Vibration Analysis Of Sandwich Beams Research Articles

Thermally induced vibration analysis of sandwich beam with metal foam core subjected to blast loading by a framework of two-unknown higher-order beam theory

Vibrational characteristics of a sandwich beam in thermal environments subjected to blast pressure are investigated in this paper. The sandwich beam is composed of two isotropic skins and an open-cell metal foam core with either uniform or symmetric distribution of internal pores. The pressure of blast loading is modelled by Friedlander’s equation. A two-unknown higher-order beam theory combined with Hamilton’s principle is used to establish the governing equations. Navier-type solution and Newmark-beta method are applied to deal with the governing equation and obtain the dynamic responses. The efficiency and accuracy of the present study are examined through numerical examples. Effects of temperature-dependent material properties, porosity coefficient, core-to-skin thickness ratio, length-to-height ratio, and structural damping on the natural frequencies and dynamic deflection of the sandwich beam are investigated in detail.

Large amplitude free vibration of sandwich beams with flexible core and FG Graphene Platelet Reinforced Composite (FG-GPLRC) face sheets based on extended higher-order sandwich panel theory

The present article deals with the nonlinear free vibration analysis of sandwich beams with flexible core integrated with face sheets which are reinforced with graphene platelets (GPLs). Each layer of the composite media may have a different amount of graphene platelets which leads to a functionally graded (FG) distribution. The elastic modulus of the reinforced composite (RC) is calculated via the Halpin–Tsai model. Following the extended higher order sandwich panel theory (EHSAPT) which captures the core thickness compressibility effect and the axial stress of the core, the complete set of governing equations is obtained using the Lagrangian formulation. To analyze the effect of the inclusion of nonlinear terms in the core, hitherto not reported in the literature, results are computed considering the von Kármán type of geometrical nonlinearity assumptions for the core and face sheets. With the aid of the Ritz-based method, Chebyshev functions are implemented as admissible functions of the displacement fields. Furthermore, the nonlinear governing equations are solved using a direct displacement control technique. As the EHSAPT can be applied with any combination of the core and face sheets and not only the soft cores that the other theories demand, the results for the sandwich beam with stiff core and consist of functionally graded carbon nanotube-reinforced composite face sheets provided for validation. Since this study is the first in the open literature to develop nonlinear vibration of the sandwich beam based on EHSAPT, Timoshenko beam theory (TBT) is also applied to investigate the problem and to extract nonlinear frequencies with various stiffness of the core, meanwhile, the results are compared with those obtained by the EHSAPT. Parametric studies are conducted in detail to examine the influences of weight fraction and distribution pattern of graphene platelets, core to face sheet thickness ratio, boundary conditions, length to thickness ratio, and amplitude of vibrations. It is found that by increasing the stiffness of the core, the inclusion of nonlinear effects in the core as well as the face sheet strain nonlinearity is more significant. Finally, the nonlinear vibration analysis of sandwich beams can change the variation trend of frequency predicted in the linear analysis, and the different trends are observed depending on the vibration amplitude.

Free vibration analysis of sandwich beam with porous FGM core in thermal environment using mesh-free approach

Free vibration analysis of sandwich beam with porous FGM core in thermal environment using mesh-free approach

Vibration analysis of sandwich beam with honeycomb core and piezoelectric facesheets affected by PD controller

Free vibration analysis of a sandwich beam with honeycomb core and piezoelectric face sheets, which is rested on the viscoelastic foundation is investigated. The thermal environment and the electric field are applied to this structure. Also, it is affected by the proportional-derivative (PD) controller. The amount of gain in this controller can affects the vibration frequency. The displacement components are expressed by improved high-order sandwich panel theory (IHSAPT) that considers continuity conditions for transverse shear stress at the interfaces and the zero transverse shear stresses conditions on the upper and lower surfaces of the beam and core flexibility. The motion equations are derived and solved by Hamilton's principle and Navier's method, respectively. This paper examines the effects of various parameters, such as the internal aspect ratio and the cell angle/thickness of the honeycomb core, temperature variations, viscoelastic environment, electric load, and control gain on its natural frequencies. The results show when the honeycomb core's to face sheet's thickness ratio increases, the beam dimensionless frequency increases, too. Also, by increasing the internal aspect ratio of honeycomb core, the frequency of sandwich beam decreases. The results of this study can be used to vibration control in aerospace engineering and constructions.

