• Advances in aircraft and spacecraft science
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• v.4 no.4
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• pp.353-369
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• 2017

Flutter is a dangerous phenomenon encountered in flexible structures subjected to aerodynamic forces. This includes aircraft, buildings and bridges. Flutter occurs as a result of interactions between aerodynamic, stiffness, and inertia forces on a structure. In an aircraft, as the speed of the flow increases, there may be a point at which the structural damping is insufficient to damp out the motion which is increasing due to aerodynamic energy being added to the structure. This vibration can cause structural failure, and therefore considering flutter characteristics is an essential part of designing an aircraft. Scientists and engineers studied flutter and developed theories and mathematical tools to analyze the phenomenon. Strip theory aerodynamics, beam structural models, unsteady lifting surface methods (e.g., Doublet-Lattice) and finite element models expanded analysis capabilities. Periodic Structures have been in the focus of research for their useful characteristics and ability to attenuate vibration in frequency bands called "stop-bands". A periodic structure consists of cells which differ in material or geometry. As vibration waves travel along the structure and face the cell boundaries, some waves pass and some are reflected back, which may cause destructive interference with the succeeding waves. This may reduce the vibration level of the structure, and hence improve its dynamic performance. In this paper, for the first time, we analyze the flutter characteristics of a wing with a periodic change in its sandwich construction. The new technique preserves the external geometry of the wing structure and depends on changing the material of the sandwich core. The periodic analysis and the vibration response characteristics of the model are investigated using a finite element model for the wing. Previous studies investigating the dynamic bending response of a periodic sandwich beam in the absence of flow have shown promising results.

• Geomechanics and Engineering
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• v.36 no.4
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• pp.407-416
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• 2024

Dynamic response of a rock tunnels by laminated porous concrete beam reinforced by nanoparticles subjected to harmonic transverse dynamic load is investigated considering structural damping. The effective nanocomposite properties are evaluated on the basis of Mori-Tanaka model. The concrete beam is modeled by the exponential shear deformation theory (ESDT). Utilizing nonlinear strains-deflection, energy relations and Hamilton's principal, the governing final equations of the concrete laminated beam are calculated. Utilizing differential quadrature method (DQM) as well as Newmark method, the dynamic displacement of the concrete laminated beam is discussed. The influences of porosity parameter, nanoparticles volume percent, agglomeration of nanoparticles, boundary condition, geometrical parameters of the concrete beam and harmonic transverse dynamic load are studied on the dynamic displacement of the laminated structure. Results indicated that enhancing the nanoparticles volume percent leads to decrease in the dynamic displacement about 63%. In addition, with considering porosity of the concrete, the dynamic displacement enhances about 2.8 time.

• Steel and Composite Structures
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• v.44 no.4
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• pp.503-517
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• 2022

This paper presents the mechanical buckling of bi-directional functionally graded sandwich beams (BFGSW) with various boundary conditions employing a quasi-3D beam theory, including an integral term in the displacement field, which reduces the number of unknowns and governing equations. The beams are composed of three layers. The core is made from two constituents and varies across the thickness; however, the covering layers of the beams are made of bidirectional functionally graded material (BFGSW) and vary smoothly along the beam length and thickness directions. The power gradation model is considered to estimate the variation of material properties. The used formulation reflects the transverse shear effect and uses only three variables without including the correction factor used in the first shear deformation theory (FSDT) proposed by Timoshenko. The principle of virtual forces is used to obtain stability equations. Moreover, the impacts of the control of the power-law index, layer thickness ratio, length-to-depth ratio, and boundary conditions on buckling response are demonstrated. Our contribution in the present work is applying an analytical solution to investigate the stability behavior of bidirectional FG sandwich beams under various boundary conditions.

