In the present work, the mathematical model of a homogeneous, isotropic thermoelastic double porous Micro-beam, based on the Euler-Bernoulli theory is developed in the context of Lord-Shulman [1] theory of thermoelasticity. Laplace transform technique has been used to obtain the expressions for lateral deflection, axial stress, axial displacement, volume fraction field and temperature distribution. A numerical inversion technique has been applied to recover the resulting quantities in the physical domain. Variations of axial displacement, axial stress, lateral deflection, volume fraction field and temperature distribution with axial distance are depicted graphically to show the effects of porosity and thermal relaxation time. Some particular cases are also deduced.             

In this article, in reference to the modified couple stress theory and Euler-Bernoulli beam theory, the free lateral vibration response of a Micro-beam carrying a moveable attached mass is investigated. This is a decent model for biological and biomedical applications beneficial to the early-stage diagnosis of diseases and malfunctions of human body organs and enzymes. The Micro-cantilever beam is composed of functionally graded materials (FGMs). The material properties are supposed to show variations through-thickness of the beam in consonance to the power of law. Rayleigh-Ritz method is applied in order to explore the natural frequencies of the first three vibration modes. In order to manifest the accuracy of the proposed method, the results are established and juxtaposed with technical literature. Influences of the material length-scale parameter that captures the size-dependency, ratio of the mass of the beam to the mass of the attached mass and power index of the graded material consequent to the vibrational behavior of the system are contemplated. This technical research denotes the value of the material gradation besides to the inertia of an attached mass in the dynamic behavior of the bio-Micro-systems. As a result, the adoption of suitable power index, mass ratio and position of the attached mass lead to the superior design of bio-Micro-systems persuading early-stage diagnostics.

This paper investigates damping ratio in Micro-beam resonators based on magneto-thermo-elasticity. A unique aspect of the present study is the effect of permanent magnetic field on the stiffness and thermo-elastic damping of the Micro resonators. In our modeling the theory of thermo-elasticity with interacting of an externally applied permanent magnetic field is taken into account. Combined theoretical and numerical studies investigate the permanent magnetic field effect on the damping ratio in clamped-clamped and cantilever Micro-beams. Furthermore, the influence of the magnetic field intensity on the frequency of the Micro-beams with thermo-elastic damping effect is evaluated. Such evaluations are used to determine the influence of magnetic field on the vibration amplitude of the resonators. The meaningful conclusion is that the magnetic field increases the equivalent stiffness and thermo-elastic damping and consequently the energy consumption of the resonators.

In this research dynamic instability and nonlinear vibration of a clamped-clamped Micro-beam sandwiched with piezoelectric layers based on parametric excitation in sub-harmonic region is investigated. The equation of motion is derived based on Hamiltonian principle, and nondimensionalized using appropriate non-dimensional parameters. Applying a harmonic AC voltage to the piezoelectric layers results in the time varying of the linear stiffness of the Micro-beam. The resultant motion equation in non-dimensional form is discretized to single degree of freedom model using Galerkin technique. The governing equation is a nonlinear Mathieu type ODE, and the periodic attractors are captured based on the shooting technique. The nonlinearity of governing equation is due to the geometric nonlinearity which originates from the clamped-clamped boundary conditions. The effect of various parameters including magnitude of the nonlinear stiffness, damping coefficient, the frequency and the amplitude of the harmonic excitation on the parametric resonance region is investigated. The results depict that increased damping coefficient leads to the decreased aria of the parametric resonance region. It is concluded that the magnitude of the nonlinear stiffness, does not affect on the area of the resonance region, however it considerably influences on the amplitude of the parametric resonance.

The nonlinear pull-in behavior for different electrostatic Micro-actuators is simulated in this work. The difficulty of nonlinear equation is overcome using the differential quadrature method and Wilson−q method. Several characteristics of different combination of shaped fixed-fixed beam and curved electrode are also observed to optimize the design in this paper. The nonlinear deflection of uniform actuator and non-uniform actuator solved using the differential quadrature methods are efficient. The stresses are determined for this par electrostatic Micro-actuator design. The effects of applied voltage, squeeze film force, external loading and residual axial loading on the behavior of the electrostatic actuator are investigated. It is needed to consider the squeeze film force and residual axial loading in the fixedfixed Micro-actuator design.

In this article bending analysis of composite Euler-Bernoulli Micro-beam made of functionally graded materials resting on elastic foundation by strain gradient theory has been studied. The material properties of structure have been assumed by Reddy’s power law model such as the bottom layer and top layer being ceramic and metal material respectively. At first, by using the assumptions of elasticity strain gradient theory and calculating the total potential energy of system after determining the work of external distributed load by using the Hamilton's principal the equations of motion have been derived. Note that the work down by the Winkler elastic foundation is considered. Because the solutions of mentioned equations are not possible by analytical method, the equations have been solved by generalized differential quadrature method in simply supported boundary conditions. By comparing the answers of problem with other published references, we confident form the obtained results. At the end, effect of material length scale and power law index coefficient of functionally graded materials and stiffness of elastic foundation on deflection of Micro-beam has been studied.

This paper presents mechanical behavior of a functionally graded (FG) cantilever Micro-beam subjected to a nonlinear electrostatic pressure and thermal moment considering effects of material length scale parameters. Material properties through the beam thickness direction are graded. The top surface of the Micro-beam is made of pure metal and the bottom surface from a mixture of metal and ceramic. The material properties through the thickness direction follow the volume fraction of the constitutive materials in exponential function form. The governing nonlinear thermo-electro-mechanical differential equation based on Euler-Bernoulli beam theory assumptions is derived using modified couple stress theory (MCST) and is solved using the Galerkin based weighted residual method. The effects of the electrostatic pressure and temperature changes on the deflection and stability of the FGM Micro-beam, having various ceramic constituent percents, are studied. The obtained results are compared with the results predicted by classic theory (CT) and for some cases are verified with those reported in the literature.

The buckling and nonlinear free vibration problems of functionally graded porous (FGP) Micro-beam resting on an elastic foundation are presented through the nonlocal strain gradient theory (NSGT) and the Euler-Bernoulli beam theory (EBT) with the von-Kármán’s geometrical nonlinearity. The Micro-beam is made up of metal and ceramic in which the material properties are assumed to be varied continuously in the thickness direction through a simple exponential law. Two porosity distribution models, including even and uneven distributions, are considered. The governing equation of motion is derived by employing Hamilton’s principle. The analytical expressions of the critical buckling force and nonlinear frequency of the FGP Micro-beam with simply supported (S-S) boundary conditions (BCs) are obtained by utilizing the Galerkin technique and the equivalent linearization method (ELM). The reliability of the obtained results has been checked. Effects of the power-law index, the porosity distribution factor, the length-thickness ratio, the material length scale parameter (MLSP), the nonlocal parameter (NP), and the coefficients of the elastic foundation on the buckling and nonlinear free vibration responses of the FGP Micro-beam are investigated and discussed in this work.