جستجوی مقالات مرتبط با کلیدواژه « length scale parameter » در نشریات گروه « مکانیک »

The length-scale parameter as a primary factor has an important role in approximation of natural frequencies of micro-structures. Applying the exact length scale parameters which are recently determined by researchers, natural frequencies of porous microstructures are determined. In view of the fact that assumption of constant length-scale parameter leads to deviation of natural frequencies from their exact value, this research applies a length scale parameter which is function of plate thickness and material. To model the porous structures of the plate, the proposed porous models including evenly porosity mode, unevenly symmetric porosity model, and unevenly asymmetric porosity model are employed. The micro-plate is assumed to be thin, and classical plate theory is applied to displacement field of the micro-plate. The modified stress couple theory is employed to approximate the behavior of the plate in micro-scale. The trial functions which satisfy the boundary conditions are taken as the polynomial form. Evaluating the energy values of the system, the Rayleigh-Ritz method is imposed to solve the governing equations of the system. Validated the solution procedure with data given in the literature search, effects of various parameters on natural frequency of the plate are studied in the form of tables and curves.

In this article, the sensitivity and resonant frequency of the atomic force microscope made of functionally graded materials is investigated by couple stress theory (MCST). In MCST, the size effect of the system is taking into account by means of the material length scale parameter. is made of a mixture of metal and ceramic with properties varying through the thickness following a simple In this work, due to the kinematic energy and potential energy of , the governing equations of motion and corresponding boundary conditions are derived on the basis of Hamilton principle by considering Euler-Bernoulli beam theory. Based on the results, it is clear that when the contact stiffness increases, the sensitivity of the system decreases, and resonant frequency increases. Moreover, when the thickness comes approximately close to material length scale parameter, the difference between MCST and classical continuum mechanic becomes significant. Furthermore, in low contact stiffness, increasing the power reduces the sensitivity of , while in high contact stiffness, increasing the power  increases the sensitivity of the system. Results also show that at each value of contact stiffness, as ceramic volume fraction increases the resonant frequency will be increased, too.

In this study, the hydrostatic vibration analysis of an isotropic rectangular microplate in partial contact with a bounded fluid is studied. Modified couple stress theory based on the Kirchhoff plate assumptions are used to mathematically model the problem. The extended Hamilton’s principle is employed to drive the governing differential equation of motion and the corresponding boundary conditions. The transverse displacement of the microplate is approximated by a set of admissible functions which must satisfy the geometric boundary conditions. The fluid is assumed to be incompressible, inviscid and irrotational and the fluid velocity potential is obtained using the boundary and compatibility conditions. Natural frequencies of the microplate are calculated using the Rayleigh-Ritz method. To validate the present results, the natural frequencies of an isotropic macroplate in contact with fluid are compared with the available data in the literature and very good agreements are observed. Finally using the numerical data, the effect of different parameters such as thickness to length scale parameter, aspect ratio, length to thickness ratio and boundary conditions on the natural frequencies of the microplate are discussed in detail. We have observed that the difference between the natural frequencies predicted using the classical theory and the one evaluated by the modified couple stress theory is significant when thickness of the microplate is small, but diminishes as thickness increases.

Topology optimization of structure seeks to achieve the best material distribution in the Pre-determined design domain. In this paper, the effect of design parameters contains length scale parameter and evolutionary volume ratio in improved bi-directional evolutionary structural optimization method with soft kill approach is discussed. The main aim of this method is searching for the stiffest structure with a given volume of material using finite element method. At each iteration of finite element analysis, sensitivity number is calculated for each individual element in design domain and then converted to the nodal sensitivity number. With Filter Scheme and using length scale, an improved sensitivity numbers is defined. This number is used as a criterion for rating each element in design domain and determining the addition and elimination (remove) of elements. To increase the convergence of the optimization process, the accuracy of the new elemental sensitivity numbers is improved by considering the sensitivity history. This method is convergent and mesh-independent and there are no checkerboard pattern and local solutions in optimal topologies. Using three design samples, a cantilever and classical beam and Michell type structure, affecting factors will be discussed on the final design of the structure. Change of length scale parameter makes various schemes in final structures in which with increasing this parameter, more iteration is needed for convergent solution. Reducing evolutionary volume ratio forms different and even asymmetric topologies. Better final topologies are obtained with higher evolutionary volume ratios.

Size dependent behavior of materials appears for a structure when the characteristic size such as thickness or diameter is close to its internal length-scale parameter. In these cases, ignoring this behavior in modeling may leads to incorrect results. In this paper, strong effects of the size dependence on the static and dynamic behavior of the electrostatically actuated micro-beams have been studied. The equilibrium positions or fixed points of the gold and nickel micro-beams have been determined and shown that for a given DC voltage, there is a considerable difference between the fixed points gained using the classic beam theory and the modified couple stress theory. In addition, it has been shown that the static and dynamic pull-in voltages gained using the couple stress theory are several times higher than those gained using the classic beam theory. Some previous studies have applied the classic beam theory in their models and introduced a considerable hypothetical value of residual stress to match their experimental and incorrect theoretical results. It has been shown that using the modified couple stress theory decreases considerably the difference with the experimental results.