• Structural Engineering and Mechanics
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• 제49권5호
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• pp.537-554
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• 2014

In this paper, free vibration of a sandwich curved beam with a functionally graded (FG) core was investigated. Closed-form formulations of two-dimensional (2D) refined higher order beam theory (RHOBT) without neglecting the amount of z/R was derived and used. The present RHOBT analysis incorporated a trapezoidal shape factor that arose due to the fact that stresses through the beam thickness were integrated over a curved surface. The solutions presented herein were compared with the available numerical and analytical solutions in the related literature and excellent agreement was obtained. Effects of some dimensionless parameters on the structural response were investigated to show their effects on fundamental natural frequency of the curved beam. In all the cases, variations of the material constant number were calculated and presented. Effect of changing ratio of core to beam thickness on the fundamental natural frequency depended on the amount of the material constant number.

• Advances in nano research
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• 제16권3호
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• pp.313-324
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• 2024

The main aims of this study are to develop a new nonlocal quasi-3D theory for the free vibration behaviors of the functionally graded sandwich nanobeams. The sandwich beams consist of a ceramic core and two functionally graded material layers resting on elastic foundations. The two layers, linear spring stiffness and shear layer, are used to model the effects of the elastic foundations. The size-effect is considered using nonlocal elasticity theory. The governing equations of the motion of the functionally graded sandwich nanobeams are obtained via Hamilton's principle in combination with nonlocal elasticity theory. Then the Navier's solution technique is used to solve the governing equations of the motion to achieve the nonlocal free vibration behaviors of the nanobeams. A deep parametric study is also provided to demonstrate the effects of some parameters, such as length-to-height ratio, power-law index, nonlocal parameter, and two parameters of the elastic foundation, on the free vibration behaviors of the functionally graded sandwich nanobeams.

• Composites Research
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• 제16권3호
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• pp.18-24
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• 2003

샌드위치 구조물들은 적은 무게의 첨가로 높은 강성(stiffness)을 요구하는 조선업에 널리 사용되어져 왔다. 국부하중 조건 하에서 샌드위치 구조물에 대한 디자인 변수들을 고려하는 것은 중요시되어졌다. 이 연구는 샌드위치 보의 강도에 대한 core층의 밀도, core층의 두께 그리고 face층의 두께 비율의 영향을 기술하였다. 이차원 탄성이론에 바탕을 둔 파손 하중은 AS4/3501-6 facing과 polyurethane foam core 샌드위치 보의 3점 굴곡 실험 결과와 잘 일치 하였다. 또한 그러한 파손 하중들은 face층의 비율의 변화와 함께 비교되었다. 파괴 mode들의 교차점으로 결정되어진 최적조건은 강도(strength)와 강성(stiffness)에 대한 샌드위치 빔의 최적 core 밀도의 값이 결정되었다. 추가적으로 강도에 대한 최적조건과 그렇지 못한 샌드위치 보에 대한 face 두께 비율 효과가 하중 길이에 따라 비교되었으며, 강도와 강성이 core/face무게 비율과 항께 검토하였다.

• Steel and Composite Structures
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• 제44권5호
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• pp.721-740
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• 2022

In this paper, an accurate kinematic model has been developed to study the mechanical response of functionally graded (FG) sandwich beams, mainly covering the bending, buckling and free vibration problems. The studied structure with homogeneous hardcore and softcore is considered to be simply supported in the edges. The present model uses a new refined shear deformation beam theory (RSDBT) in which the displacement field is improved over the other existing high-order shear deformation beam theories (HSDBTs). The present model provides good accuracy and considers a nonlinear transverse shear deformation shape function, since it is constructed with only two unknown variables as the Euler-Bernoulli beam theory but complies with the shear stress-free boundary conditions on the upper and lower surfaces of the beam without employing shear correction factors. The sandwich beams are composed of two FG skins and a homogeneous core wherein the material properties of the skins are assumed to vary gradually and continuously in the thickness direction according to the power-law distribution of volume fraction of the constituents. The governing equations are drawn by implementing Hamilton's principle and solved by means of the Navier's technique. Numerical computations in the non-dimensional terms of transverse displacement, stresses, critical buckling load and natural frequencies obtained by using the proposed model are compared with those predicted by other beam theories to confirm the performance of the proposed theory and to verify the accuracy of the kinematic model.

• Steel and Composite Structures
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• 제32권6호
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• pp.795-806
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• 2019

In this paper, free vibration of sandwich beam with flexible core resting on orthotropic Pasternak is investigated. The top and bottom layers are reinforced by carbon nanotubes (CNTs). This sandwich structural is modeled by Euler and Frostig theories. The effect of agglomeration using Mori-Tanaka model is considered. The Eringen's theory is applied for size effect. The structural damping is investigated by Kelvin-voigt model. The motion equations are calculated by Hamilton's principle and energy method. Using analytical method, the frequency of the structure is obtained. The effect of agglomeration and CNTs volume percent for different parameter such as damping of structure, thickens and spring constant of elastic medium are presented on the frequency of the composite structure. Results show that with increasing CNTs agglomeration, frequency is decreased.

