Dynamic stability of a viscoelastic cylindrical panel with concentrated masses

We discuss the problem of the dynamic stability of a viscoelastic cylindrical panel with concentrated masses in a geometrically nonlinear formulation that is based on the Kirchhoff-Love hypothesis. The effect of the action of concentrated masses is introduced into the equation of motion of a cylindrical panel using the Dirac δ-function. The problem is solved by the Bubnov-Galerkin method based on a polynomial approximation of deflections together with a numerical method based on the use of quadrature formulas. The choice of the Koltunov-Rzhanitsyn singular kernel is justified. Comparisons between the results obtained from different theories are presented. The Bubnov-Galerkin method convergence is investigated for all problems. The effect of the material viscoelastic properties and concentrated masses on the process of the dynamic stability of a cylindrical panel is shown. __________ Translated from Problemy Prochnosti, No. 4, pp. 132–147, July–August, 2008.     

Procedure for numerical investigation of forced vibrations of three-dimensional structures with nonlinear elastic elements based on the finite-element method

We describe a numerical procedure which allows one to investigate forced vibrations of complex three-dimensional structures with nonlinear elastic elements, develop a computational dynamic model on the basis of the finite-element method and the method of generalized coordinates, and investigate vibrations of an actual structure of a load-bearing mounting of an aircraft engine. We also analyze the effect of nonlinear elastic elements on the dynamic behavior of the structure and evaluate the efficiency of their application. Kiev State Technical University of Civil Engineering and Architecture, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 4, pp. 107–116, July–August, 1997.     

Analysis of the stressed state of a circular thin-walled cylinder under complex loading and with nonlinear hardening of the material

The generalized differential equations of plastic flow for a material with nonlinear hardening are derived using the Prager kinematic model. An example of numerical analysis for stress variation under elastoplastic deformation of a thin-walled cylinder of a structural carbon steel is given for different elastoplastic material models. Translated from Problemy Prochnosti, No. 3, pp. 58–65, May–June, 2009.     

Nonlinear vibrations of hydraulic shock absorbers

A method of equivalent linearization for a nonlinear dynamic system of vibrations with a hydraulically elastic shock absorber is presented. An integral estimation of the exact and approximate solutions is obtained. It is shown that with an appropriate choice of the parameter λ the linearized dynamic system differs insignificantly from the nonlinear one. The influence of nonlinear factors on the coefficients of the dynamic rigidity and transmission has been established. These results agree well with the experimental curves published in the foreign scientific literature. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 6, pp. 1154–1157, November–December, 2008.     

Iterative mesh partitioning optimization for parallel nonlinear dynamic finite element analysis with direct substructuring

 This work presents a novel iterative approach for mesh partitioning optimization to promote the efficiency of parallel nonlinear dynamic finite element analysis with the direct substructure method, which involves static condensation of substructures' internal degrees of freedom. The proposed approach includes four major phases – initial partitioning, substructure workload prediction, element weights tuning, and partitioning results adjustment. The final three phases are performed iteratively until the workloads among the substructures are balanced reasonably. A substructure workload predictor that considers the sparsity and ordering of the substructure matrix is used in the proposed approach. Several numerical experiments conducted herein reveal that the proposed iterative mesh partitioning optimization often results in a superior workload balance among substructures and reduces the total elapsed time of the corresponding parallel nonlinear dynamic finite element analysis. Received 22 August 2001 / Accepted 20 January 2002     

Nonlinear forced vibration of damped plates coupling asymptotic numerical method and reduction models