Free Vibration Analysis of Sandwich Beams with Functionally-Graded-Cores by Complementary Functions Method

A plane vibration study of a sandwich thermal protection system insulation panel with a functionally graded core is conducted. The panel is assumed to be under plane-stress conditions and subjected to simply supported boundary conditions. The two-dimensional elasticity formulations are used to derive the equations of motion for each layer. The effects of the in-plane normal stresses as well as the shear stress are taken into consideration for all layers. Material properties of layers may vary through the transverse coordinate resulting in a pair of second-order coupled variable- coefficient governing differential equations. The governing equations are reduced to an uncoupled fourth-order differential equation, which is solved by the complementary functions method (CFM). The novelty of the present study includes the vibration analysis of functionally graded core sandwich beam using plane elasticity and implementation of CFM as the solution procedure. The influences of face sheets and core materials and the grading model on the free vibration behavior are studied. The solutions are compared with results available in the literature and those obtained from finite element software (ANSYS) for a three-layered isotropic panel to display the accuracy and efficiency of the presented method. The mode shapes dominated by vertical and horizontal displacements are also depicted. The method that is applicable for both symmetric and unsymmetric beams is shown to be accurate and efficient in the analysis of sandwich panels with a core graded in the thickness direction.

Vibration analysis of sandwich beams with viscoelastic coating described by fractional constitutive equation

In this study, a dynamic model of a sandwich beam with viscoelastic coating based on a fractional constitutive equation was developed. The fractional model is a generalized model of sandwich beams and can be modified into integer models. The wave propagation method was extended for vibration analysis of fractional sandwich beams. Further, the influence of fractional order and size parameters on the dynamic characteristics of the sandwich beam was investigated, and the steady-state frequency response of the laminated beam was calculated. The results can provide a theoretical basis for the size design of laminated beams with damping requirements.

A Finite Element Model for the Vibration Analysis of Sandwich Beam with Frequency-Dependent Viscoelastic Material Core.

In this work, a finite element model was developed for vibration analysis of sandwich beam with a viscoelastic material core sandwiched between two elastic layers. The frequency-dependent viscoelastic dynamics of the sandwich beam were investigated by using finite element analysis and experimental validation. The stiffness and damping of the viscoelastic material core is frequency-dependent, which results in complex vibration modes of the sandwich beam system. A third order seven parameter Biot model was used to describe the frequency-dependent viscoelastic behavior, which was then incorporated with the finite elements of the sandwich beam. Considering the parameters identification, a strategy to determine the parameters of the Biot model has been outlined, and the curve fitting results closely follow the experiment. With identified model parameters, numerical simulations were carried out to predict the vibration and damping behavior in the first three vibration modes, and the results showed that the finite model presented here had good accuracy and efficiency in the specific frequency range of interest. The experimental testing on the viscoelastic sandwich beam validated the numerical predication. The experimental results also showed that the finite element modeling method of sandwich beams that was proposed was correct, simple and effective.

Free vibration analysis of sandwich beams with FG porous core and FGM faces resting on Winkler elastic foundation by various shear deformation theories

This paper studies the free vibration behavior of a sandwich beam resting on Winkler elastic foundation. The sandwich beam is composed of two FGM face layers and a functionally graded (FG) porous core. A common general form of different beam theories is proposed and the equations of motion are formulated using Hamilton's principle. The result of the general form is validated against those of a particular case and shows a good agreement. The effect of different parameters on the fundamental natural frequency of the sandwich beam is investigated.
 Article history: Received 02 March 2018, Revised 26 March 2018, Accepted 27 April 2018

Nonlinear damping and forced vibration behaviour of sandwich beams with transverse normal stress

This paper deals with the nonlinear forced vibration analysis of sandwich beam with viscoelastic core layer. In the analytical formulation, normal, transverse and shear deformations are considered in the core layer by mean of the refined higher-order zig-zag theory. The harmonic balance method for a doubly supported beam is adopted as a solution procedure. Thus, the obtained nonlinear frequency amplitude equation is governed by several complex parameters. These ones are arising for the geometrically non-linear coupling due to the viscoelastic layer core. The frequency response curves are presented and discussed by varying the material and geometric properties of the viscoelastic layer.