• Structural Engineering and Mechanics
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• 제68권1호
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• pp.53-66
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• 2018

This paper presents an analysis of the bending, buckling and free vibration of functionally graded sandwich beams resting on elastic foundation by using a refined quasi-3D theory in which both shear deformation and thickness stretching effects are included. The displacement field contains only three unknowns, which is less than the number of parameters of many other shear deformation theories. In order to homogenize the micromechanical properties of the FGM sandwich beam, the material properties are derived on the basis of several micromechanical models such as Tamura, Voigt, Reuss and many others. The principle of virtual works is used to obtain the equilibrium equations. The elastic foundation is modeled using the Pasternak mathematical model. The governing equations are obtained through the Hamilton's principle and then are solved via Navier solution for the simply supported beam. The accuracy of the proposed theory can be noticed by comparing it with other 3D solution available in the literature. A detailed parametric study is presented to show the influence of the micromechanical models on the general behavior of FG sandwich beams on elastic foundation.

• Smart Structures and Systems
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• 제22권1호
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• pp.27-40
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• 2018

The governing equations of motion are derived for analysis of a sandwich microbeam in this paper. The sandwich microbeam is including an elastic micro-core and two piezoelectric micro-face-sheets. The microbeam is subjected to transverse loads and two-dimensional electric potential. Higher-order sinusoidal shear deformation beam theory is used for description of displacement field. To account size dependency in governing equations of motion, strain gradient theory is used to mention higher-order stress and strains. An analytical approach for simply-supported sandwich microbeam with short-circuited electric potential is proposed. The numerical results indicate that various types of parameters such as foundation and material length scales have significant effects on the free vibration responses and dynamic results. Investigation on the influence of material length scales indicates that increase of both dimensionless material length scale parameters leads to significant changes of vibration and dynamic responses of microbeam.

• Coupled systems mechanics
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• 제13권2호
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• pp.133-151
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• 2024

In this paper, an improved theoretical interfacial stress analysis is presented for simply supported composite aluminum- sandwich honeycomb beam strengthened by imperfect FGM plateusing linear elastic theory. The adherend shear deformations have been included in the present theoretical analyses by assuming a linear shear stress through the thickness of the adherends, while all existing solutions neglect this effect. Remarkable effect of shear deformations of adherends has been noted in the results.It is shown that both the sliding and the shear stress at the interface are influenced by the material and geometry parameters of the composite beam. This new solution is intended for applicationto composite beams made of all kinds of materials bonded with a thin plate. Finally, numerical comparisons between the existing solutions and the present new solution enable a clear appreciation of the effects of various parameters.

• Steel and Composite Structures
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• 제27권2호
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• pp.149-159
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• 2018

Thermo-mechanical buckling of sandwich beams with a stiff core and face sheets made of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) within the framework of Timoshenko beam theory is presented. The material properties of FG-CNTRC are supposed to vary continuously in the thickness direction and are estimated through the rule of mixture. Also the properties of these materials should be considered temperature dependent. The governing equations and boundary conditions are derived by using Hamilton's principle and solved using an efficient technique called the Differential Transform Method (DTM) to achieve the critical buckling of the sandwich beam in uniform thermal environment. A detailed parametric study is guided to investigate the effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, and clamped-clamped, simply-simply and clamped-simply end supports on the critical buckling behavior of sandwich beams with FG-CNTRC face sheets. Numerical results for comparison of sandwich beams with uniformly distributed carbon nanotube-reinforced composite (UD-CNTRC) face sheets with those with FG-CNTRC face sheets are also presented.

• Steel and Composite Structures
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• 제32권6호
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• pp.753-767
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• 2019

Vibration control in mechanical equipments is an important problem where unwanted vibrations are vanish or at least diminished. In this paper, free vibration active control of the porous sandwich piezoelectric polymeric nanocomposite microbeam with microsensor and microactuater layers are investigated. The aim of this research is to reduce amplitude of vibration in micro beam based on linear quadratic regulator (LQR). Modified couple stress theory (MCST) according to sinusoidal shear deformation theory is presented. The porous sandwich microbeam is rested on elastic foundation. The core and face sheet are made of porous and three-phase carbon nanotubes/resin/fiber nanocomposite materials. The equations of motion are extracted by Hamilton's principle and then Navier's type solution are employed for solving them. The governing equations of motion are written in space state form and linear quadratic regulator (LQR) is used for active control approach. The various parameters are conducted to investigate on the frequency response function (FRF) of the sandwich microbeam for vibration active control. The results indicate that the higher length scale to the thickness, the face sheet thickness to total thickness and the considering microsensor and microactutor significantly affect LQR and uncontrolled FRF. Also, the porosity coefficient increasing, Skempton coefficient and Winkler spring constant shift the frequency response to higher frequencies. The obtained results can be useful for micro-electro-mechanical (MEMS) and nano-electro-mechanical (NEMS) systems.