This work concerns the computation of the nonlinear solutions of forced vibration of damped plates. In a recent work (Boumediene et al. in Comput Struct 87:1508–1515, 2009), a numerical method coupling an asymptotic numerical method (ANM), harmonic balance method and Finite Element method was proposed to resolve this type of problem. The harmonic balance method transforms the dynamic equations to equivalent static ones which are solved by using a perturbation method (ANM) and the finite element method. The numerical results presented in reference (Boumediene et al. in Comput Struct 87:1508–1515, 2009) show that the ANM is very efficient and permits one to obtain the nonlinear solutions with few matrix triangulation numbers compared to a classical incremental iterative method. However, putting a great number of harmonics (6 or greater) into the load vector leads to tangent matrices with a great size. The computational time necessary for the triangulation of such matrices can then be large. In this paper, reduced order models are proposed to decrease the size of these matrices and consequently the computational time. We consider two reduced bases. In the first one, the reduced basis is obtained by the resolution of a classical eigenvalue problem. The second one is obtained by using the nonlinear solutions computed during the first step of the calculus which is realized with the ANM. Several classical benchmarks of nonlinear damped plates are presented to show the efficiency of the proposed numerical methods.     

Influence of gas bubbles on nonlinear dynamic characteristics of the oil film of a tilting pad bearing

The influence of a comparatively low volume concentration of gas microbubbles contained in oil on nonlinear characteristics describing the behavior of an oil film in the guide gap of a hydrodynamic tilting pad bearing under action of a low-frequency harmonic force is analyzed using a numerical dynamic model of a collar-oil film-pad system. It is shown that bubbles in the oil greatly affect the efficiency of the tilting pad bearing. Results of oil-film-dynamics investigations reported previously (including those of the present author) are generalized. Ship Building S. O. Makarov Institute, Nikolaev, Ukraine. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 69, No. 1, pp. 90–97, January–February, 1996.     

Determination of the amplitude-frequency characteristic of a vibroprotective system with two-mass pendulum damper in the linear statement

We study the dynamic behavior of a vibroprotective system with a two-mass pendulum damper. By using the Ritz averaging method, we deduce the equations for the amplitude-frequency characteristics of this system in the linear statement. A numerical method for the evaluation of the damper adjusted parameters is proposed. Translated from Problemy Prochnosti, No. 6, pp. 100–109, November–December, 2008.     

Nonlinear dynamic buckling of asymmetrical suspended roofs under step loading

In the present investigation, the nonlinear static as well as dynamic buckling of asymmetrical suspended roofs, acted upon by step conservative loading of infinite duration is examined in detail. This is achieved via a two-degrees-of-freedom imperfect dissipative model simulating the real roof structure. Natural and complementary equilibrium paths are determined for different characteristic values of the parameters involved, revealing a variety of equilibrium configurations. Evolution from symmetry to asymmetry, especially for high roofs, changes the static response from limit point instability to monotonically rising stable paths and increases the amplitude of horizontal displacement. For all cases considered the corresponding dynamic response is associated with point attractors, being either remote stable physical equilibria or prebuckling fixed points, simultaneously locally and globally asymptotically stable, although the dynamic buckling phenomenon has already occurred. The main feature of suspended roofs – sensitivity to horizontal vibrations – is captured by the proposed model, while eliminating the effect of suspension the model yields snap–through buckling as expected.     

Non-linear vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated mass

Summary In the present paper, the problems of the vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated mass are investigated, based on the Kirchhoff-Love hypothesis in the geometrically non-linear statement. The effect of the action of concentrated mass is introduced into the equation of motion of the cylindrical panel using the δ function. To solve integro-differential equations of non-linear problems of the dynamics of viscoelastic systems, a numerical method is suggested. It is based on the quadrature formula and eliminates the distinctions in the kernel of relaxation. With the Bubnov–Galerkin method, based on a polynomial approximation of the deflection, in combination with the suggested numerical method, the problems of non-linear vibration and dynamic stability of a viscoelastic cylindrical panel with concentrated masses were solved. The choice of the Koltunov–Rzhanitsyn singular kernel was substantiated. Results obtained using different theories are compared. Bubnov–Galerkin's convergence was studied in all problems. The influence of the viscoelastic properties of the material and concentrated masses on the process of vibration and dynamic stability of a cylindrical panel is shown.     

