Automatic locking of a parametrically resonating, base excited, nonlinear beam

Presented is a closed-loop, phase control scheme of a parametrically excited nonlinear structure, capable of stabilizing open-loop unstable solutions while automatically locking onto a desired point on any solution branch. Axially driven slender beams develop large transverse vibration under suitable amplitude and precise frequency base-excitation. The latter can induce parametric excitation along with a nonlinear response. The phase-lag of the 2:1 response over the excitation serves as a tunable parameter affecting the operating point of steady vibrations of a limit cycle. The operating point is tuned to exhibit great sensitivity to small interaction forces thus paving the way towards an ultrasensitive sensor. The paper analyzes the behavior of the mentioned configuration using asymptotic analysis, numerical simulations and an experimental system. Detailed analysis of the dynamical behavior, experimental verifications and demonstrations shed light on some features of the system dynamics.

Applied theory of bending vibration of the piezoelectric and piezomagnetic bimorph

Based on the variational principle, equations and boundary conditions for transverse steady vibrations of a bimorph consisting of a piezoelectric and piezomagnetic layers are obtained. The results of calculations of natural frequencies are compared with the finite element model of the device in ACELAN.

Steady vibration problems in the coupled linear theory of porous elastic solids

This paper concerns the coupled linear theory of elasticity for isotropic porous materials. In this theory the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The basic internal and external boundary value problems (BVPs) of steady vibrations are investigated. Indeed, the fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions, and its basic properties are presented. The radiation conditions are established and Green’s identities are obtained. The uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single layer and double layer) and volume potentials are constructed and the basic properties of these potentials are given. Finally, the existence theorems for classical solutions of the BVPs are proved by means of the potential method (boundary integral equation method) and the theory of singular integral equations.

Boundary Integral Equations Method in the Coupled Theory of Thermoelasticity for Porous Materials

This paper concerns with the coupled linear theory of thermoelasticity for porous materials and the coupled phenomena of the concepts of Darcy’s law and the volume fraction is considered. The system of governing equations based on the equations of motion, the constitutive equations, the equation of fluid mass conservation, Darcy’s law for porous materials, Fourier’s law of heat conduction and the heat transfer equation. The system of general governing equations is expressed in terms of the displacement vector field, the change of volume fraction of pores, the change of fluid pressure in pore network and the variation of temperature of porous material. The fundamental solution of the system of steady vibration equations is constructed explicitly by means of elementary functions and its basic properties are presented. The basic internal and external boundary value problems (BVPs) of steady vibrations are formulated and on the basis of Green’s identities the uniqueness theorems for the regular (classical) solutions of the BVPs are proved. The surface (single-layer and double-layer) and volume potentials are constructed and their basic properties are established. Finally, the existence theorems for classical solutions of the BVPs of steady vibrations are proved by means of the boundary integral equations method (potential method) and the theory of singular integral equations.

Fundamental solutions in the linear theory of thermoelasticity for solids with triple porosity

This paper deals with the fully coupled linear theory of thermoelasticity for triple porosity materials. The system of general governing equations of motion is expressed in terms of the displacement vector field, the pressures in the three pore systems (macro-, meso- and micropores) and the temperature. The fundamental solutions are constructed explicitly by means of elementary functions for the five special cases of the equations of motion: (1) equations of steady vibrations; (2) equations in the Laplace transform space; (3) equations of steady vibrations in the quasi-static theory; (4) equations of equilibrium; and (5) equations of steady vibrations for rigid body with triple porosity. Finally, the basic properties of these solutions are established.

Feed Material Influence on the Dynamics of the Suspended Screen at Its Steady State Operation and Transient States

The influence of the feed material on steady vibrations as well as on the transient resonance during the start-up and coasting of the suspended screen, was analysed in the hereby paper. The influence of the feed material presence on the possibility of performing the first half-turn of the vibrator was also established. The original, feed material simulation model reflecting its layer properties and diversification of feed particles vibrations along the screen riddle – specially developed for this aim – was applied in investigations.