Study of the Resonant Vibrations and Dissipative Heating of Thin-Walled Elements Made of a Physically Nonlinear Material

An approximate formulation is given to a dynamic coupled thermomechanical problem for physically nonlinear inelastic thin-walled structural elements within the framework of a geometrically linear theory and the Kirchhoff–Love hypotheses. A simplified model is used to describe the vibrations and dissipative heating of inhomogeneous physically nonlinear bodies under harmonic loading. Nonstationary vibroheating problem is solved. The dissipative function obtained from the solution for steady-state vibrations is used to simulate internal heat sources. For the partial case of forced vibrations of a beam, the amplitude–frequency characteristics of the field quantities are studied within a wide frequency range. The temperature characteristics for the first and second resonance modes are compared.     

Studying the harmonic vibrations of a cylindrical shell made of a nonlinear elastic piezoelectric material

The paper examines the harmonic vibrations of an infinitely long thin cylindrical shell made of a nonlinear elastic piezoceramic material and subjected to periodic electric loading. Amplitude-frequency characteristics are plotted for different amplitudes of the load. Points of these characteristics are analyzed for stability. The transients occurring while harmonic vibrations attain the steady state are studied __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 101–106, April 2008.     

Method of characteristics in analysis of the propagation of electroelastic thickness oscillations in a piezoceramic layer under electric excitation

The method of characteristics is used to obtain an analytical solution describing the thickness vibrations of a piezoelectric layer polarized across the thickness and subjected to a nonstationary electric potential. The features of how the vibrations are excited and propagate under electric loading are studied. The dynamic electromechanical state of the layer is analyzed. The electric and mechanical characteristics as functions of time are plotted Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 23–27, October 2008.     

Nonlinear oscillatory processes in wheeled vehicles

The free damped vibrations of a wheeled vehicle with independent suspension are analyzed with allowance for the nonlinear characteristics of the suspension springs and shock absorbers. The vibrations of a wheeled vehicle with a suspension with smooth nonlinear characteristics are studied for a model with seven degrees of freedoms. The skeleton curves and nonlinear normal modes are obtained. For a model with two degrees of freedoms (quarter-car) that corresponds to axisymmetric vibrations, the nonlinear normal modes are found in the case of a shock absorber with nonsmooth nonlinear characteristic     

Modeling the dynamic behavior of shape memory alloys

The paper studies the single degree of freedom vibration of a rigid mass suspended by a thin-walled shape memory alloy tube under torsional loading. The behavior is analyzed for the cases of quasiplasticity (low temperatures) and pseudoelasticity (high temperatures) on the basis of an improved version of the Müller–Achenbach model. To illustrate the strong hysteresis-induced damping capacity and the non-linear vibration characteristics, both, free and forced vibrations are considered in the first part of the paper. This is done on the basis of an isothermal version of the model, while the second part of the paper focuses on the effect of non-constant temperature caused by the rate-dependent release and absorption of latent heats.     

Harmonic vibrations and waves in a cylindrical helically anisotropic shell

A Kirchhoff-Love type applied theory is used to study the specific characteristics of harmonic waves and vibrations of a helically anisotropic shell. Special attention is paid to axisymmetric and bending vibrations. In both cases, the dispersion equations are constructed and a qualitative and numerical analysis of their roots and the corresponding elementary solutions is performed. It is shown that the skew anisotropy in the axisymmetric case generates a relation between the longitudinal and torsional vibrations which is mathematically described by the amplitude coefficients of homogeneous waves. In the case of a shell with rigidly fixed end surfaces, the dependence of the first two natural frequencies on the shell length and the helical line slope α, i.e., the geometric parameter of helical anisotropy, is studied. A boundary value problem in which longitudinal vibrations are generated on one of the end surfaces and the other end is free of forces and moments is considered to analyze the degree of transformation of longitudinal vibrations into longitudinally torsional vibrations. In the case of bending vibrations, two problems for a half-infinite shell are studied as well. In the first problem, the waves are excited kinematically by generating harmonic vibrations of the shell end surface in the plane of the axial cross-section, and it is shown that the axis generally moves in some closed trajectories far from the end surface. In the second problem, the reflection of a homogeneous wave incident on the shell end is examined. It is shown that the “boundary resonance” phenomenon can arise in some cases.     

