امروزه پیش‌بینی رفتار ارتعاشی و دینامیکی سازه‌های میکرو مورد توجه بسیاری از پژوهشگران قرار گرفته است. در این پژوهش تحلیل ارتعاشات و کنترل میکروتیر یکسر گیردار به همراه لایه‌های پیزوالکتریک عملگر و حسگر با فرض اثرات تنش سطح مورد ارزیابی قرار گرفته است. معادلات دیفرانسیل حاکم با استفاده از روش انرژی و اصل همیلتون استخراج شده و از روش مجموع مربعات دیفرانسیلی تعمیم یافته برای گسسته-سازی و تبدیل معادلات دیفرانسیل پاره‌ای به دسته معادلات دیفرانسیل معمولی استفاده شده است. اثر تغییرات هندسه مدل و مدول الاستیسیته سطح، تنش پسماند سطح و چگالی سطحی بر فرکانس طبیعی مدل میکروتیر با لایه‌های پیزوالکتریک بررسی شده است. همچنین تأثیر طراحی کنترلر بهینه خطی بر تغییرات پاسخ دینامیکی و ولتاژ کنترلی پیزوالکتریک مورد ارزیابی قرار گرفته است. نتایج نشان دهنده‌ی افزایش سرعت پاسخ و کاهش سریعتر دامنه ارتعاشی مدل با طراحی کنترل بهینه خطی است. Manuscript profile

In this paper, the free vibration analysis of sandwich micro beam with piezoelectric layers based on the modified couple stress and surface elasticity theories are investigated. The Hamilton’s principle is employed to derive the sandwich micro beam with piezoelectric based on modified couple stress theory incorporating with Gurtin- Murdoch surface theory. The generalized differential quadrature method is used to discretize the partial differential equation into the ordinary differential equation. The effect of various parameters such as thickness to material length scale parameter ratio, the surface residual stress, Young's modulus of surface layer, surface mass density and surface piezoelectric constant are investigated by comparing the results obtained using the modified couple and classical theories. Numerical results of this problem evaluate the effect of micro length scale parameters on natural frequency. The results show that surface parameter effects are significant when the model is small, but can be neglected with increasing model size. Manuscript profile

This study investigates the dynamic stability of the Euler-Bernoulli functionally graded (FGM) nanobeam based on the nonlocal elasticity theory while considering surface effects. Nanoparticles pass over nanobeam sequentially with a constant velocity, and the nanoparticle inertia is also considered. A thermal gradient with constant temperature changes is applied to this nanobeam. The functionally graded nanobeam properties, including Young’s modulus, density, surface residual stress, and surface modulus are taken by the power law. The classical equations of motion are obtained by applying the Hamilton’s principle according to the energy method. The governing equations are extracted using nonlocal elasticity theory, and the surface effects are taken by Gurtin-Murdoch theory. The dynamic stability graphs will be presented on nanoparticle mass-velocity coordinates. This article investigated the small scale effect parameter, temperature changes, Pasternak environment shearing and elastic constants, and the volume fraction parameter in power law. The results show that increasing Pasternak foundation constants increase the functionally graded nanobeam stability, and increasing small scale parameter reduces its stability. Increasing nanobeam temperature shifts the functionally graded stability region of nanobeam towards faster nanoparticle velocity, which indicates a higher dynamic stability for the nanobeam. Manuscript profile

This paper deals with dynamic Stability of single walled carbon nanotube. Strain gradient theory and Euler-Bernouli beam theory are implemented to investigate the dynamic stability of SWCNT embedded in an elastic medium. The equations of motion were derived by Hamilton principle and non-local elasticity approach. The nonlocal parameter accounts for the small-size effects when dealing with nano- size structures such as single-walled carbon nanotubes. Influences of nonlocal effects, modulus parameter of elastic medium and aspect ratio of the SWCNT on the critical buckling loads and instability regions are analyzed. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanotubes. Manuscript profile

In the present study, stress analysis and explicit solution of rectangular plate with arbitrarily located circular hole, subjected to linear normal stresses on two opposite edges, has been investigated. Airy function and hoop stresses occurring at the edge of the circular have been computed. In this method 2D dimension elasticity and Airy stress function was used. The present method for explicit solution and finding airy stress function are stronger and simpler than prior methods. By using Stress function, the stress distribution around circular hole were calculated. By using obtained airy stress relation the stress distribution around the circle was obtained, plotted and compared with distribution of stress (computed by finite element method in Abaqus). This comparison shows the accuracy of this solution method. It has been observed that stress distribution of stress function is independent from hole location and only depends on the hole's size. Manuscript profile

Vibration of double-graphene sheet-system is considered in this study. Graphene sheets are coupled by Pasternak elastic medium. Classic and Mindlin plate theories are utilized for modeling the coupled system. Upper sheet carries a moving mass. Governing equations are derived using energy method and Hamilton’s principle considering surface stress effects and nonlocal parameter. Using Galerkin method, figures of frequency versus nonlocal parameter are drawn and the effects of different parameters such as moving mass, surface effects and etc. are discussed. Results show considering surface effects, the frequency of coupled system increases. Also heavier mass and farther mass away from supports will result in lower frequencies Manuscript profile

Based on the nonlocal Timoshenko beam theory, the dynamic stability of functionally gradded (FG) nanoeams under axial load is studied in thermal environment, with considering surface effect. It is used power law distribution for FGM and the surface stress effects are considered based on Gurtin-Murdoch continuum theory. Using Von Karman geometric nonlinearity, governing equations are derived based on Hamilton’s principle. The developed nonlocal models have the capability to interpret small scale effects. Winkler and Pasternak types elastic foundation are employed to represent the interaction of the nano FG beam and the surrounding elastic medium. A parametric study is conducted to investigate the influences of the static load factor, temperature change, nonlocal elastic parameter, slenderness ratio, surface effect and springs constant of the elastic medium on the dynamic stability characteristics of the FG beam, with simply-supported boundary conditions. It is found that the difference between instability regions predicted by local and nonlocal beam theories is significant for nanobeams with lower aspect ratios. Moreover, it is observed that in contrast to high temperature environments, at low temperatures, increasing the temperature change moves the origins of the instability regions to higher excitation frequencies and leads to further stability of the system at lower excitation frequencies, considering surface stress effect shifts the FG beam to higher frequency zone Manuscript profile