Dynamics and stability analysis of a flexible liquid-filled rotor in a constant thermal environment

In this study, the dynamics and stability of a flexible rotor containing liquid in a constant thermal environment are investigated. According to thermoelastic theory, the thermal axial force exerted on the rotor is calculated by using the analytical method. A spinning Rayleigh beam is used as a simplified model of the rotor. Applying the Hamilton principle, the governing equation of motion for the flexible liquid-filled rotor system is derived. Using the obtained model, the stability prediction model and the critical spinning speed for the rotor system are formulated. To demonstrate the validity of the developed model, the present analysis is compared with the results reported in the previous study, and good agreement is observed from the comparison results. Finally, numerical results based on the obtained model are performed for a better understanding of the parameters including filling parameters, mode number, rotatory inertia and thermal effect on the stability, and critical spinning speed of the rotor system.

On the decay of the energy for radial solutions in Moore–Gibson–Thompson thermoelasticity

In this paper, we consider the Moore–Gibson–Thompson thermoelastic theory. We restrict our attention to radially symmetric solutions and we prove the exponential decay with respect to the time variable. We demonstrate this fact with the help of energy arguments. Later, we give some numerical simulations to illustrate this behaviour.

The Effect of a Hyperbolic Two-Temperature Model with and without Energy Dissipation in a Semiconductor Material

In this work, the new model of photothermal and elastic waves, with and without energy dissipation, under a hyperbolic two-temperature model, is used to compute the displacement, carrier density, thermodynamic temperature, conductive temperature and stress in a semiconductor medium. The medium is considered in the presence of the coupling of plasma and thermoelastic waves. To get the complete analytical expressions of the main physical fields, Laplace transforms and the eigenvalue scheme are used. The outcomes are presented graphically to display the differences between the classical two-temperature theory and the new hyperbolic two-temperature theory, with and without energy dissipation. Based on the numerical results, the hyperbolic two-temperature thermoelastic theory offers a finite speed of mechanical waves and propagation of thermal waves.

Analysis of the Thermoelastic Damping Effect in Electrostatically Actuated MEMS Resonators

An important aspect that must be considered when designing micro-electro-mechanical systems (MEMS) for all domains, including robotics, is the thermoelastic damping which occurs when the MEMS material is subjected to cyclic stress. This paper is focused on a model for the thermoelastic damping developed based on the generalized thermoelastic theory with the non-Fourier thermal conduction equation. The model was implemented in MATLAB and several simulations were performed. The theoretical results show a decrease in the deflection amplitude with the increase in time. The deflection amplitude decrease was validated by the experimental investigations, consisting of measuring the loss in amplitude and velocity of oscillations as a function of time. Moreover, this paper also presents the influence of the geometric dimensions on the mentioned decrease, as well as on the initial and final values of the amplitude for several polysilicon resonators investigated in this paper.