• Coupled systems mechanics
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• 제9권3호
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• pp.265-280
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• 2020

In this paper, a new refined hyperbolic shear deformation beam theory for the free vibration analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equations of motion are derived from the Hamilton's principle. Navier type solution method was used to obtain frequencies, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the free vibration response of a simply supported FG beams.

• Steel and Composite Structures
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• 제48권2호
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• pp.191-206
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• 2023

The present research investigates how micromechanical models affect the behavior of Functionally Graded (FG) plates under different boundary conditions. The study employs diverse micromechanical models to assess the effective material properties of a two-phase particle composite featuring a volume fraction of particles that continuously varies throughout the thickness of the plate. Specifically, the research examines the vibrational response of the plate on a Winkler-Pasternak elastic foundation, considering different boundary conditions. To achieve this, the governing differential equations and boundary conditions are derived using Hamilton's principle, which is based on a four-variable shear deformation refined plate theory. Additionally, the Galerkin method is utilized to compute the plate's natural frequencies. The study explores how the plate's natural frequencies are influenced by various micromechanical models, such as Voigt, Reuss, Hashin-Shtrikman bounds, and Tamura, as well as factors such as boundary conditions, elastic foundation parameters, length-to-thickness ratio, and aspect ratio. The research results can provide valuable insights for future analyses of FG plates with different boundaries, utilizing different micromechanical models.

• Geomechanics and Engineering
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• 제38권4호
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• pp.409-420
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• 2024

In this research the hygro-thermo-mechanical loading and micromechanical model effects on bending behavior of functionally graded material plates resting on Winkler and Pasternak elastic foundations, the higher order shear deformation theory is used here. The material properties of the plate: young's modulus, thermal coefficient and moisture expansion coefficient are assumed to be graded in the thickness direction according to various micromechanical models starting with the Voigt's model which is commonly used in most functionally graded plates studies to the Reuss's, LRVE's and Mori-Tanaka's models. The principle of virtual displacement is used to determine the equilibrium equations and the a several numerical results are given to validate the precision of the present method for bending behavior of FGM plates subjected to hygro-thermo-mechanical loading resting on elastic foundations. Afterwards, a parametric study is conducted to determine the effect of different parameters on the deflection of the FGM plates like micromechanical models, type of loading and plate geometry. In the lights of the present research, it can be concluded that the present theory is accurate and simple in predicting the deflection behavior of functionally graded plates under hygro-thermo-mechanical effects and micromechanical models.

• 대한기계학회논문집A
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• 제31권11호
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• pp.1077-1082
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• 2007

We present a micromechanical active amplifier, inspired from the principle of the outer hair cells in cochlea, amplifying both displacement and force. The present micromechanical active amplifier modulates the resonant carrier motion using the variable stiffness spring whose stiffness changes proportionally to the input motion. We design, fabricate, and characterize two types of the amplifiers A and B, each having the variable stiffness spring fur the maximum displacement gain and force gain, respectively. In the experimental study, the amplifier A shows the displacement gain of 5.62, which is 2.15 times larger than that of the amplifier 3. The amplifier B shows the force gain of 10.0, resulting in 1.26 times larger value compared to that of the amplifier A. We experimentally verify that the haircell-inspired micromechanical amplifiers are capable to amplify both displacement and force.

• Earthquakes and Structures
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• 제16권2호
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• pp.177-183
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• 2019

In this paper, a new refined hyperbolic shear deformation beam theory for the bending analysis of functionally graded beam is presented. The theory accounts for hyperbolic distribution of the transverse shear strains and satisfies the zero traction boundary conditions on the surfaces of the functionally graded beam without using shear correction factors. In addition, the effect of different micromechanical models on the bending response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present theory, the equilibrium equations are derived from the principle of virtual work. Navier type solution method was used to obtain displacement and stresses, and the numerical results are compared with those available in the literature. A detailed parametric study is presented to show the effect of different micromechanical models on the flexural response of a simply supported FG beams.

• 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.

