Search Results (11)

In this paper, the bending behavior of microbeams resting on elastic foundations is analyzed. Due to the widespread use of Micro-Electro-Mechanical Systems (MEMSs) in sensing and actuation applications, various approaches have been developed for modeling such beams. Numerous specialized analytical and numerical models exist for specific configurations of beams and elastic foundations. This work proposes a novel approach. Separate models for the beam and the elastic foundation are developed using the finite element method. These models are then coupled using a variable reduction technique, in which only the degrees of freedom of the beam are retained in the solving system. This approach enables the coupling of any beam and foundation model and allows for independent refinement of the foundation mesh without increasing the size of the solving system. This method is particularly effective for analyzing configurations where the substrate exhibits nonlinear or non-homogeneous characteristics, or where gaps are present between the beam and the substrate. The nonlocal effects due to the small scale of the beam are also considered. This paper focuses on both the static deformation and frequency response of the microbeam. The proposed approach is validated against previously published models. Compared with existing models, the method presented here offers a simpler and more flexible formulation, while allowing the inclusion of nonlinearities in both the beam and foundation, as well as the modeling of gaps. Full article

This study aims to investigate the behavior of viscoelastic materials exhibiting complex mechanical behavior characterized by both elastic and viscous properties. They are widely used in various engineering applications, such as structural components, transportation systems, energy storage devices, microelectromechanical systems (MEMS), and earthquake research and detection. Accurate modeling of viscoelastic behavior is crucial for predicting its performance under dynamic loading conditions. In this study, we modify the equations governing the thermoelastic resistance to describe the thermal variables of a thermoelastic micro-beam supported by a two-parameter Pasternak viscoelastic foundation by using a fractional Moore–Gibson–Thompson (MGT) model in the context of non-locality. The temperature, bending displacement, and moment were computed and graphically displayed using the Laplace transform method. Different theoretical approaches have been compared in order to explain how the phase delay affects physical phenomena. Numerical results show that the wave fluctuations of variables in thermoelastic micro-beams are slightly smaller for the studied model and that the speed of these plane waves depends on fractional and non-local parameters. Full article

This study used scanning electron microscopy via 3D dissection coupled with synchrotron radiation with microfocal beams of both small-angle X-ray scattering and wide-angle X-ray diffraction to analyze the periodic crystal aggregates of unusual poly(p-dioxanone) (PPDO) dendritic cactus-arm-like ring bands upon crystallization with a diluent poly(vinyl alcohol) (PVA) that is capable of hydrogen bonding interactions with PPDO. Three-dimensional microscopy interior dissection clearly expounds that the banded periodic architectures are packed by alternately normal-oriented flat-on crystals underneath the valley, periodically interfaced/branched with horizontal-oriented edge-on fibrils underneath the ridge. The oblique angles between the valley’s flat-on crystals with the branches are ca. 25–45° (depending on gradient inclines and bending), which is also proved by the azimuthal angle in microbeam X-ray diffraction. The grating-like strut-rib assembly in the PPDO cactus-arm-like ring bands is further proved by novel iridescence tests. Full article

Polarized optical microscopy (POM), scanning electron microscopy (SEM), and synchrotron microbeam wide-angle X-ray diffraction (WAXD) were used to investigate the mechanisms of periodic assemblies leading to ring-banded crystal aggregates with light-grating capacity for iridescence in poly (1,4-butylene adipate) (PBA) modulated with poly (ethylene oxide) (PEO). A critical finding is that the PBA crystal assembly on the top surface and in the interior constitutes a grating architecture, with a cross-bar pitch equaling the inter-band spacing. The inner lamellae are arranged perpendicularly to the substrate under the ridge region, where they scroll, bend, and twist 90° to branch out newly spawned lamellae to form the parallel lamellae under the valley region. The cross-hatch grating with a fixed inter-spacing in the PBA aggregated crystals is proved in this work to perfectly act as light-interference entities capable of performing iridescence functions, which can be compared to those widely seen in many of nature’s organic bio-species or inorganic minerals such as opals. This is a novel breakthrough finding for PBA or similar polymers, such as photonic crystals, especially when the crystalline morphology could be custom-made and modulated with a second constituent. Full article

We studied flexoelectrically excited/detected bending vibrations in perpendicular directions of a micro-beam spinning about its axis. A set of one-dimensional equations was derived and used in a theoretical analysis. It is shown that the Coriolis effect associated with the spin produces an electrical output proportional to the angular rate of the spin when it is small. Thus, the beam can be used as a gyroscope for angular rate sensing. Compared to conventional piezoelectric beam gyroscopes, the flexoelectric beam proposed and analyzed has a simpler structure. Full article

