Mathematical modeling of MEMS elements subjected to external forces, temperature and noise, taking account of coupling of temperature and deformation fields as well as a nonhomogenous material structure

Use of Bispectrum Analysis to Inspect the Non-Linear Dynamic Characteristics of Beam-Type Structures Containing a Breathing Crack

“…V.A. Krysko-Jr. concluded in [ 41 ] that with the increase in the external transverse load, even a relatively small intensity of white noise has an essential influence on the character of structural vibrations. Theoretically, the bispectrum analysis method used for this paper was immune to Gaussian noise.…”

Thermoelastic vibrations of a Timoshenko microbeam based on the modified couple stress theory

“…(1) By θ = T − T 0 , we denote the temperature change with respect to the initial temperature T 0 , and we assume that the shear deformations generated by the temperature change can be neglected. Then, in the case of a linear, isotropic and homogeneous body, heat (T ) and mechanical (M) deformations are governed by the following formula [100]…”

“…In the case when beam thickness (in direction of the O Z axis) and its width (in direction of the OY axis) is sufficiently small in comparison to the beam length (in direction of the O X axis), then assumption of the plane stress state implies that all components of the stress tensor in directions of the axes OY and O Z are equal zero (σ 12 = σ 22 = σ 32 = 0, σ 23 = σ 33 = 0). However, in the case of the Timoshenko beams we have σ 13 = 0 [100]. In the latter case, components of the deformations tensor can be recast to the following simple form…”

“…Phase synchronization of beam vibrations versus both character and intensity of the applied temperature field is investigated. A mathematical model describing the nonlinear dynamics of a plate-beam system is proposed in [100]. The model takes account of coupling between temperature and deformation fields as well as external mechanical, temperature, and noise excitations.…”

Nonlinear dynamics of a third-order reduced model of thermomechanically coupled plate under different thermal excitations

“…Recently, a two-way coupled ROM with three mechanical and two thermal variables has been used to investigate the role played by mechanical and thermomechanical impedances in forecasting bifurcation events in a beam, with also experimental validation, as well as the influence of slowly changing thermal loads on the beam post-buckled and snapthrough vibrations [26]. A general theory to study nonlinear dynamics of beam-plate structures for MEMS devices, taking into account the coupling of deformation and temperature fields, has also been proposed, however with the coupling being neglected in the particular case of quasi-static formulation considered as application [27]. Overall, getting rid of the complicatedness generally occurring in the analysis and interpretation of nonlinear phenomena when using richer (e.g., finite element) models, low-order models preserving the main features of the underlying continuum formulations may allow easier analyses and deeper understanding of the basic, yet possibly involved, effects of coupling on the finite amplitude vibrations of geometrically nonlinear structures.…”