possible to reduce the considered problems to Mathieu-Hill-type equations taking into account energy dissipation, which are solved by the method of harmonic linearization, which allows to determine the boundaries of the regions of dynamic instability.

Panel flutter mechanism of rectangular solar sails based on traveling mode analysis

The solar radiation pressure acting on the sail surface provides a force, which depends on the deformation of the surface itself, and thus the coupling between the force and the deformation may lead to flutter. The panel flutter mechanism of two-dimensional solar sail subjected to solar radiation pressure is investigated in this study based on the traveling mode analysis. The partial differential equations governing the panel vibrations are truncated into a set of ordinary differential equations. Two types of flutter have been detected, namely, traditional coupled-mode flutter and novel coupled-direction flutter especially existing in two-dimensional cases. Varying mode shapes with solar radiation pressure and critical values have been studied by considering the eigenvalue problem. By studying the mode shapes in standing wave contour or traveling wave contour, the flutter phenomena have been described based on the mechanism of energy accumulation.

Improved High-order Analysis of Linear Vibrations of a Thick Sandwich Panel With an Electro-rheological Core by Using Exponential Shear Deformation Theory

In In this paper, the behavior of free vibrations of the thick sandwich panel with multi-layer face sheets and an electrorheological (ER) fluid core using Exponential Shear Deformation Theory were investigated. For the first time, Exponential shear deformation theory is used for the face sheets while the Displacement field based on the second Frostig's model is used for the core. The governing equations and the boundary conditions are derived by Hamilton’s principle. Closed form solution is achieved using the Navier method and solving the eigenvalues. Primary attention is focused on the effects of electric field magnitude, geometric aspect ratio,and ER core layer thickness on the dynamic characteristics of the sandwich plate. The rheological property of an ER material, such as viscosity, plasticity, and elasticity may be changed when applying an electric field. When an electric field is applied, the damping of the system is more effective. The effects of the natural frequencies and loss factors on the dynamic behaviorof the sandwich plate are studied.the natural frequency of the sandwich plate increases and the modal loss factor decreases. With increasing the thickness of the ER layer, the natural frequencies of the sandwich plate are decreased.

Semi-analytical solutions for buckling and free vibration of composite anisogrid lattice cylindrical panels

In this study, highly accurate approximate closed-form solution is presented for buckling and free vibration of clamped composite anisogrid lattice cylindrical panels. Using theory of orthotropic cylindrical shallow shells based on the continuous model of lattice structures, the system of governing partial differential equations (PDEs) of motion is derived. The resulted PDEs are converted to a couple of systems of ordinary differential equations (ODEs) by employing of the Extended Kantorovich Method (EKM). Semi-analytical solutions are presented for both buckling and free vibration of anisogrid lattice panels via iterative application of infinite power series solution for the sets of ODEs. Efficiency of the presented method in terms of accuracy, stability, fast convergence and low computational cost for prediction of the critical buckling loads and natural frequencies are examined. Accuracy of the predictions for various cases are studied by comparing with available numerical and analytical results. Moreover, it is shown that the method can be used to obtain accurate solutions for buckling and free vibration of composite lattice rectangular plates by assuming large values for the radius together with small values for the angle of the panel. This implies stability of the method for large or small values while providing accurate predictions.

Coarse mesh finite element model for cruise ship global and local vibration analysis

This paper presents a practical procedure for creating finite element (FE) model for vibration analysis of cruise ships. The most preferable FE modelling approaches are studied and discussed through case studies of common ship structures, which cover the range from low to high frequencies. The application of homogenized equivalent single layer (ESL) theory based equivalent element for stiffened panel is extended to local forced vibration analysis, where inertia induced interaction between plate and stiffener occurs. Modal method is used with an energy-based correction for accounting the plate-stiffener interaction into modal properties. Case study results reveal that mesh density of one 4-node element per web frame spacing is suitable for global FE-model when vibration analysis is limited to global hull girder modes. For such modes it is sufficient to only include the membrane stiffness of stiffened panels. For investigating the response at higher frequencies, bending properties of stiffened panel should be included and mesh density should be at least two elements per web frame spacing. Then forced vibration analysis can be performed with an excellent accuracy up to frequencies about one third of the local plate natural frequencies between the stiffeners. Beyond that, the influence of the local plate vibration becomes more significant in panel vibration, making the ESL-theory based element limited. With the applied correction method, the validity of the ESL-model can be extended to approximately two thirds of the local plate natural frequency.