The Nonlinear Vibrations and Stability of Orthotropic Cylindrical Liquid-Carrying Shells Under Periodic Actions

The nonlinear resonance vibrations and stability of nonlinear orthotropic shells partially filled with a liquid and subjected to longitudinal and transverse periodic loading are studied. The equations of motion are derived with regard for the existence and nonlinear interaction of conjugate flexural modes of the shell. Stationary regimes for forced and parametric vibrations are found and analyzed for stability under the conditions of fundamental and subharmonic resonances. The amplitude–frequency characteristics of these regimes are constructed for various parameters of the system     

Experimental studies of the vibrations and dynamic stability of laminated composite shells

The paper discusses the results of systematic experimental studies of vibrations and dynamic instability of thin shells of revolution made of laminated composite materials (glassfiber-reinforced plastics). The basic patterns in the dynamic deformation of shells during natural, forced, and parametric vibrations are considered. The damping parameters of natural vibrations are analyzed. The wave deformation modes of shells subject to periodic excitation are studied. The effect of long-term vibratory loading (torsion) on the dynamic characteristics of three-layer glassfiber-reinforced plastic shells is examined     

Stability of convective motion in a vertical layer in the presence of longitudinal vibrations

The influence of vibrations of a cavity containing a fluid on the convective stability of the equilibrium has been investigated on a number of occasions [1]. The stability of convective flows in a modulated gravity field has not hitherto been studied systematically. There is only the paper of Baxi, Arpaci, and Vest [2], which contains fragmentary data corresponding to various values of the determining parameters of the problem. The present paper investigates the linear stability of convective flow in a vertical plane layer with walls at different temperatures in the presence of longitudinal harmonic vibrations of the cavity containing the fluid. It is assumed that the frequency of the vibrations is fairly high; the motion is described by the equations of the averaged convective motion. The stability boundaries of the flow with respect to monotonic perturbations in the region of Prandtl numbers 0 ? P ? 10 are determined. It is found that high-frequency vibrations have a destabilizing influence on the convective motion. At sufficiently large values of the vibration parameter, the flow becomes unstable at arbitrarily small values of the Grashof number, this being due to the mechanism of vibrational convection, which leads to instability even under conditions of weightlessness, when the main flow is absent [3, 4].     

Resonant vibrations of a clamped thermoviscoelastic rectangular plate with sensors and actuators

The paper discusses the active damping of the resonant flexural vibrations of a clamped thermoviscoelastic rectangular plate with distributed piezoelectric sensors and actuators. The thermoviscoelastic behavior of the passive and active materials is described using the concept of complex characteristics. The interaction of the mechanical and thermal fields is taken into account. The Bubnov–Galerkin method is used. The effect of self-heating, the dimensions of the piezoelectric inclusions, and the feedback factor on the effectiveness of active damping of the resonance vibrations of the plate is studied     

Resonant vibrations of a hinged thermoviscoelastic rectangular plate with sensors and actuators

The paper discusses the active damping of the resonant flexural vibrations of a hinged thermoviscoelastic rectangular plate with distributed piezoelectric sensors and actuators. The thermoviscoelastic behavior of the passive and active materials is described using the concept of complex characteristics. The interaction of mechanical and thermal fields is taken into account. The Bubnov–Galerkin method is used. The effect of dissipative heating, the dimensions of the piezoelectric inclusions, and the feedback factor on the effectiveness of active damping of resonance vibrations of the plate is studied     

Resonance Vibrations and Dissipative Heating of Thin-Walled Laminated Elements Made of Physically Nonlinear Materials

The dynamic thermomechanical problem for thin-walled laminated elements is formulated based on the geometrically linear theory and Kirchhoff–Love hypotheses. A simplified model of vibrations and dissipative heating of structurally inhomogeneous inelastic bodies under harmonic loading is used. The mechanical properties of materials are described using strain-dependent complex moduli. A nonstationary vibration-heating problem is solved. The dissipative function, derived from the stationary solution, is used to specify internal heat sources. The amplitude–frequency characteristics and spatial distributions of the main field variables are studied for a sandwich beam subjected to forced vibrations     

Harmonic thickness vibrations of inhomogeneous elastic layers with curved boundaries

The thickness vibrations of elastic inhomogeneous bodies of different geometry under dynamic harmonic loading are studied. The dependence of the amplitude–frequency characteristics of homogeneous and inhomogeneous bodies on excitation frequency is analyzed in detail. The frequency spectra for plane, cylindrical, and spherical layers are determined     