This paper presents a novel non-classical Timoshenko–Ehrenfest beam model based on a reformulated strain gradient elasticity theory. The strain gradient effect, couple stress effect, and velocity gradient effect for vibration are included in the new model by only one material length scale parameter for each. The variational formulation and Hamilton’s principle are applied to derive the governing equations and boundary conditions. Both an analytical solution and an isogeometric analysis approach are proposed for static bending and free vibration of the microbeam. A non-uniform rational B-splines (NURBS) isogeometric analysis with high-order continuity can effectively fulfill the higher derivatives of the displacement variables in the reformulated gradient beam model. Convergence studies and comparisons to the corresponding analytical solutions verify the model’s performance and accuracy. Finally, different boundary conditions, material length scale parameters, and beam thicknesses are investigated in order to certify the applicability of the proposed approach. Full article

In this paper, a microstructure-dependent magneto-electro-elastic functionally graded porous (MEEFGP) beam model is proposed using a variational approach. To account for the microstructure effect, the extended modified couple stress theory is incorporated in the new model. In addition, the porosity variation of the two-phase beam model through the thickness direction is also considered. The new developed model is verified in terms of its correctness with a FEM model. Based on the equations of motion and boundary conditions derived by Hamilton’s principle, the static bending and wave propagation behaviors of the new model are analytically determined. The results prove the existence of the microstructure effect and the magneto-electro-elastic multi-field coupling effect. There are significant differences between the new model and the classical model at the microscale. Moreover, the porosity also has an important influence on the mechanical properties of the new model. The results predicted by the new model can provide the theoretical basis for the design of microscale acoustic wave devices and micro-electro-mechanical systems. Full article

In this study, the limits of the Euler–Bernoulli theory in micromechanics are explored. Raman spectroscopy, which is extremely accurate and reliable, is employed to study the bending of a microbeam of a length of 191 μm. It is found that at the micro-scale, the Euler–Bernoulli theory remains an exact and consistent tool, and, possibly, other elasticity theories (such as micropolar theory, gradient elasticity theory, and couple stress theory) are not always required to study this phenomenon. More specifically, good correlation was achieved between the theoretical and experimental results, the former acquired via the theoretical equations and the latter obtained with the use of atomic force microscopy and Raman spectroscopy. The exact predicted strain of an atomic force microscope microbeam under bending, by Euler–Bernoulli equations is confirmed by Raman spectroscopy. Full article

In this paper, a new magneto-electro-elastic functionally graded Timoshenko microbeam model is developed by using the variational formulation. The new model incorporates the extended modified couple stress theory in order to describe the microstructure effect. The power-law variation through the thickness direction of the two-phase microbeams is considered. By the direct application of the derived general formulation, the static bending and free vibration behavior of the newly developed functionally graded material microbeams are analytically determined. Parametric studies qualitatively demonstrate the microstructural effect as well as the magneto-electro-elastic multi-field coupling effect. The proposed model and its classic counterpart produce significant differences for thin graded magneto-electro-elastic Timoshenko microbeams. The thinner the microbeam is, the larger the difference becomes. Full article

Carbonation of hydrated cement paste (HCP) causes numerous chemo–mechanical changes in the microstructure, e.g., porosity, strength, elastic modulus, and permeability, which have a significant influence on the durability of concrete structures. Due to its complexity, much is still not understood about the process of carbonation of HCP. The current study aims to reveal the changes in porosity and micromechanical properties caused by carbonation using micro-beam specimens with a cross-section of 500 μm × 500 μm. X-ray computed tomography and micro-beam bending tests were performed on both noncarbonated and carbonated HCP micro-beams for porosity characterization and micromechanical property measurements, respectively. The experimental results show that the carbonation decreases the total porosity and increases micromechanical properties of the HCP micro-beams under the accelerated carbonation. The correlation study revealed that both the flexural strength and elastic modulus increase linearly with decreasing porosity. Full article

A class of bipolar electrostatically actuated micro-resonators is presented in this paper. Two parametric equations are proposed for changing the microbeam shape of the upper and lower sections. The mechanical properties of a micro-resonator can be enhanced by optimizing the two section parameters. The electrostatic force nonlinearity, neutral surface tension, and neutral surface bending are considered in the model. First, the theoretical results are verified with finite element results from COMSOL Multiphysics simulations. The influence of section variation on the electrostatic force, pull-in behaviors and safe working area of the micro-resonator are studied. Moreover, the impact of residual stress on pull-in voltage is discussed. The multi-scale method (MMS) is used to further study the vibration of the microbeam near equilibrium, and the relationship between the two section parameters of the microbeam under linear vibration was determined. The vibration amplitude and resonance frequency are investigated when the two section parameters satisfy the linear vibration. In order to research dynamic analysis under the case of large amplitude. The Simulink dynamics simulation was used to study the influence of section variation on the response frequency. It is found that electrostatic softening increases as the vibration amplitude increases. If the nonlinearity initially shows hardening behavior, the frequency response will shift from hardening to softening as the amplitude increases. The position of softening-hardening transition point decreases with the increase of residual stress. The relationship between DC voltage, section parameters, and softening-hardening transition points is presented. The accuracy of the results is verified using theoretical, numerical, and finite element methods. Full article