• Steel and Composite Structures
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• v.17 no.5
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• pp.753-776
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• 2014

In this paper, nonlinear vibration and post-buckling analysis of beams made of functionally graded materials (FGMs) resting on nonlinear elastic foundation subjected to thermo-mechanical loading are studied. The thermo-mechanical material properties of the beams are assumed to be graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents, and to be temperature-dependent. The assumption of a small strain, moderate deformation is used. Based on Euler-Bernoulli beam theory and von-Karman geometric nonlinearity, the integral partial differential equation of motion is derived. Then this PDE problem which has quadratic and cubic nonlinearities is simplified into an ODE problem by using the Galerkin method. Finally, the governing equation is solved analytically using the variational iteration method (VIM). Some new results for the nonlinear natural frequencies and buckling load of the FG beams such as the influences of thermal effect, the effect of vibration amplitude, elastic coefficients of foundation, axial force, end supports and material inhomogenity are presented for future references. Results show that the thermal loading has a significant effect on the vibration and post-buckling response of FG beams.

• Structural Engineering and Mechanics
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• v.63 no.3
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• pp.401-415
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• 2017

In this article, hygro-thermo-mechanical vibration and buckling of exponentially graded (EG) nanoplates resting on two-parameter Pasternak foundations are studied using the four-unknown shear deformation plate theory. The material properties are presumed to change only in the thickness direction of the EG nanoplate according to two exponential laws distribution. The boundary conditions of the nanoplate may be simply supported, clamped, free or combination of them. To consider the small scale effect on forced frequencies and buckling, Eringen's differential form of nonlocal elasticity theory is employed. The accuracy of the present study is investigated considering the available solutions in literature. A detailed analysis is executed to study the influences of the plate aspect ratio, side-to-thickness ratio, temperature rise, moisture concentration and volume fraction distributions on the vibration and buckling of the nanoplates.

• Advances in nano research
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• v.4 no.3
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• pp.197-228
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• 2016

In the present study, thermo-electro-mechanical vibration characteristics of functionally graded piezoelectric (FGP) Timoshenko nanobeams subjected to in-plane thermal loads and applied electric voltage are carried out by presenting a Navier type solution for the first time. Three kinds of thermal loading, namely, uniform, linear and non-linear temperature rises through the thickness direction are considered. Thermo-electro-mechanical properties of FGP nanobeam are supposed to vary smoothly and continuously throughout the thickness based on power-law model. Eringen's nonlocal elasticity theory is exploited to describe the size dependency of nanobeam. Using Hamilton's principle, the nonlocal equations of motion together with corresponding boundary conditions based on Timoshenko beam theory are obtained for the free vibration analysis of graded piezoelectric nanobeams including size effect and they are solved applying analytical solution. According to the numerical results, it is revealed that the proposed modeling can provide accurate frequency results of the FGP nanobeams as compared to some cases in the literature. In following a parametric study is accompanied to examine the effects of several parameters such as various temperature distributions, external electric voltage, power-law index, nonlocal parameter and mode number on the natural frequencies of the size-dependent FGP nanobeams in detail. It is found that the small scale effect and thermo-electrical loading have a significant effect on natural frequencies of FGP nanobeams.

• Structural Engineering and Mechanics
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• v.59 no.2
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• pp.343-371
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• 2016

In this paper thermo-mechanical vibration analysis of a porous functionally graded (FG) Timoshenko beam in thermal environment with various boundary conditions are performed by employing a semi analytical differential transform method (DTM) and presenting a Navier type solution method for the first time. The temperature-dependent material properties of FG beam are supposed to vary through thickness direction of the constituents according to the power-law distribution which is modified to approximate the material properties with the porosity phases. Also the porous material properties vary through the thickness of the beam with even and uneven distribution. Two types of thermal loadings, namely, uniform and linear temperature rises through thickness direction are considered. Derivation of equations is based on the Timoshenko beam theory in order to consider the effect of both shear deformation and rotary inertia. Hamilton's principle is applied to obtain the governing differential equation of motion and boundary conditions. The detailed mathematical derivations are presented and numerical investigations are performed while the emphasis is placed on investigating the effect of several parameters such as porosity distributions, porosity volume fraction, thermal effect, boundary conditions and power-low exponent on the natural frequencies of the FG beams in detail. It is explicitly shown that the vibration behavior of porous FG beams is significantly influenced by these effects. Numerical results are presented to serve benchmarks for future analyses of FG beams with porosity phases.

• Steel and Composite Structures
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• v.27 no.6
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• pp.761-775
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• 2018

In the present work, the recently developed non-polynomial shear deformation theories are assessed for thermo-mechanical response characteristics of laminated composite plates. The applicability and accuracy of these theories for static, buckling and free vibration responses were ascertained in the recent past by several authors. However, the assessment of these theories for thermo-mechanical analysis of the laminated composite structures is still to be ascertained. The response characteristics are investigated in linear and non-linear thermal gradient and also in the presence and absence of mechanical transverse loads. The laminated composite plates are modelled using recently developed six shear deformation theories involving different shear strain functions. The principle of virtual work is used to develop the governing system of equations. The Navier type closed form solution is adopted to yield the exact solution of the developed equation for simply supported cross ply laminated plates. The thermo-mechanical response characteristics due to these six different theories are obtained and compared with the existing results.