Vibrations of a complex-shaped panel

The free vibrations of flexible shallow shells with complex planform are studied. To analyze the natural frequencies and modes of linear vibrations, the R-function and Rayleigh–Ritz methods are used. A discrete model is obtained using the Bubnov–Galerkin method. The nonlinear vibrations are studied by combining the nonlinear normal mode method and the multiple-scales method. Skeleton curves of natural vibrations are drawn     

The Complex-Moduli Solution of an Axisymmetric Dynamic Problem of Coupled Thermoviscoplasticity Under Harmonic Loading

An approximate formulation is given to the axisymmetric dynamic thermoviscoplastic problem with coupled mechanical and thermal fields. The formulation employs an approximate cyclic thermoviscoplastic model based on the concept of complex moduli. The distribution of the field quantities and the temperature— and amplitude—frequency resonant characteristics of a circular disk under forced flexural vibrations are studied. The capabilities of the approximate model in solving this class of problems are also studied     

One-dimensional unsteady-state flow in a rotating grid

The article discusses the problem of determining the dynamic characteristics of rotating and fixed grids in turbine-type machines. The grid is regarded as a linear system with distributed parameters. In problems involved with determining the stability of complex systems and in control problems, the dynamic characteristics of the turbine-type machines must be known. Such characteristics have been studied, for example, in [1]. However, in [1] the discussion is limited to a system with lumped parameters, which is admissible only at small perturbation frequencies. Article [2] discusses the problem of the propagation of vibrations in a flow with a constant mean velocity. In what follows, this problem is solved with a variable velocity of the mean motion. In addition, it is assumed that, with vibrations, there is removal or supply of mechanical energy.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 5, pp. 77–83, September–October, 1971.     

Flexural Vibrations and Heating of a Circular Bimorph Piezoplate under Electric Excitation Applied to Nonuniformly Electroded Surfaces

The flexural vibrations and dissipative heating of a circular bimorph piezoceramic plate are studied. The plate is excited by a harmonic electric field applied to nonuniformly electroded surfaces. The viscoelastic behavior of piezoceramics is described in terms of temperature-dependent complex moduli. The nonlinear coupled problem of thermoviscoelasticity is solved by step-by-step integration in time, using the discrete-orthogonalization method to solve the mechanics equations and the finite-differences method to solve the heat-conduction equations. A numerical analysis is conducted for TsTStBS-2 piezoceramics to study the influence of the nonuniform electroding on the resonant frequency, amplitude, and modes of flexural vibrations and the amplitude- and temperature-frequency characteristics of the plate __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 9, pp. 94–100, September 2005.     

Analysis of the Nonstationary Slow Passage of a Cylindrical Vessel Partially Filled with a Liquid Through Resonant Zones

The features of the dynamic behavior of the free liquid surface in a rigid cylindrical body that executes translational quasistationary vibrations are studied. The frequency of these vibrations is a slowly varying function of time. The liquid motion is studied in the resonant zones corresponding to two cases of body excitation — longitudinal and transverse     

A new numerical procedure for free vibrations of pretwisted plates

Summary  A numerical procedure is proposed for the analysis of free vibrations of pretwisted thin plates. An accurate strain–displacement relationship based on the thin-shell theory combined with the finite element method using triangular plate elements with three nodes and nine degrees of freedom for each node is utilized. The vibration characteristics of pretwisted thin plates with different twist rates and aspect ratios are studied. The numerical results are compared with the previous results obtained by various types of finite elements and by the Rayleigh–Ritz method. The effect of the twist rate on the vibration characteristics is studied briefly. Received 28 February 2001; accepted for publication 18 December 2001     

旋转碰摩板热冲击振动的解析法研究

提出了热冲击和碰摩故障共同作用下的旋转悬臂板系统动力特性解析解法. 基于变分原理,推导出考虑碰摩力沿宽度方向差异性的薄板系统运动微分方程,将该方程的解分解为热冲击悬臂板准静态解和碰摩薄板热冲击动力解. 通过计算旋转悬臂板的模态特性和温度分布函数,获得了碰摩叶片旋转悬臂板模型的热冲击振动解析解,讨论分析得出热冲击和碰摩故障对薄板振动的影响规律. 研究表明:碰摩振动表现为复杂的多频率耦合振动,高频振动较为显著;热冲击振动表现为简单的低频振动形式,强烈的热冲击导致碰摩薄板趋于低频振动. 碰摩引起的振动形式较热冲击故障更加复杂,更容易引起叶片的破坏. 增大的摩擦系数加剧了碰摩引起的振动,利用减小表面粗糙程度等方法降低摩擦系数,可以达到减小碰摩破坏程度的目的.