• Advances in nano research
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• v.10 no.2
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• pp.115-128
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• 2021

In this article, free vibration behavior of electro-magneto-thermo sandwich Timoshenko beam made of porous core and Graphene Platelet Reinforced Composite (GPLRC) in a thermal environment is investigated. The governing equations of motion are derived by using the modified strain gradient theory for micro structures and Hamilton's principle. The magneto electro are under linear function along the thickness that contains magnetic and electric constant potentials and a cosine function. The effects of material length scale parameters, temperature change, various distributions of porous, different distributions of graphene platelets and thickness ratio on the natural frequency of Timoshenko beam are analyzed. The results show that an increase in aspect ratio, the temperature change, and the thickness of GPL leads to reduce the natural frequency; while vice versa for porous coefficient, volume fractions and length of GPL. Moreover, the effect of different size-dependent theories such as CT, MCST and MSGT on the natural frequency is investigated. It reveals that MSGT and CT have most and lowest values of natural frequency, respectively, because MSGT leads to increase the stiffness of micro Timoshenko sandwich beam by considering three material length scale parameters. It is seen that by increasing porosity coefficient, the natural frequency increases because both stiffness and mass matrices decreases, but the effect of reduction of mass matrix is more than stiffness matrix. Considering the piezo magneto-electric layers lead to enhance the stiffness of a micro beam, thus the natural frequency increases. It can be seen that with increasing of the value of WGPL, the stiffness of microbeam increases. As a result, the value of natural frequency enhances. It is shown that in hc/h = 0.7, the natural frequency for WGPL = 0.05 is 8% and 14% less than its for WGPL = 0.06 and WGPL = 0.07, respectively. The results show that with an increment in the length and width of GPLs, the natural frequency increases because the stiffness of micro structures enhances and vice versa for thickness of GPLs. It can be seen that the natural frequency for aGPL = 25 ㎛ and hc/h = 0.6 is 0.3% and 1% more than the one for aGPL = 5 ㎛ and aGPL = 1 ㎛, respectively.

• Journal of the Korean Society for Precision Engineering
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• v.23 no.8 s.185
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• pp.127-136
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• 2006

Metallic sandwich plates with inner dimpled shell subject to 3-point bending have been analyzed and then optimized for minimum weight. Inner dimpled shells can be easily fabricated by press or roll with high precision and bonded with same material skin sheets by resistance welding or adhesive bonding. Metallic sandwich plates with inner dimpled shell structure can be optimally designed for minimum weight subject to prescribed combination of bending and transverse shear loads. Fundamental findings for lightweight design are presented through constrained optimization. Failure responses of sandwich plates are predicted and formulated with an assumption of narrow sandwich beam theory. Failure is attributed to four kinds of mechanisms: face yielding, face buckling, dimple buckling and dimple collapse. Optimized shape of inner dimpled shell structure is a hemispherical shell to minimize weight without failure. It is demonstrated that bending stiffness of sandwich plate is 2 or 3 times larger than solid plates with the same strength. Failure mode boundaries and iso-strength lines dependent upon the geometry and yield strain of the material are plotted with respect to geometric parameters on the failure map. Because optimal parameters of maximum strength for given material weight can be selected from the map, analytic solutions for maximum strength are expressed as a function of only material property and proposed strength. These optimal parameters match well with numerical optimal parameters.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2005.11b
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• pp.110-113
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• 2005

Theoretical models to study the vibro-acoustic performance of a sandwich panel are proposed. The wave propagation characteristics are analyzed, and dispersion relation is derived. The vibration Is analyzed using the Mindlin plate theory. The vibration of the compliantly supported Mindlin plate is investigated using the Rayleigh-Ritz method. The Timoshenko beam functions are used as trial functions. The model is applied to numerically investigate the influence of the plate mechanical properties. The vibro-acoustic properties are mostly determined by bending deformation at low frequencies. At higher frequencies, the shear deformation has a strong influence. The proposed numerical model is used to estimate the optimal panel properties that result in minimum sound radiation. With increasing dynamic stiffnesses the vibration response decreases but the radiating wavenumber components increase.

• Advances in nano research
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• v.10 no.3
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• pp.235-251
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• 2021

In the current study, the free vibrational behavior of a Porous Micro (PM) beam which is integrated with Functionally Graded Piezoelectric (FGP) layers with initial curvature is considered based on the two trigonometric shear deformation theories namely SSDBT and Tan-SDBT. The structure's mechanical properties are varied through its thicknesses following the given functions. The curved microbeam is exposed to electro-mechanical preload and also is rested on a Pasternak type of elastic foundation. Hamilton's principle is used to extract the motion equations and the MCST is used to capture the size effect. Navier's solution method is selected as an analytical method to solve the motion equations for a simply supported ends case and by validating the results for a simpler state with previously published works, effects of different important parameters on the behavior of the structure are considered. It is found that although increasing the porosity reduces the natural frequency, but enhancing the volume fraction of CNTs increasing it. Also, by increasing the central angle of the curved beam the vibrations of the structure increases. Designing and manufacturing more efficient smart structures such as sensors and actuators are of the aims of this study.

