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Sensitivity and resolution of an atomic force microscope (AFM) can be affected by the nonlinear vibrational behavior of its microcantilever. So, the main purpose of this paper is to analyze the chaotic vibration of an AFM microcantilever under base excitation. Based on the modified couple stress theory (MCST) and the Euler–Bernoulli beam model, the...
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Some complex engineering structures can be modeled as multiple beams connected through coupling elements. When the coupling element is elastic, it can be simplified as a mass-spring system. The existing studies mainly concentrated on the double-beam coupled through elastic connectors, where the connector is simplified as the equivalent linear stiff...
Citations
... Among these, the modified couple stress theory has garnered preference due to its balanced combination of accuracy and ease of application in modeling. Of these, the modified couple stress theory has gained favor due to its balance between accuracy and simplicity of application in modeling [9][10][11][12][13][14][15][16]. In the modified couple stress theory, the strain energy is a function of both the curvature tensor and the strain tensor. ...
This paper investigates the instability and buckling characteristics of a porous microplate under the influence of electrostatic fields, taking into account the implications of the intermolecular Casimir forces. Employing the modified couple stress theory, this research formulates equations that encapsulate the interplay between electrostatic and Casimir forces within porous plates. The analysis integrates distributed support loads, employing both Galerkin mode summation and finite element methods to solve static deformation equations and determine pull-in instability voltages and buckling loads. A novel approach is introduced, and equilibrium relationships are derived with respect to displacement to determine both the buckling load and instability voltage. This study effectively compares classical and non-classical theories, scrutinizing the effects of dimensionless length scale parameters and porosity ratios on maximum displacement, pull-in instability voltages, and buckling loads. The results demonstrate that the analytical method converges swiftly and aligns with the findings of the finite element method. The method for deriving equilibrium relationships proves to be accurate in predicting both instability voltage and buckling load. Additionally, the instability voltage exhibits an almost linear relationship with variations in the percentage of porosity, and similarly, the buckling load undergoes linear changes with alterations in porosity percentage. Hence, formulas for the linear relationships are calculated for both of these associations.
