Longitudinal vibrations of a composite isotropic plate

Approximate integration of the longitudinal vibrations equations for composite plates is considered. A numerical investigation is performed of the potential energy distribution in a two-layered ring when a pulsating pressure acts on the inner contour.Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 20, pp. 63–67, 1989.     

Calculation of nonlinear vibrations of a viscoelastic bar

The problem of forced nonlinear vibrations of a viscoelastic bar is reduced by the Bubnov—Galerkin method to a nonlinear integro-differential equation. Transverse vibrations with small amplitude are considered, and therefore the approximate solution is constructed by the small-parameter method.     

Chaotic vibrations in nonlinear problems of bar structures

In the response of nonlinear mathematical models which describe vibrations of structural elements one could observe an irregular behaviour which is called chaos. Loss of the information on initial states in deterministic dynamical systems after a short time of theirs evolution, increasing amplitudes of displacements, velocities and accelerations, sensitive dependency on initial conditions makes chaos dangerous phenomenon in mechanics of construction. In this article quantitative (bifurcation diagrams, Poincare sections and Fourier power spectrum analysis) identication methods of the chaotic dynamics in geometrically nonlinear model of one DOF Mises truss are shown. Main goal of this article is to show and verify dangerous influence of chaos (in the engineering sense) on the analyzed structure. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural vibrations of composite viscoelastic cylinders

Free damping spatial and axisymmetrical vibrations of short cylinders consisting of elastic and viscoelastic layers are considered. A numerical study is made of the dependence of natural frequencies and damping coefficients on the ratio of geometric cylinders.Translated from Dinamicheskie Sistemy, No. 5, pp. 55–58, 1986.     

Coupled damping vibrations of composite structures

This paper summarizes the results of a series of papers on developing methods for deter-mining elastic-dissipative characteristics of polymer composite materials (PCM) and predicting the corresponding dynamical responses from structures. For a prismatic anisotropic bar which is arbitrarily oriented with respect to the axes of elastic symmetry of an orthotropic plate, a mathematical model and a method for solving the problem of damping bending-torsional vibrations are developed. The interaction between the vibration modes of a composite bar is examined. Basic provisions of an iterative method for determining elastic and dissipative characteristics of PCM are formulated. Mathematical models of damping vibrations of fibrous composite thin-walled bars and plates are developed, and a two-stage method for solving the resulting complex eigenvalue problems is put for-ward. The effect of the composition and the reinforcement structure on the eigenfrequencies and the coefficients of mechanical losses of the structures in question is discussed. Controlability of the values of resonance frequencies and the coefficients of the mechanical losses due to variation of the degree of anisotropy of fiber materials and the degree of inhomogeneity of the structure over thickness has been demonstrated. The widely used method of potential energy of eigenforms is shown as being capable of providing correct values of the coefficients of mechanical losses only up to η = 0.02–0.03, resulting in significant errors for higher dissipative characteristics of composite structures. For the method presented, examples of practical implementation in developing vibration absorptive composite structures are given.     

Effective wave propagation in a prestressed nonlinear elastic composite bar

The problem of determining the effective incremental responseof nonlinearly elastic composite materials given some initialprestress is of interest in numerous application areas. In particular,the case when small-amplitude elastic waves pass through a prestressedinhomogeneous structure is of great importance. Of specificinterest is how the initial finite deformation affects the microstructureand thus the subsequent response of the composite. Modellingthis effect is in general extremely difficult. In this article,we consider the simplest problem of this type where the materialis a one dimensional composite bar consisting of two distinctphases periodically distributed. Neglecting lateral contractions,the initial deformation is thus piecewise homogeneous and wecan therefore determine the incremental behaviour semi-analytically,given the constitutive behaviour (strain energy function) ofthe phases in question. We apply asymptotic homogenization theoryin the deformed configuration in order to find the effectiveresponse of the deformed material in the low-frequency limitwhere the wavelength of the propagating waves is much longerthan the characteristic length scale of the microstructure.We close by considering the arbitrary frequency case and illustratehow the initial deformation affects the location of stop bandsand pass bands of the material. Work is under way to confirmthese results experimentally.     

Torsion of a composite,viscoelastic prismatic bar of rectangular cross-section

The generalization of Ilyushin's approximation method is used to determine the stresses in the quasistatic problem of torsion of a composite, layered viscoelastic prismatic bar of rectangular cross-section. Numerical computations are carried out for the special case of a step function torsional moment.     