Nonlinear vibration analysis of CFRP spherical shell panel under hygrothermal effects

Based on the nonlinear static stability analysis, this paper establishes the governing equations of the nonlinear dynamic stability of a spherical shell panel of carbon fiber-reinforced polymer (CFRP) under the hygrothermal effects; the Galerkin method is used to solve the governing equations. Then, for the free vibration of CFRP spherical shell panel, the analytical expression of the ratio of nonlinear vibration frequency to natural frequency is obtained by employing the multiscale method; for forced vibration, the analytical expression of the ratio of excitation frequency to natural frequency is obtained by considering the harmonic excitation load. Finally, the effects of geometric parameters, boundary conditions, loads, and the hygrothermal effects on the amplitude-frequency response curves of the CFRP spherical shell panel are discussed.

Error Sensing Strategy for Active Control of Low-Frequency Sound Absorption of Micro-Perforated Panel Absorber by Using a Point Force Controlled Thin Plate

This paper presents an analytical investigation on constructing an error sensing strategy of a new type of active MPPA. The proposed active MPPA is composed of MPP, air cavity, and point force-controlled backing panel, which can actively improve the low-frequency sound absorption of the MPPA. Constructing an appropriate error sensing strategy for obtaining an error signal that is highly correlated with the sound absorption coefficient of the active MPPA is a key problem encountered in practical implementation. The theoretical model of the active MPPA is firstly established using the modal analysis approach. Then, the active control performance and surface impedance characteristics in the controlled condition are analyzed in detail. Finally, the error sensing strategy of the active MPPA is constructed by measuring the surface average impedance ratio with an acoustic vector sensor (AVS). Simulation results show that, due to the antisymmetric property of the vibration of the backing panel on the resonant frequency, the surface impedance of the active MPPA after control also has symmetry or antisymmetry properties. Hence, the surface average impedance ratio of the active MPPA can be measured by using the limited number of acoustic vector sensors (sensing pressure and particle velocity). This variable is also highly correlated with the sound absorption coefficient of the active MPPA and thus can be used to construct the cost function (error signal). The active control result obtained by the proposed error sensing strategy is in good agreement with the theoretically optimal result, which validates the feasibility of this approach.

Buckling and free vibration of laser-welded web-core sandwich panels: Extreme sensitivity to variation of weld rotational stiffness

T-joints in laser-welded web-core sandwich panels connect face-plates with web-plates. Rotational stiffness of the T-joints affects transverse shear stiffness of the panels. In this paper we describe the effect of geometric and material parameters on the rotational stiffness of the T-joints, and show that laser weld thickness bears the highest influence. The analysis is performed using detailed FEM models of the joints that include laser welds. The effect is translated to critical buckling and first natural frequency of laser-welded web-core sandwich panels. Structural analyses are performed using equivalent single layer model with the first order shear deformation theory. The models used in this research are validated using experiments and numerical results from literature. The most sensitive and the least sensitive panels to variation of the rotational stiffness are outlined by means of global optimization. We describe them in terms of stiffness coefficients and design variables. The analysis reveals that insensitive panels have small height and small distance between web-plates, and as such have low structural performance for their area density. Panels with the best structural performance are generally quite sensitive to variation of the rotational stiffness, but the sensitivity can be even higher in other panels. It was found that rotational stiffness of T-joints is important in design and optimization of the panels, since the best performing panels of the same area density have different cross-sections for different rotational stiffness.

Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach

Geometrically nonlinear vibrations of FG-GPLRC cylindrical panels with cutout based on HSDT and mixed formulation: a novel variational approach

Studying nonlinear vibrations of composite conical panels with arbitrary-shaped cutout reinforced with graphene platelets based on higher-order shear deformation theory

In this article, the vibrational behavior of conical panels in the nonlinear regime made of functionally graded graphene platelet–reinforced composite having a hole with various shapes is investigated in the context of higher-order shear deformation theory. To achieve this aim, a numerical approach is used based on the variational differential quadrature and finite element methods. The geometrical nonlinearity is captured using the von Karman hypothesis. Also, the modified Halpin–Tsai model and rule of mixture are applied to calculate the material properties of graphene platelet–reinforced composite for various functionally graded distribution patterns of graphene platelets. The governing equations are derived by a variational approach and represented in matrix-vector form for the computational purposes. Moreover, attributable to using higher-order shear deformation theory, a mixed formulation approach is presented to consider the continuity of first-order derivatives on the common boundaries of elements. In the numerical results, the nonlinear free vibration behaviors of functionally graded graphene platelet–reinforced composite conical panels including square/circular/elliptical hole and with crack are studied. The effects of boundary conditions, graphene platelet reinforcement, and other important parameters on the vibrational response of panels are comprehensively analyzed.

Dynamic characteristics of LIWELL flip-flow screen panel and particle movement

Flip-flow screen is an effective solution for screening high-viscosity and fine-grained materials, because of the large vibration intensity of the screen panel. Therefore, investigating the dynamic characteristics of the screen panel is the key to improving the flip-flow screen. In this paper, a new dynamic model is proposed to do dynamic analysis of screen panel. The vibration of the screen panel is simplified into a string vibration model, and the energy equation is established. Then, the Hamilton principle and the Galerkin method are employed to transform the energy equations into ordinary differential equations, with the numerical solutions obtained using MATLAB. The vibration model is established by ABAQUS to obtain the displacement data of each point on the screen panel. To verify the correctness and accuracy of the theory, the simulation results are compared with the theoretical calculation results, and the dynamic characteristics of the vibration of the screen panel are analyzed. Besides, displacement and velocity equations of particle on the screen panel based on the screen panel vibration theory are proposed. A new FEM-DEM (Finite Element Method-Discrete Element Method) coupling simulation model is established in ABAQUS, which is used to investigate the trajectory of one particle and the effect of screen panel’s acceleration on particles’ movement and screening percentage.

A numerical study on the free vibrations of nanocomposite conical panels with variously shaped cutout

A numerical study on the free vibrations of nanocomposite conical panels with variously shaped cutout

Investigation of broadband sound absorption of smart micro-perforated panel (MPP) absorber

A smart micro-perforated panel (MPP) is investigated in order to enhance sound absorption performance of MPP absorbers, especially at low frequencies. The smart MPP consists of a conventional MPP and a surface-bonded piezoelectric ceramic (PZT) shunted with single- or multiple-resonance circuit. A three-dimensional (3D) finite element model is used to investigate the coupling effects between MPP and the shunted PZT. The numerical results demonstrate three energy-dissipation mechanisms: mechanical damping, electrical shunt damping, and Helmholtz resonance of the MPP. The effects of different multimode shunt design methods are explored so as to intensify the panel vibration and hence improve sound absorption. A low-frequency broadband sound absorber can then be constructed based on the strong coupling among the acoustical, electrical, and mechanical domains. Several absorption peaks induced by electromechanical coupling are found in the frequencies lower than the Helmholtz resonance frequency of MPP. The electrical and mechanical responses of the proposed absorber are investigated in detail. In the experiment, the transfer function of the shunt circuit of the proposed absorber is tested with a network analyser, and the sound absorption coefficients are measured in the impedance tube based on the two-microphone transfer function method. Fair agreement between experimental and numerical results is obtained.