Andrzej Tylikowski

Vibration of a non-linear single degree of freedom system due to poissonian impulse excitation

Abstract The behaviour of a non-linear single degree of freedom system, subjected to a random excitation in the form of Poissonian impulse sequence is investigated. The stochastic linearization technique and the generalized FPK equation are used to obtain a characteristic function and moments of system response probability distribution. A digital simulation method is applied to verify the results obtained.

Effects of piezoactuator delamination on the transfer functions of vibration control systems

Abstract The purpose of this theoretical work is to present a general bending–extensional model of the response of a simply supported laminated beam to excitation by a nonsymmetric actuator made using piezoelectric elements. The edge delamination is modeled by changing the effective length of debonded actuator. Dynamic equations, joint conditions between sections with and without active layers as well as the boundary conditions at the two ends of the beam form a boundary value problem. The dynamic strain response to the excitation by the applied voltage term is determined from the solution of this boundary value problem. The dynamic extensional strain on the beam surface is calculated by including the free stress conditions at the piezoelectric actuator boundaries, by considering the dynamic coupling between the actuator and the beam, and by taking into account a finite bonding layer with the finite stiffness. The analysis indicates that the edge delamination has a harmful effect on the performance of piezoactuators, but the significant decrease of natural frequencies with an increase in delamination length is not observed. The influence of the delamination length on the system transfer functions (the beam surface strain, the beam transverse displacement and the shear stresses in bonding layers) is shown.

Dynamic stability of viscoelastic shells under time-dependent membrane loads

Abstract The stability of the undeflected middle surface of a uniform Voigt-Kelvin cylindrical circular shell is studied. The shell is being subjected to a time-varying axial compression as well as a time-varying uniformly distributed radial loading. Using the direct Liapunov method sufficient criteria for the asymptotic stability and the almost sure asymptotic stability are obtained. Asymptotic stability regions as functions of a reduced retardation time, geometric and material parameters of shell and characteristics of loading are calculated. It was shown that the stability regions do not change qualitatively in going from a Gaussian force to a harmonic one. The change of membrane loading direction from the axial direction to the circumferential one on the stability regions is also discussed.

Dynamic stability of rotating shafts

SummaryIn the paper, using the direct method, stability of elastic rotating shafts (beams, pipes) working in different conditions is analysed. It is taken into consideration a constant axial force as well as a uniformly distributed load in the case of long shafts. The case of conservative load (e.g. dead weight) as well as nonconservative load acting tangentially to the shaft axis is considered. The case when the force is a wide-band Gaussian stochastic process is also discussed.ÜbersichtMit der direkten Methode von Ljapunov wird die Stabilität von sich um die Längsachse drehenden elastischen Wellen (Rohre, Balken) unter verschiedenen Arbeitsbedingungen untersucht. Bei Wellen mit vertikaler Achse wird außer einer konstanten Längskraft auch eine gleichmäßig über die Länge der Welle verteilte Belastung berücksichtigt. Es wird dabei sowohl die konservative Belastung (Eigengewicht) als auch die in der Wellenachse gelegene, tangential wirkende, nichtkonservative Belastung und schließlich der Fall einer Längskraft aus einem breitbandigem Gaußschen stochastischen Prozeß betrachtet.

Stability and stabilization of circular plate parametric vibrations

The stability of parametric vibrations of circular plate subjected to in-plane forces is analyzed by the Liapunov method. Assuming that the compressing forces are physically realizable ergodic processes the plate dynamics is described by stochastic classical partial differential equations. The energy-like functional is proposed; its positiveness is equivalent to the condition in which static buckling does not occur. Taking into account that a plate is compressed radially by time-dependent and uniformly distributed along its edge forces, a dynamic stability of an undeflected state of isotropic elastic circular plate is analyzed. The rate velocity feedback is applied to stabilize the plate parametric vibration. The critical damping coefficient has been expressed by the variance and the mean value of compressing force. The admissible variances of loading strongly depend on the feedback gain factor.

