The paper investigates the nonlinear modal interaction of longitudinal and bending vibrations of a beam resonator under periodic thermal loading. The mode of parametric oscillations is investigated under conditions of internal multiple resonance between some flexural and longitudinal forms of free oscillations of the resonator. The possibility of generation in the system of the longitudinal-bending mode was found, the frequency of the slow envelope of which essentially depends on the parameter of the internal frequency detuning, which is directly related to the magnitude of external disturbances subject to high-precision measurement.

The present article is the first part of the work devoted to investigation of the nonlinear dynamics of parametrically excited flexural vibrations of a clamped-clamped microbeam - the basic sensitive element of a promising class of microsensors of various physical quantities - under laser thermooptical action in the form of periodically generated pulses acting on a certain part of the surface of the beam element. An analytical solution of the heat transfer problem is found for the steady harmonic distribution of temperature in the volume of the resonator. The static and dynamic components of temperature-induced axial force and bending moment are determined. Using the Galerkin method, the discretization of nonlinear coupled partial differential equations describing the longitudinal-flexural oscillations of the resonator is performed. Using the asymptotic method of multiple time-scales, an approximate analytical solution is obtained for the nonlinear dynamics problem under the conditions of primary parametric resonance.

This work is devoted to numerical and partly experimental investigation of the electromechanical models of micro and nanoresonators. The main purpose of this resonators is detected the adherence of micro or nanoparticles and measurement its mass. The periodical oscillations of mono and many layers nanocapacitors, from which nanoresonator situated in electric field is constructed, are studied. The purpose of this work is creating of electromechanical models of MEMS and NEMS the aim of which is to identify the changes introduced into dynamic systems due to adhesion of micro or nanoparticles. It’s significant to note that the time of overcharge of the nano-capacitor is much less, then the period of excited oscillations. This fact gives the possibility to apply asymptotic methods in numerical investigation. Physical experiments similar in model to the electromechanical nanoresonators were carried out. This work is an extended review article based on the results of previous our works.

In the presented work, a model of a microelectromechanical accelerometer with two movable beam elements located between two fixed electrodes is proposed. The action of the transfer forces of inertia in the longitudinal direction leads to a change in the spectral properties of the system, which is a useful output signal of the sensor. The dynamics of the system in the presence of a weak electrostatic coupling between the sensitive elements is characterized by the phenomenon of modal localization - a significant change in the amplitude ratios for the forms of inphase and antiphase oscillations with small changes in the measured component of the acceleration vector of the moving object. Diagrams of equilibrium positions are plotted for varying the potential difference between a fixed electrode and a movable element and between two movable elements. The dependences of the frequencies and the ratio of the components of the eigenvectors on the magnitude of the inertial action are investigated. It is shown that the sensitivity of a sensor based on modal localization can be orders of magnitude higher than the sensitivity of known systems based on measuring the shift of natural frequencies. A nonlinear dynamic model of an accelerometer with external harmonic electrostatic excitation of oscillations is constructed. Resonance characteristics are obtained, a comparison is made between the model describing the modal characteristics of the system and the model describing the real dynamic mode of operation taking into account nonlinear factors.