• Earthquakes and Structures
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• 제14권2호
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• pp.117-128
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• 2018

In this research work, free vibrations of simply supported functionally graded plate resting on a Winkler-Pasternak elastic foundation are investigated by a new shear deformation theory. The influence of alternative micromechanical models on the macroscopic behavior of a functionally graded plate based on shear-deformation plate theories is examined. Several micromechanical models are tested to obtain the effective material properties of a two-phase particle composite as a function of the volume fraction of particles which continuously varies through the thickness of a functionally graded plate. Present theory exactly satisfies stress boundary conditions on the top and the bottom of the plate. The energy functional of the system is obtained using Hamilton's principle. The closed form solutions are obtained by using Navier technique, and then fundamental frequencies are found by solving the results of eigenvalue problems. Finally, the numerical results are provided to reveal the effect of explicit micromechanical models on natural fundamental frequencies.

• Structural Engineering and Mechanics
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• 제69권2호
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• pp.231-241
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• 2019

In this paper, a new higher order shear deformation model is developed for static and free vibration analysis of functionally graded beams with considering porosities that may possibly occur inside the functionally graded materials (FGMs) during their fabrication. Different patterns of porosity distributions (including even and uneven distribution patterns, and the logarithmic-uneven pattern) are considered. In addition, the effect of different micromechanical models on the bending and free vibration response of these beams is studied. Various micromechanical models are used to evaluate the mechanical characteristics of the FG beams whose properties vary continuously across the thickness according to a simple power law. Based on the present higher-order shear deformation model, the equations of motion are derived from Hamilton's principle. Navier type solution method was used to obtain displacement, stresses and frequencies, and the numerical results are compared with those available in the literature. A comprehensive parametric study is carried out to assess the effects of volume fraction index, porosity fraction index, micromechanical models, mode numbers, and geometry on the bending and natural frequencies of imperfect FG beams.

• Structural Engineering and Mechanics
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• 제89권3호
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• pp.265-281
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• 2024

The sound radiation responses of multi-layer composite plates subjected to harmonic mechanical excitation in hygrothermal environment is numerically investigated. A homogenized micromechanical finite element (FE) based on the higher-order mid-plane kinematics replicating quadratic function as well as the through the thickness stretching effect together with the indirect boundary element (IBE) scheme has been first time employed. The isoparametric Lagrangian element (ten degrees of freedom per node) is used for discretization to attain the hygro-thermo-elastic natural frequencies and the modes of the plate via Hamilton's principle. The effective material properties under combined hygrothermal loading are considered via a micromechanical model. An IBE method is then implemented to attain structure-surrounding coupling and the Helmholtz wave equation is solved to compute the sound radiation responses. The effectiveness of the model is tested by converging it with the similar analytical/numerical results as well as the experimentally acquired data. The present scheme is further hold out for solving diverse numerical illustrations. The results revealed the relevance of the current higher-order FE-IBE micromechanical model in realistic estimation of hygro-thermo-acoustic responses. The geometrical parameters, volume fraction of fiber, layup, and support conditions alongside the hygrothermal load is found to have significant influence on the vibroacoustic characteristics.

• Computers and Concrete
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• 제26권2호
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• pp.127-136
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• 2020

There is an inherent randomness for concrete microstructure even with the same manufacturing process. Meanwhile, the concrete material under the aqueous environment is usually not fully saturated by water. This study aimed to develop a stochastic micromechanical framework to investigate the probabilistic behavior of the unsaturated concrete from microscale level. The material is represented as a multiphase composite composed of the water, the pores and the intrinsic concrete (made up by the mortar, the coarse aggregates and their interfaces). The differential scheme based two-level micromechanical homogenization scheme is presented to quantitatively predict the concrete's effective properties. By modeling the volume fractions and properties of the constituents as stochastic, we extend the deterministic framework to stochastic to incorporate the material's inherent randomness. Monte Carlo simulations are adopted to reach the different order moments of the effective properties. A distribution-free method is employed to get the unbiased probability density function based on the maximum entropy principle. Numerical examples including limited experimental validations, comparisons with existing micromechanical models, commonly used probability density functions and the direct Monte Carlo simulations indicate that the proposed models provide an accurate and computationally efficient framework in characterizing the material's effective properties. Finally, the effects of the saturation degrees and the pore shapes on the concrete macroscopic probabilistic behaviors are investigated based on our proposed stochastic micromechanical framework.