• Coupled systems mechanics
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• v.6 no.2
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• pp.207-227
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• 2017

In this paper Timoshenko beam theory is employed to investigate the vibration characteristics of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) Beams with a stiff core in thermal environment. The material characteristic of carbon nanotubes (CNT) are supposed to change in the thickness direction in a functionally graded form. They can also be calculated through a micromechanical model where the CNT efficiency parameter is determined by matching the elastic modulus of CNTRCs calculated from the rule of mixture with those gained from the molecular dynamics simulations. The differential transform method (DTM) which is established upon the Taylor series expansion is one of the effective mathematical techniques employed to the differential governing equations of sandwich beams. Effects of carbon nanotube volume fraction, slenderness ratio, core-to-face sheet thickness ratio, different thermal environment and various boundary conditions on the free vibration characteristics of FG-CNTRC sandwich beams are studied. It is observed that vibration response of FG-CNTRC sandwich beams is prominently influenced by these parameters.

• Structural Engineering and Mechanics
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• v.65 no.4
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• pp.435-445
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• 2018

This paper is concerned with thermo-mechanical vibration behavior of flexoelectric/piezoelectric nanobeams under uniform and linear temperature distributions. Flexoelectric/piezoelectric nanobeams have higher natural frequencies compared to conventional piezoelectric ones, especially at lower thicknesses. Both nonlocal and surface effects are considered in the analysis of flexoelectric/piezoelectric nanobeams for the first time. Hamilton's principle is employed to derive the governing equations and the related boundary conditions which are solved applying a Galerkin-based solution. Comparison study is also performed to verify the present formulation with those of previous data. Numerical results are presented to investigate the influences of the flexoelectricity, nonlocal parameter, surface elasticity, temperature rise, beam thickness and various boundary conditions on the vibration frequencies of thermally affected flexoelectric/piezoelectric nanobeam.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
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• 2006.05a
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• pp.1061-1064
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• 2006

Optimal design of functionally graded plates is investigated considering stress and critical temperature. Material properties are assumed to be temperature dependent and varied continuously in the thickness direction. The effective material properties are obtained by applying linear rule of mixtures. The 3-D finite element model is adopted using an 18-node solid element to analyze more accurately the variation of material properties and temperature field in the thickness direction. For stress analysis, the tensile stress ratio and compressive stress ratio of the structure under mechanical load are investigated. In the thermo-mechanical buckling analysis, temperature at each node is obtained by solving the steady-state heat transfer problem and Newton-Raphson method is used for material nonlinear analysis. Finally, the optimal design of FGM plates is studied for stress reduction and improving thermo-mechanical buckling behavior, simultaneously.

• Structural Engineering and Mechanics
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• v.63 no.2
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• pp.171-180
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• 2017

Static and dynamic instability of a viscoelastic carbon nanotube (CNT) embedded on a thermo-elastic foundation are investigated, in this research. The CNT is modeled based on Euler-Bernoulli beam (EBB) and nonlocal small scale elasticity theory is utilized to analyze the structure. Governing equations of the system are derived using Hamilton's principle and differential quadrature (DQ) method is applied to solve the partial differential equations. The effects of variable axial load and diverse boundary conditions on static/vibration instability are studied. To verify the result of the DQ method, the Galerkin weighted residual approach is used for the instability analysis. It is observed appropriate agreement for results of two different solution methods and satisfactory accuracy with those obtained in prior studies. The results of this work could be useful for engineers and designers in order to produce and design nano/micro structures in thermo-elastic medium.

• Journal of Dental Anesthesia and Pain Medicine
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• v.23 no.6
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• pp.327-335
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• 2023

Background: Pain control is a crucial aspect of pediatric dentistry for patient management. Thermo-mechanical devices (Buzzy^TM Pain Care Labs, USA) work on the concept of vibration and cooling and have shown promising results in pain control during local anesthesia in pediatric dentistry. On the other hand, audio distraction has also been used for pain management. The amount of pain endured is determined by the patient's perception and attentiveness. Thus, if audio function is added to the thermomechanical device it might increase its efficiency. Hence, the present study aimed to compare pain on injection using a thermo-mechanical device with and without audio during inferior alveolar nerve block (IANB) injection in children aged 5-10 years old. Methods: Twenty-eight children aged between 5 and 10 indicated for IANB were included in this randomized study. Children who were undergoing the dental procedure were divided into 2 groups, with 14 children in each group. The study group was the thermo-mechanical device with audio distraction; the control group was the thermo-mechanical device without audio distraction. IANB was administered. Subjective pain evaluation was performed using the Wong-Baker Faces Pain Rating Scale (WBFPR) and objective pain evaluation was done using the Faces, Leg, Activity, Consolability, Cry (FLACC) scale. Results: The outcome depicted a significant reduction in pain on injection for both objective and subjective evaluations in the thermo-mechanical device with an audio distraction group. Conclusions: Less pain on injection was observed, when a thermo-mechanical device was used with audio distraction for IANB procedures.