Thermo-acoustic random response of temperature-dependent functionally graded material panels

A nonlinear finite element model is provided for the nonlinear random response of functionally graded material panels subject to combined thermal and random acoustic loads. Material properties are assumed to be temperature-dependent, and graded in the thickness direction according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are derived using the first-order shear-deformable plate theory with von Karman geometric nonlinearity and the principle of virtual work. The thermal load is assumed to be steady state constant temperature distribution, and the acoustic excitation is considered to be a stationary white-Gaussian random pressure with zero mean and uniform magnitude over the plate surface. The governing equations are transformed to modal coordinates to reduce the computational efforts. Newton–Raphson iteration method is employed to obtain the dynamic response at each time step of the Newmark implicit scheme for numerical integration. Finally, numerical results are provided to study the effects of volume fraction exponent, temperature rise, and the sound pressure level on the panel response.     

Mathematical simulation of fluid flow in hydraulic drives of apparatuses

Problems of numerical simulation of branched hydraulic systems are considered. Difference schemes in Riemann invariants are constructed for nonlinear equations of poorly compressed fluid that are prescribed on hydraulic networks. Results of numerical simulation of fluid flow in the hydraulic drive of a mechanism for lowering cargo are presented. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 2, pp. 323–329, March–April, 1998.     

Dynamic mechanical thermal analysis of all-PP composites based on β and α polymorphic forms

All polypropylene (all-PP) composites were manufactured by exploiting the polymorphic forms of PP, in which alpha (α)-PP tapes worked as reinforcement and beta (β)-PP served as matrix. The mechanical performance of the composite was investigated in a range of frequencies and temperatures using dynamic mechanical thermal analysis (DMTA). The volume fractions of matrix and reinforcement were estimated using optical microscope images. Both the DMTA and the static flexural bending tests revealed that the α-PP tapes act as an effective reinforcement for the β-PP matrix. Time–temperature superposition (TTS) was applied to estimate the stiffness of the composites as a function of frequency (f = 10⁻⁹...10²³) in the form of a master curve. The Williams–Landel–Ferry (WLF) model described properly change in the experimental shift factors used to create the storage modulus versus frequency master curve. The activation energies for the α and β relaxations were also calculated by using the Arrhenius equation.     

Functional Identification of the Nonlinear Thermal-Conductivity Coefficient by Gradient Methods. II. Numerical Modeling

Algorithms for the gradient method of solution of the inverse problem on determination of the nonlinear thermal-conductivity coefficients are given. Results of numerical experiments are discussed. __________ Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 78, No. 4, pp. 75–81, July–August, 2005.     

Internal stresses, rheology, and structure formation in drying of a concentrated disperse system

A mathematical model is suggested for the stress strain state and structure formation in drying of a concentrated disperse system. The interrelated process of deformation of the medium and motion of the liquid in a saturated region is described by equations of filtration consolidation. The rheological relationship of a saturated medium is determined on the basis of the micromechanics of the relative motion of the particles. A system of nonlinear integrodifferential equations that describe the process is obtained and numerical analysis of the problem is carried out under different drying conditions. Translated from Inzhenerno-Fizicheskii Zhurnal, Vol. 71, No. 3, pp. 417–423, May–June, 1998.     

Microstructural and wear behavior of dual reinforced particle (DRP) aluminum alloy composite

The present investigations are a comparative study of single and dual reinforcement particles on microstructural features and wear behavior in LM-13 aluminum–silicon alloy. Silicon carbide and zircon sand particles of 20–32 μm are reinforced in the alloy by two-step stir casting method. Wear study reveals that the dual particle reinforcement enhances the wear resistance as compared to single particle reinforcement if mixed in a definite proportion. Study also indicate that a combination of 15 % reinforcement of zircon sand and silicon carbide particles in the ratio of 1:3 into the composite exhibits better wear resistance as compared to other combination.     

