Vibration Of Sandwich Plates Research Articles

Influence of Transverse Normal Strain on Buckling and Vibration of Sandwich Plates

This study presents the buckling and free vibration behavior of simply supported square and rectangular sandwich plates. A third-order shear deformation theory considering both the transverse shear and normal deformations is used. The condition of zero transverse shear stresses on the top and bottom surfaces of the plate is satisfied. Hence, the present theory does not require the shear correction factor generally associated with the first-order shear deformation theory. Governing equations and boundary conditions are obtained using the principle of minimum potential energy. The closed-form solutions of simply supported sandwich plates are obtained. The effect of the side-to-thickness ratio and plate aspect ratio on buckling and free vibration responses of simply supported square and rectangular sandwich plates is examined. Parametric effects of face sheet thickness ratios and load factor upon the critical buckling load for uniaxial and biaxial buckling analysis of square and rectangular sandwich plates for different staking sequences are studied. All numerical solutions are obtained using MATLAB® programs. The results obtained from the present theory are compared with those from classical plate theory, first-order shear deformation theory, higher-order shear deformation theories, and the exact three-dimensional elasticity solutions as applicable.

Nonlinear forced vibration of sandwich plate with considering FG core and CNTs reinforced nano-composite face sheets

Nonlinear vibration of sandwich plate with functionally graded material (FGM) core and carbon nano tubes reinforced (CNTs) nano-composite layers by considering temperature-dependent material properties are studied in this paper. Base on Classical plate theory (CPT), the governing partial differential equations of motion for sandwich plate are derived using Hamilton principle. The Galerkin procedure and multiple scales perturbation method are used to find relation between nonlinear frequency and amplitude of vibration response. The dynamic responses of the sandwich plate are also investigated in both time and frequency domains. Then, the effects of nonlinearity, excitation, power law index of FG core, volume fraction of carbon nanotube, the function of material variations of FG core, temperature changes, scale transformation parameter and damping factor on the frequency responses are investigated.

Free and forced vibration of sandwich plates with electrorheological core and functionally graded face layers

The free and forced vibration of a sandwich plate with functionally graded face layers and electrorheological fluid core is presented in this article. Assuming classical thin plate theory for face sheets and first order shear theory for the core layer, the equations of motions are derived using Hamilton’s principle. The simply-supported boundary condition is considered for all edges and the generalized Fourier series are employed to represent the displacements of the sandwich plate. The natural frequencies and loss factors are obtained by solving the complex eigenvalue problem. The results of free and forced responses are compared and validated with the previous articles and effects of electric field, geometric aspect ratio, functionally graded component ratios and core layer thickness on the dynamic behavior of the sandwich plate are studied.

Vibration of sandwich plates considering elastic foundation,temperature change and FGM faces

This study presents a comprehensive nonlinear dynamic approach to investigate the linear and nonlinear vibration of sandwich plates fabricated from functionally graded materials (FGMs) resting on an elastic foundation. Higher-order shear deformation theory and Hamilton's principle are employed to obtain governing equations. The Runge–Kutta method is employed together with the commercially available mathematical software MAPLE 14 to solve the set of nonlinear dynamic governing equations. Method validity is evaluated by comparing the results of this study and those of previous research. Good agreement is achieved. The effects of temperature change on frequencies are investigated considering various temperatures and various volume fraction index values, N. As the temperature increased, the plate frequency decreased, whereas with increasing N, the plate frequency increased. The effects of the side-to-thickness ratio, c/h, on natural frequencies were investigated. With increasing c/h, the frequencies increased nonlinearly. The effects of foundation stiffness on nonlinear vibration of the sandwich plate were also studied. Backbone curves presenting the variation of maximum displacement with respect to plate frequency are presented to provide insight into the nonlinear vibration and dynamic behavior of FGM sandwich plates.

Experimental and Numerical Investigation on Vibration of Sandwich Plates with Honeycomb Cores Based on Radial Basis Function

The vibration characteristic of the sandwich plate with a honeycomb core was investigated by experimental measurements and numerical calculation based on radial basis function (RBF). RBF method was used not only in the meshless approach but also in the post-processing of the experimental data. During the experiment, amplitude-fluctuation electronic speckle pattern interferometry was applied to access the resonant frequencies and the corresponding vibration mode shapes simultaneously. Then RBF method was used to improve the quality of patterns and reconstruct the out-of-plane vibration amplitude after fringe analysis. As for numerical calculation, the modal parameters were numerically predicted using the first-order shear deformation theory. The computation approach was based on collocation with multi-quadric radial basis function. To understand the influence of the thickness of face sheet on dynamic behaviors, three types of specimens with different thickness were tested and analyzed. Of particular interest was that the vibration modes show veering due to the thickness increment. Furthermore, the numerical predicted results were compared with the experimental measurements for the first five modes. They are in good agreement with each other for resonant frequencies, mode shapes and relative out-of-plane amplitudes.