• Advances in aircraft and spacecraft science
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• v.9 no.5
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• pp.377-400
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• 2022

The aim of this work is a numerical comparison (FEM) between lattice pyramidal-core panel and honeycomb core panel for different core thicknesses. By evaluating the mid-span deflection, the shear rigidity and the shear modulus for both core types and different core thicknesses, it is possible to define which core type has got the best mechanical behaviour for each thickness and the evolution of that behaviour as far as the thickness increases. Since a specific base geometry has been used for the lattice pyramidal core, the comparison gives us the opportunity to investigate the unit cell strut angle giving the higher mechanical properties. The presented work considers a detailed FEM modelling of a standard 3-point bending test (ASTM C393/C393M Standard Practice). Detailed FEM modelling addresses to detailed discretization of cores by means of beam elements for lattice core and shell elements for honeycomb core. Facings, instead, have been modelled by using shell elements for both sandwich panels. On lattice core structure, elements of core and facings are directly connected, to better simulate the additive manufacturing process. Otherwise, an MPC-based constraint between facings and core has been used for honeycomb core structure. Both sandwich panels are entirely built of Aluminium alloy. Prior to compare the two models, the FEM sandwich panel model with lattice pyramidal core needs to be validated with 3-point bending test experimental results, in order to ensure a good reliability of the FEM approach and of the comparison. Furthermore, the analytical validation has been performed according to Allen's theory. The FEM analysis is linear static with an increasing midspan load ranging from 50N up to 500N.

• Computers and Concrete
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• v.26 no.1
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• pp.75-94
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• 2020

The aim of this research is to investigate free vibration of a novel five layer Timoshenko microbeam which consists of a transversely flexible porous core made of Al-foam, two graphen platelets (GPL) nanocomposite reinforced layers to enhance the mechanical behavior of the structure as well as two piezo-magneto-electric face sheets layers. This microbeam is subjected to a thermal load and resting on Pasternak's foundation. To accomplish the analysis, constitutive equations of each layer are derived by means of nonlocal strain gradient theory (NSGT) to capture size dependent effects. Then, the Hamilton's principle is employed to obtain the equations of motion for five layer Timoshenko microbeam. They are subsequently solved analytically by applying Navier's method so that discretized governing equations are determined in form of dynamic matrix giving the possibility to gain the natural frequencies of the Timoshenko microbeam. Eventually, after a validation study, the numerical results are presented to study and discuss the influences of various parameters such as nonlocal parameter, strain gradient parameter, aspect ratio, porosity, various volume fraction and distributions of graphene platelets, temperature change and elastic foundation coefficients on natural frequencies of the sandwich microbeam.

• Structural Engineering and Mechanics
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• v.42 no.4
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• pp.471-488
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• 2012

An efficient one dimensional finite element model has been presented for the dynamic analysis of composite laminated beams, using the efficient layerwise zigzag theory. To meet the convergence requirements for the weak integral formulation, cubic Hermite interpolation is used for the transverse displacement ($w_0$), and linear interpolation is used for the axial displacement ($u_0$) and shear rotation (${\psi}_0$). Each node of an element has four degrees of freedom. The expressions of variationally consistent inertia, stiffness matrices and the load vector are derived in closed form using exact integration. The formulation is validated by comparing the results with the 2D-FE results for composite symmetric and sandwich beams with various end conditions. The employed finite element model is free of shear locking. The present zigzag finite element results for natural frequencies, mode shapes of cantilever and clamped-clamped beams are obtained with a one-dimensional finite element codes developed in MATLAB. These 1D-FE results for cantilever and clamped beams are compared with the 2D-FE results obtained using ABAQUS to show the accuracy of the developed MATLAB code, for zigzag theory for these boundary conditions. This comparison establishes the accuracy of zigzag finite element analysis for dynamic response under given boundary conditions.