Numerical study of vibrations of a nonlinear mechanical system simulating a cracked body

The paper presents the results of a numerical study of forced and decaying vibrations of a system simulating a body with a closing crack under the action of various modes of a nonlinear restoring force and nonlinear viscous friction or the hysteresis-type energy dissipation. We obtained the general patterns of appearance of higher harmonics of the Fourier expansion of time dependence of vibration of a cracked body model. The sensitivity of the higher-harmonic method to the presence of a crack is compared with that of some other vibration damage indicators. Institute of Problems of Strength, National Academy of Sciences of Ukraine, Kiev, Ukraine. Translated from Problemy Prochnosti, No. 6, pp. 65–80, November–December, 1999.     

Stability and Load-Carrying Capacity of Elastic Reinforced Cylindrical Shells

By using the equilibrium equations in displacements, we develop an analytic method for the evaluation of upper critical loads in elastic cylindrical shells with transverse reinforcement. As a result, we deduce analytic expressions for the evaluation of critical stresses in momentless shells and propose a procedure for the evaluation of the lower limit of the load-carrying capacity of shells based on the application of the method of reduced stiffness. The numerical results are compared with the available theoretical and experimental data. __________ Translated from Problemy Prochnosti, No. 6, pp. 103 – 113, November – December, 2005.     

Fracture Assessment of Carbon Fibre/Epoxy Reinforcing Rings through a Combination of Full-Scale Testing, Small-Scale Testing and Stress Modeling

Carbon fibre/epoxy rings are used as radial reinforcement for polymer bearing elements with nominal diameter 250 mm functioning under 150 MPa. Full-scale static and dynamic testing revealed no catastrophic failure for loading to 400 MPa, although there was circumferential splitting of carbon fibres at the machined top edge causing counterface wear under sliding. A combined numerical–experimental analysis was applied for design improvement with a representative small-scale qualification test on the real ring geometry, inducing additional stress concentrations compared to ASTM standards. Full-scale modelling revealed high radial–axial shear stresses (33 MPa) in non-hydrostatically loaded zones, while it increased towards 104 MPa under hydrostatic load conditions. The former is the most critical and should be simulated either on a small-scale unidirectional compression test or on a representative short beam shear test, respectively, measuring the radial–axial or radial–tangential shear strength. A relation between both small-scale states of stress was experimentally and numerically studied, experiencing that the composite ring has lower radial–tangential shear stress compared to radial–axial shear stress as a different hydrostatic stress state is observed in the bulk of the composite ring. As a compressive test is however more difficult to perform than a short-beam-shear test, a representative design criterion for shear fracture is determined from failure at 27 kN normal load in a short-beam-shear test. Finally, fracture is avoided by optimising the cross-sectional geometry of the composite reinforcing ring and close control of the processing parameters.     

Effects of polymer–cement ratio and accelerated curing on flexural behavior of hardener-free epoxy-modified mortar panels

This experimental study reports the applicability of hardener-free epoxy-modified mortar panels to permanent forms as precast concrete products. Hardener-free epoxy-modified mortars are mixed using a Bisphenoal A-type epoxy resin without any hardener with various polymer–cement ratios and steel fiber reinforcement, and subjected to different curings. Hardener-free epoxy-modified mortar panels are prepared with same polymer–cement ratios and steel fiber reinforcement on trial, and tested for flexural behavior under four-point (third-point) loading. The effects of polymer–cement ratios and curings on strength properties of hardener-free epoxy-modified mortars, and on the flexural strength, flexural stress-extreme tension fiber strain relation, flexural load–deflection relation of hardener-free epoxy-modified mortar panels were examined. The adhesion in tension (to placed concrete) of the hardener-free epoxy-modified mortar panels was also tested. As a result, the hardener-free epoxy-modified mortar panels develop a high flexural strength, large extensibility and good adhesion to the placed concrete. The epoxy-modified mortar panels are more ductile and have high load-bearing capacity than unmodified mortar panels and can be used as precast concrete permanent forms in practical applications.