Free vibration analysis of sandwich beams with honeycomb-corrugation hybrid cores

The vibration performance of sandwich beams with honeycomb-corrugation hybrid cores was investigated in this paper. The method of homogenization was employed to obtain the equivalent macroscopic stiffness of honeycomb-corrugation hybrid cores. Finite element methods and modal analysis techniques have been used to predict their vibration characteristics (i.e. their natural frequencies and mode shapes). It is shown that in most cases the predictions by using the equivalent homogenization model (2D model) agree well with the experimental and three-dimensional finite element calculated results. For sandwich beams with corrugated cores, the filling honeycomb not only enhances their flexural rigidity and increases their natural frequency of higher orders, but also more or less eliminates the anisotropy of the structural stiffness and suppresses the local modes of vibration. In addition, considering mass efficiency, a dimensionless frequency parameter was proposed. It was found that the frequency parameter has different sensitivity to the geometry parameters, i.e. the slenderness ratio of corrugated member, the face sheet thickness ratio and the relative density of filling honeycomb.

Thermo-mechanical vibration analysis of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets based on a higher-order shear deformation beam theory

ABSTRACTThis article proposes a higher-order shear deformation beam theory for free vibration analysis of functionally graded carbon nanotube-reinforced composite sandwich beams in a thermal environment. The temperature-dependent material properties of functionally graded carbon nanotube-reinforced composite beams are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. The governing equations and boundary conditions are derived by using Hamilton's principle, and the Navier solution procedure is used to achieve the natural frequencies of the sandwich beam in a thermal environment. A parametric study is led to carry out the effects of carbon nanotube volume fractions, slenderness ratio, and core-to-face sheet thickness ratio on free vibration behavior of sandwich beams with functionally graded carbon nanotube-reinforced composite face sheets. Numerical results are also presented in order to compare the behavior of sandwich beams including uniformly distributed carbon nanotube-reinforced composite face sheets to those including functionally graded carbon nanotube-reinforced composite face sheets.

Free vibration analysis of sandwich beams with carbon nanotube reinforced face sheets based on extended high-order sandwich panel theory

Free vibration analysis of a sandwich beam with soft core and carbon nanotube reinforced composite face sheets, hitherto not reported in the literature, based on extended high-order sandwich panel theory is presented. Distribution of fibers through the thickness of the face sheets could be uniform or functionally graded. In this theory, the face sheets follow the first-order shear deformation theory. Besides, the two-dimensional elasticity is used for the core. The field equations are derived via the Ritz-based solution which is suitable for any essential boundary conditions. Chebyshev polynomials multiplying boundary R-functions are used as admissible functions and evidence of their good performance is given. A detailed parametric study is conducted to study the effects of nanotube volume fraction and their distribution pattern, core-to-face sheet thickness ratio, and boundary conditions on the natural frequencies and mode shapes of sandwich beams with functionally graded carbon nanotube reinforced composite face sheets and soft cores. Since the extended high-order sandwich panel theory can be used with any combinations of core and face sheets and not only the soft cores that the other theories demand, the results for the same beam with functionally graded carbon nanotube reinforced composite face sheets and stiff core are also provided for comparison. It is concluded that the sandwich beam with X and V distribution figures of face sheets, no matter what the boundary conditions, has higher vibration performance than the beam with UD-CNTRC face sheets.

Effects of Material and Geometrical Parameters on the Free Vibration of Sandwich Beams

The aim of present study is to investigate the effect of various parameters such as length, thickness, density, shear modulus of the core and Young modulus of skins for various boundary conditions: clamped-free and simply supported. By applying the model of Khalili et al for frees vibration analysis of sandwich beams by using finite element methods. Where, the core density is taken on consideration. The flexural vibrations of beams are analyzed by the finite element method, using the stiffness and mass matrix of beam element with three degrees of freedom per node. The three first natural frequencies are calculated by using Matlab commercial software. A comparison is established between three different lengths for each configuration. There is a good agreement between the results obtained by the present study with the results obtained by Khalili et al.

Free vibration analysis of sandwich beams using the Refined Zigzag Theory: an experimental assessment

The paper is devoted to the experimental assessment of the Refined Zigzag Theory (RZT) for the free-vibration analysis of sandwich beams. To investigate the model performance, the effect of the face-to-core stiffness and thickness ratios as well as beam slenderness are taken into consideration. For comparison purposes, the results obtained by using the Timoshenko’s beam model, adopting an adequate shear correction factor, are given. The RZT demonstrates its remarkable accuracy with respect to the Timoshenko’s beam theory even when the latter is used with the ad-hoc calculated shear correction factor.

Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation

Abstract In this study, free vibration behavior of a multilayered symmetric sandwich beam made of functionally graded materials (FGMs) with variable cross section resting on variable Winkler elastic foundation are investigated. The elasticity and density of the functionally graded (FG) sandwich beam vary through the thickness according to the power law. This law is related to mixture rules and laminate theory. In order to provide this, a 50-layered beam is considered. Each layer is isotropic and homogeneous, although the volume fractions of the constituents of each layer are different. Furthermore, the width of the beam varies exponentially along the length of the beam, and also the beam is resting on an elastic foundation whose coefficient is variable along the length of the beam. The natural frequencies are computed for conventional boundary conditions of the FG sandwich beam using a theoretical procedure. The effects of material, geometric, elastic foundation indexes and slenderness ratio on natural frequencies and mode shapes of the beam are also computed and discussed. Finally, the results obtained are compared with a finite-element-based commercial program, ANSYS®, and found to be consistent with each other.

Free Vibration Analysis of FGM Sandwich Beams Containing Edge Cracks

This paper presents a vibration analysis of sandwich beams with functionally-graded skins containing edge cracks. Finite Element models of FGM sandwich beams are created with different depths and locations of the edge-cracks, and the first four natural frequencies of the beam are obtained for each crack configuration. The integrity of the data is validated for the FGM skins in comparison to a previously published reference. Finally, an inspection is conducted on the data to show the influences of the location and depth of cracks and material properties on the flexural vibration characteristics of cracked FGM sandwich beams.

Free vibration analysis of simply supported sandwich beams with lattice truss core

Abstract Free vibration of AISI 304 stainless steel sandwich beams with pyramidal truss core is investigated in the present paper. The lattice truss core is transformed to a continuous homogeneous material. Considering the deformation characteristics of the sandwich beam, the following assumptions are made: (1) the thickness of the sandwich beam remains constant during deformation; (2) for the thin face sheets, only bending deformation is considered, neglecting the effect of transverse shear deformation; (3) for the core, only shear deformation is considered as the core is too weak to provide a significant contribution to the bending stiffness of the sandwich beam. The shear stress is assumed to be constant along the thickness of the core. The governing equation of free vibration is derived from Hamilton's principle, and the natural frequencies are calculated under simply supported boundary conditions. Finally, numerical simulation is carried out to get the mode shapes and natural frequencies. Our results show that the theoretical solutions agree well with the numerical results. It indicates the present method would be useful for free vibration analysis of sandwich beams with lattice truss core.

High-order free vibration analysis of sandwich beams with a flexible core using dynamic stiffness method

In this paper, high-order free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness method. The governing partial differential equations of motion for one element are derived using Hamilton’s principle. This formulation leads to seven partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are divided into two ordinary differential equations by considering the symmetrical sandwich beam. Closed form analytical solutions of these equations are determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. The element dynamic stiffness matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by use of numerical techniques and the known Wittrick–Williams algorithm. Finally, some numerical examples are discussed using dynamic stiffness method.

Free vibration analysis of sandwich beam carrying sprung masses

In this paper, free vibration of three-layered symmetric sandwich beam carrying sprung masses is investigated using the dynamic stiffness method and the finite element formulation. First the governing partial differential equations of motion for one element are derived using Hamilton’s principle. Closed form analytical solution of these equations is determined. Applying the effect of sprung masses by replacing each sprung mass with an effective spring on the boundary condition of the element, the element dynamic stiffness matrix is developed. These matrices are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the well known Wittrick–Williams algorithm. Free vibration analysis using the finite element method is carried out by increasing one degree of freedom for each sprung mass. Finally, some numerical examples are discussed using the dynamic stiffness method and the finite element formulation. After verification of the present model, the effect of various parameters such as mass and stiffness of the sprung mass is studied on the natural frequencies.

Free vibration analysis of sandwich beams using improved dynamic stiffness method

Abstract In this paper, free vibration of three-layered symmetric sandwich beam is investigated using dynamic stiffness and finite element methods. To determine the governing equations of motion by the present theory, the core density has been taken into consideration. The governing partial differential equations of motion for one element contained three layers are derived using Hamilton’s principle. This formulation leads to two partial differential equations which are coupled in axial and bending deformations. For the harmonic motion, these equations are combined to form one ordinary differential equation. Closed form analytical solution for this equation is determined. By applying the boundary conditions, the element dynamic stiffness matrix is developed. They are assembled and the boundary conditions of the beam are applied, so that the dynamic stiffness matrix of the beam is derived. Natural frequencies and mode shapes are computed by the use of numerical techniques and the known Wittrick–Williams algorithm. After validation of the present model, the effect of various parameters such as density, thickness and shear modulus of the core for various boundary conditions on the first natural frequency is studied.