Nonlinear flexural vibrations of composite shallow open shells

This paper addresses geometrically nonlinear flexural vibrations of open doubly curved shallow shells composed of three thick isotropic layers. The layers are perfectly bonded, and thickness and linear elastic properties of the outer layers are symmetrically arranged with respect to the middle surface. The outer layers and the central layer may exhibit extremely different elastic moduli with a common Poisson's ratio ν. The considered shell structures of polygonal planform are hard hinged supported with the edges fully restraint against displacements in any direction. The kinematic field equations are formulated by layerwise application of a first order shear deformation theory. A modification of Berger's theory is employed to model the nonlinear characteristics of the structural response. The continuity of the transverse shear stress across the interfaces is specified according to Hooke's law, and subsequently the equations of motion of this higher order problem can be derived in analogy to a homogeneous single-layer shear deformable shallow shell. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Natural vibrations of a strip made of a composite material with a locally curved structure

The possibility of using the finite-element method for investigating two-dimensional problems on natural vibrations in the mechanics of composite materials with curved structures is considered. With the example of a hinge-supported strip made of a composite material with a locally curved structure, the influence of geometrical and mechanical parameters of the strip on its eigenfrequencies is examined. It is established that the presence of local curving in the structure of strip material decreases the magnitude of eigenfrequencies.Translated from Mekhanika Kompozitnykh Materialov, Vol. 41, No. 1, pp. 71–78, January–February, 2005.     

Analysis of free damped vibrations of laminated composite cylindrical shells

Damped free vibrations of multilayered composite cylindrical shells are investigated. Vibration and damping analysis of cylindrical shells is performed by using the first-order shear deformation theory (FOSDT). Based on other researchers' works, two damping models are developed, i.e., the energy method (EM), and the method of complex eigenvalues (MCE). Several numerical examples of the damped free vibration problem of laminated composite cylindrical shells have been solved and comparison has been made with the results of other authors.Published in Mekhanika Kompozitnykh Materialov, Vol. 31, No. 5, pp. 646–659, September–October, 1995.     

Nonlinear parametric vibrations of cylindrical shells made from composite materials

The dynamic properties of a hinged shell made from a composite material and subjected to combined loads are investigated by means of an orthotropic model. The problem is solved by means of the geometrically nonlinear dynamic equations of the theory of sloping shells, set up on the basis of the Kirchhoff-Love hypothesis. Various cases of loading are considered, i.e., the combined action of a longitudinal pulsating load and an external static pressure and also of a pulsating external pressure and a static axial compression. The wave processes at the middle surface are not taken into account. The system of resolvents is obtained by consecutive application of the variation and averaging methods. The results of the calculations are presented graphically and are analyzed in detail.Moscow. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 531–539, May–June, 1973.     

Active suppression of nonlinear composite beam vibrations by selected control algorithms

This paper is focused on application of different control algorithms for a flexible, geometrically nonlinear beam-like structure with Macro Fiber Composite (MFC) actuator. Based on the mathematical model of a geometrically nonlinear beam, analytical solutions for Nonlinear Saturation Controller (NSC) are obtained using Multiple Scale Method. Effectiveness of different control strategies is evaluated by numerical simulations in Matlab–Simulink software. Then, the Digital Signal Processing (DSP) controller and selected control algorithms are implemented to the physical system to compare numerical and experimental results. Detailed analysis for the NSC system is carried out, especially for high level of amplitude and wide range of frequencies of excitation. Finally, the efficiency of the considered controllers is tested experimentally for a more complex autoparametric “L-shape” beam system.     

Torsional vibrations and dispersion of torsional waves in orthotropic composite rods

The Barr’s refined theory of torsional vibrations of isotropic rods of noncircular cross section is generalized for an orthotropic material. An analysis of natural frequencies of torsional vibration of free-free orthotropic prismatic rods of rectangular cross section is carried out with the help of an exact solution of the frequency equation. For orthotropic CFRP and GFRP rods, the improved theory, which takes into account the normal stresses and inertia forces in the axial direction, in some cases, predicts a noticeable raise in the natural frequencies compared with those following from the Saint-Venant classical theory. A good agreement is obtained between the experimental and calculated values of natural frequencies of torsional vibrations of rectangular quartz and fiber glass rods. The dispersion of torsional waves in an orthotropic quasi-homogeneous rod is considered. __________ Translated from Mekhanika Kompozitnykh Materialov, Vol. 44, No. 2, pp. 165–182, March–April, 2008.     

Dynamic interaction of an elastic medium with a thin-walled curvilinear piezoelectric inclusion under longitudinal vibrations of a composite

Using the method of matched asymptotic expansions, we obtain models of dynamic interaction of a thin-walled curvilinear piezoelectric inclusion of variable thickness with an elastic isotropic matrix under stationary vibrations of the composite. The elastic system is under conditions of longitudinal shear. Different cases of electric boundary conditions on the surface of the heterogeneity are considered. We propose an algorithm for the construction of boundary layer corrections for refining the behavior of displacements and stresses in the vicinity of the edge of the inclusion for its different shapes.