Dynamic stability of non-linear antisymmetrically laminated angle-ply plates

Abstract The dynamic stability problem is solved for rectangular plates compressed by time-dependent deterministic or stochastic membrane forces. The angle-ply antisymmetrically laminated plates with a twisting-extensional coupling are considered. Moderately large deflection equations taking into account a coupling of in-plane and transverse motion are used. The asymptotic stability and almost sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunovs direct method. A relation between the stability of non-linear equations and linearized ones is analyzed. An influence of the number of layers, a plate aspect ratio, material properties, a lamination angle, a constant component of in-plane force for different classes of parametric excitation on stability regions is shown.

DYNAMICAL INSTABILITY ANALYSIS OF NANOTUBES USING NONLOCAL SHEAR BEAM THEORY

The dynamics stability of distributed systems (continua) has been an object of considerable attention over the past half century. Numerous papers are available on isotropic and laminated beams, shafts, plates and shells under periodic and random forces. Most papers have applied finite dimensional or modal approximations in the analysis of vibration and stability. This paper focuses on the stochastic parametric vibrations of micro- and nanorods based on Eringens nonlocal elasticity theory and shear beam theory. The almost sure asymptotic instability criteria involving a damping coefficient, structure and loading parameters are derived using Liapunovs direct method. Using the appropriate energy-like Liapunov functional, sufficient conditions for the almost sure asymptotic instability of undeflected form of beam are derived. The nonlocal shear beam accounts for the scale effect, which becomes significant when dealing with short micro- and nanorods. From the obtained analytical formulas it is clearly seen that the small scale effect increases the dynamic instability region. Instability regions are functions of the axial force variance, the constant component of axial force and the damping coefficient.

Semiactive control of a shape memory alloy hybrid composite rotating shaft

Abstract In this paper the technique of the dynamic stability analysis proposed for the conventional laminated structures is extended to the activated shape memory alloy (SMA) hybrid rotating shafts under the time-dependent compressive axial loading. The influence of the activation through the change of the temperature on the dynamic stability domains is examined. Changing with the temperature the Youngs modulus of SMA fibers enters into a global stiffness parameter of the shaft. Thermally induced membrane forces in SMA fibers and changing with temperature damping coefficient also modify shaft dynamic equations. The activated SMA hybrid shaft is treated as a beam-like structure. The thin-walled composite shaft is flexible thus it should be supported on the both ends in order to avoid large deflections. By using the standard stability technique we arrive at the effective sufficient criterion of the dynamic and almost sure stochastic stability. The stability regions are given as functions of the loading characteristics, the external damping coefficient, the lamination angle, and the properties of the shaft material. The results indicate that the global activation causes an increase of the critical (admissible) axial force both for the glass–epoxy/NiTi–epoxy and for the graphite–epoxy/NiTi–epoxy hybrid shafts.

Instability of Thermally Induced Vibrations of Carbon Nanotubes via Nonlocal Elasticity

The dynamic stability problem of single-walled carbon nanotube embedded in a viscoelastic matrix under time-dependent temperature field is studied. Using nonlocal continuum mechanics parametric vibrations of the nano-scale Euler–Bernoulli beams are investigated. A theory of nonlocal elasticity with kernels of Helmholtz and bi-Helmholtz type is applied. The tube axial loading is caused by the Gaussian physically realizable temperature changes. The energy-like functionals are used in the instability analysis. Instability domains in the space of geometric and material parameters as well as temperature variance are presented.

DYNAMIC STABILITY OF ROTATING COMPOSITE SHELLS WITH THERMOACTTVE SHAPE MEMORY ALLOY FIBERS

In this article the technique of the dynamic stability analysis proposed for the conventional laminated shells is extended to the activated shape memory alloy hybrid cylindrical shells. The thin symmetrically balanced laminated shell contains both the conventional (e.g., graphite or glass) fibers oriented at +ϑ and − ϑ to the shell axis and the activated shape memory alloy fibers axially oriented. Rotary and coupling inertias are neglected. The rotating with a constant angular velocity shell is simply supported at the edge hoops. The effect of returning to the original geometry after a large inelastic deformation is called the shape memory effect. Changing the temperature of the layer we modify the basic mechanical properties such as Youngs modulus and the damping coefficient. The purpose of this article is to solve the dynamic stability problem and to answer the question, how does the temperature activation change dynamic stability domains of the shell. Using the standard stability technique leads to th...