Nonlinear dynamic response and vibration of sandwich composite plates with negative Poisson’s ratio in auxetic honeycombs

Auxetic cellular solids in the forms of honeycombs under blast load have great potential in a diverse range of applications, including core material in sandwich plates composite components. Based on Reddy’s first-order shear deformation plate theory, this paper presents an analysis of the nonlinear dynamic response and vibration of sandwich plates with negative Poisson’s ratio in auxetic honeycombes on elastic foundations subjected to blast and mechanical loads. A three-layer sandwich plate is considered discretized in the thickness direction by using analytical methods (stress function method, approximate solution), Galerkin method, and fourth-order Runge-Kutta method. The results show the effects of geometrical parameters, material properties, mechanical and elastic foundations on the nonlinear dynamic response, and vibration of sandwich plates.

Refined zigzag theory for vibration analysis of viscoelastic functionally graded carbon nanotube reinforced composite microplates integrated with piezoelectric layers

Damped free vibration of carbon nanotube reinforced composite microplate bounded with piezoelectric sensor and actuator layers are investigated in this study. For the mathematical modeling of sandwich structure, the refined zigzag theory is applied. In addition, to present a realistic model, the material properties of system are supposed as viscoelastic based on Kelvin–Voigt model. Distributions of single-walled carbon nanotubes along the thickness direction of the viscoelastic carbon nanotube reinforced composite microplate are considered as four types of functionally graded distribution patterns. The viscoelastic functionally graded carbon nanotube reinforced composite microplate subjected to electromagnetic field is embedded in an orthotropic visco-Pasternak foundation. Hamilton’s principle is employed to establish the equations of motion. In order to calculate the frequency and damping ratio of sandwich plate, boundary condition of plate is assumed as simply-supported and an exact solution is used. The effects of some significant parameters such as damping coefficient of viscoelastic plates, volume fraction of carbon nanotubes, different types of functionally graded distributions of carbon nanotubes, magnetic field, and external voltage on the damped free vibration of system are investigated. Results clarify that considering viscoelastic property for system to achieve accurate results is essential. Furthermore, the effects of volume fraction and distribution type of carbon nanotubes are remarkable on the vibration of sandwich plate. In addition, electric and magnetic fields are considerable parameters to control the behavior of viscoelastic carbon nanotube reinforced composite microplate. It is hoped that the results of this study could be applied in design of nano/micromechanical sensor and actuator systems.

Vibration Control of Sandwich Plates

This paper presents the active control of vibrations of sandwich plates using piezoelectric composites (PZC). The top surface of the plate is integrated with the patches of active constrained layer damping treatment. Active fiber composite, one of the commercially available PZCs, is used as the material of the constraining layer of the patches and the constrained layer of the patch is composed of a viscoelastic material. Considering the first order shear deformation theory individually for each layer of the sandwich plate, a three-dimensional finite element model has been developed. The performance of active fiber composite for the smart vibration control of the sandwich plates has been studied and numerical results are presented. Emphasis has also been placed on investigating the effect of variation of piezoelectric fiber orientation angle in the constraining layer on the control authority of the patches.

Elastic Vibrations of Sandwich Plates with Diaphragms at the Edges

The three-dimensional problem of the steady-state vibrations of isotropic sandwich plates with flat edges covered by diaphragms is solved. The layers are assumed perfectly bonded. Homogeneous solutions of the system of equations of motion for displacements are obtained. Asymptotic and numerical analyses of the dispersion equations are carried out. Spectral curves and curves of phase and group velocities are presented.

Vibration of Sandwich Plates with Random Material Properties using Improved Higher-Order Zig-Zag Theory

An improved higher-order zig-zag theory for vibration of soft core sandwich plates in random environment is proposed. It exploits all the merits of layer-wise theory, includes the effect of core transverse normal strain and simultaneously enjoys the benefits of single layer theory in terms of computational efficiency. The core is modeled as a 3-D elastic continuum. An efficient C 0 finite element is developed for the implementation of the proposed theory. A first order perturbation approach is employed to handle the randomness in the lamina material properties. Second order statistics of natural frequencies are computed and validated with independent Monte Carlo simulation.

FORCED AND FREE VIBRATIONS OF RECTANGULAR SANDWICH PLATES WITH PARAMETRIC STIFFNESS MODULATION

An active control of the resonant vibrations of a rectangular sandwich plate performed by the parametric stiffness modulation is analyzed. The controlled vibrations are those of the dominantly flexural type excited by the transverse force acting at the first resonant frequency of dominantly flexural vibrations. The stiffness modulation is performed at a comparatively high frequency identified by the resonance of a mode of the dominantly shear type. The method of direct partition of motions is used that predicts an existence of the modal interaction between these two modes of vibrations due to the parametric stiffness modulation. It is shown that such a parametric control can provide a significant shift of the first eigenfrequency of a controlled plate (the one subjected to the stiffness modulation) from its nominal value for an uncontrolled plate. Heavy fluid loading conditions are accounted for as well as the energy dissipation in the material of a plate. It is demonstrated that although heavy fluid loading reduces resonant frequencies of forced vibrations, the suggested mechanism of control remains valid in these cases. Dynamics of an elementary two-degree-of-freedom model mechanical system is considered to illustrate the mechanism of modal interaction, which is involved in the suggested way of an active control of vibrations of sandwich plates.

Wave Propagation in Sandwich Plates with Periodic Auxetic Core

The wave propagation in and the vibration of sandwich plates with cellular core are analyzed and controlled. Negative Poisson’s ratio (auxetic) core materials of different geometry placed periodically in the plate introduce the proper impedance mismatch necessary to obstruct the propagation of waves over specified frequency bands (stop bands) and in particular directions. The location and the extension of the stop bands and the directions of wave propagation can be modified by proper selection of the periodicity and of the geometrical and physical properties of the core. A finite element model is developed to predict the dynamic response of three-layered sandwich panels with honeycomb core. The finite element model along with the theory of periodic structures evaluates the influence of core materials of different geometry placed periodically along the two dimensions of the structure. This combined analysis yields the phase constant surfaces for the considered sandwich plates, which define location and extension of the stop bands, as well as the directions of wave propagation at assigned frequency values. The analysis of the phase constant surfaces and the evaluation of the harmonic response at specified frequencies demonstrate the plates’ directional properties, whose spatial patterns strongly depend on the configuration of the periodic core and on the excitation frequency. Auxetic honeycombs are here considered as core materials in order to obtain maximum design flexibility. Their elastic and inertial characteristics in fact vary substantially with their internal geometry. For given configurations they outcast up to five times the corresponding properties of traditional hexagonal honeycombs. The presented numerical results demonstrate the unique characteristics of this class of two-dimensional periodic structures, which behave as directional mechanical filters. The findings of the study suggest that optimal configurations for the periodic cellular core may be identified in order to design passive composite panels, which are stable and quiet over desired frequency bands and which fit desired transmissibility levels in particular directions. Such unique filtering capabilities are achieved without requiring additional passive or active control devices and therefore without compromising the size and the weight of the layered structure.

Membrane Analogy of Buckling and Vibration of Inhomogeneous Plates

Exact explicit eigenvalues are found for compression buckling, hygrothermal buckling, and vibration of sandwich plates with dissimilar facings and functionally graded plates via analogy with membrane vibration. These results apply to simply supported polygonal plates using the first-order shear deformation theory and the classical theory. A Winkler-Pasternak elastic foundation, a hydrostatic inplane force, hygrothermal effects, and rotary inertias are incorporated. Bridged by the vibrating membrane, exact correspondence is readily established between any pairs of eigenvalues associated with buckling and vibration of sandwich plates, functionally graded plates, and homogeneous plates. Positive definiteness is proved for the critical buckling hydrostatic pressure and, in the range of either tension loading or compression loading prior to occurrence of buckling, for the natural vibration frequency.

Non-linear vibrations of sandwich plates

A quadratic rectangular finite element having five degrees of freedom at each node is used in carrying out the non-linear free vibration analysis of a sandwich plate. The formulation includes the effects of large deformations and rotations as well as stretching, bending and transverse shear. A number of geometric and material parameters for a three-layered sandwich configuration under different boundary conditions are considered for a detailed study.

Vibrations of Sandwich Plates under Uniaxial Compression

Vibrations of Sandwich Plates under Uniaxial Compression

Symmetric vibrations of sandwich plates

Symmetric vibrations of sandwich plates

Longitudinal Wave Propagations and Vibrations of Sandwich Plates

In this paper a solution is given two-dimensionally for the problem of extensional stress wave propagations and vibrations of sandwich plates. Both the sandwich core and the facings are assumed elastic and homogeneous, and the facings are identical with each other. The solution satisfies exactly the elasticity equations and the boundary conditions. Wave velocity-wavelength curves are then obtained from frequency equations for an infinite plate in plane strain. Using these results the vibrations of finite sandwich plates are also discussed. Numerical examples are given for the plates composed of aluminum and plastics.