Nonlinear Single-Frequency Vibrations and Dissipative Heating of Inelastic Piezoelectric Bodies

A generalization is made of the results obtained at the S. P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine in developing models of single-frequency vibrations and dissipative heating of inelastic piezoelectric solids and methods for solving the associated nonlinear boundary-value problems. The solutions of specific problems and new effects due to the interaction of electromechanical and thermal fields are considered.     

Planar Flexural Vibrations and Dissipative Heating of Laminated Rectangular Plates

The coupled thermomechanical dynamic behavior of a heterogeneous solid is investigated by an example of laminated inelastic rectangular plates subjected to forced vibration and dissipative heating. The problem is solved in two formulations: complete and approximate. The complete formulation uses generalized flow theory to describe the inelastic properties of the material. The approximate formulation employs a model based on the idea of complex moduli. Special distributions of the field variables and amplitude–frequency responses of the rectangular plate are analyzed. The effect of the loading level on the mode shape and stress distribution is studied as well. A good agreement between the results obtained in the complete and approximate formulations is pointed out.     

Modelling the Stationary Vibrations and Dissipative Heating of Thin-Walled Inelastic Elements with Piezoactive Layers

A coupled dynamic problem of thermoelectromechanics for thin-walled multilayer elements is formulated based on a geometrically nonlinear theory and the Kirchhoff–Love hypotheses. In the case of harmonic loading, an approximate formulation is given using the concept of complex moduli to characterize the cyclic properties of the material. The model problem on forced vibrations of sandwich beam, whose core layer is made of a passive physically nonlinear material, and face layers, of a viscoelastic piezoactive material, is considered as an example to demonstrate the possibility of damping the vibrations by applying harmonic voltage to the oppositely polarized layers of the beam. Substantiation is given for a linear control law with a complex coefficient for the electric potential, which provides damping of vibrations in the first symmetric mode at the linear and nonlinear stages of deformation. The stress–strain state and dissipative-heating temperature are 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     

Electromechanical Vibrations and Dissipative Heating of Viscoelastic Thin-Walled Piezoelements

The results of studying the electromechanical response of thin-walled viscoelastic piezoactive elements under harmonic loading are generalized. The nonlinear electrothermoviscoelastic problem for a harmonically deformed body is formulated in a simplified form with regard for the facts that the mechanical, thermal, and electric fields are coupled, the material is physically nonlinear, and its properties depend on temperature. Classical and refined electromechanical models of single-layer and multilayer shells and plates under general and harmonic loading are reviewed. The models consider that the electromechanical characteristics of the material depend on temperature and physical and geometrical nonlinearities. Methods for solving nonlinear coupled electrothermoviscoelastic problems are discussed. Analytical and numerical solutions are given to specific quasistatic and dynamic electrothermoviscoelastic problems for thin-walled elements such as rods, plates, and shells of various shapes under harmonic electric loading. The effect of dissipation, the temperature dependence of the material properties, and physical and geometrical nonlinearities on the harmonic and parametric vibrations and stability of piezoelectric elements is studied     

Vibrations and Dissipative Heating of a Viscoelastic Beam under a Moving Load

The vibrations and dissipative heating of an infinite viscoelastic beam under a moving load are studied on the basis of Timoshenko beam theory. The influence of transverse-shear strain and rotary inertia on the critical velocities of the moving load, the amplitude of bending vibration, and the temperature of dissipative heating is analyzed__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 69–76, January 2005.     

Vibrations and Dissipative Heating of a Cylindrical Panel under a Periodic Moving Load

An analytic solution is obtained to describe the vibrations and dissipative heating of a simply supported infinite cylindrical panel under periodic normal loads moving over its surface with a constant velocity. Special attention is focused on resonant vibrations, which result in the most intensive dissipative heating. It is additionally assumed that the material of the panel is viscoelastic, its properties are independent of temperature, and Poisson’s ratio is real. The influence of thickness, radius of curvature, load velocity, and viscoelastic properties on the thermal state of the panel is analysed against the thermal state of the plate__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 4, pp. 100–109, April 2005.     

Resonant Vibrations and Dissipative Heating of an Infinite Piezoceramic Cylinder

The monoharmonic radial vibrations and dissipative heating of an infinite hollow piezoceramic cylinder are studied in dynamic formulation, taking into account the temperature dependence of the complex electromechanical characteristics over a wide range of temperatures, including depolarization temperatures. The influence of the heat exchange conditions, the level of electric load, and geometry on the thermoelectromechanical characteristics is studied in the case of forced vibrations at the first resonance__________Translated from Prikladnaya Mekhanika, Vol. 41, No. 3, pp. 101–107, March 2005.     

Thermomechanical Behavior and Durability of Shear-Compliant Inelastic Shells of Revolutionwith Piezo-Electric Pads During Axisymmetric Resonant Vibrations

International Applied Mechanics - A refined statement and methodology for solving the problem of electrothermomechanical behavior and predicting the durability of inelastic shells of revolution...     

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.     

Transverse Vibrations of a Centrally Clamped Rotating Circular Disk

The transverse vibrations of a circular disk of uniform thickness rotatingabout its axis with constant angular velocity are analyzed. The resultsspecialized to the linear case of disks clamped at the center and free atthe periphery are in good agreement with those reported in the literature.The natural frequencies of spinning hard and floppy disks are obtained for various nodal diameters and nodal circles. Primary resonance is shown to occur at the critical rotational speed at which, in the linear analysis, the spinning disk is unable to support arbitraryspatially fixed transverse loads. Using the method of multiple scales, wedetermine a set of four nonlinear ordinary-differential equations governingthe modulation of the amplitudes and phases of two interacting modes. Thesymmetry of the system and the loading conditions are reflected in thesymmetry of the modulation equations. They are reduced to an equivalentset of two first-order equations whose equilibrium solutions aredetermined analytically. The stability characteristics of thesesolutions is studied; the qualitative behavior of the response isindependent of the mode being considered.     

Forced Axisymmetric Nonlinear Vibrations of Reinforced Conical Shells

A numerical method for analysis of the axisymmetric nonlinear vibrations of conical shells is developed based on the integro-differential method of constructing difference schemes. A prediction analysis is conducted of the response of shells with various taper angles to an impulsive load     

Transverse Vibrations of Laminated Beams in Three-Dimensional Formulation

A new asymptotic method is proposed to describe the free and forced transverse vibrations of elastic laminated beams of arbitrary cross section using the three-dimensional elastic equations without additional hypotheses and constraints. For beams with layers of equal Poisson's ratio, the zero-order natural frequencies are equal to the natural frequencies predicted by classical beam theory based on the Bernoulli hypothesis. The method makes it possible to calculate the frequencies of free vibrations and amplitudes of forced vibrations with prescribed accuracy for the first natural modes __________ Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 56–71, June 2005.     

Moment of Resistance of a Disk Rotating in a Closed Axisymmetric Cavity

A turbulent flow in a closed axisymmetric cavity with a rotating disk is considered. The moment of resistance to disk rotation is calculated as a function of the dimensionless gap between the motionless casing and rotating disk and of the Reynolds number. Results calculated on the basis of different turbulence models are compared with data of a physical experiment and with available correlations. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 47, No. 1, pp. 153–160, January–February, 2006.     

层状压电半导体板的稳态弯曲振动分析

论文针对具有变形-极化-载流子耦合的层状压电半导体复合悬臂结构,理论研究了其自由端在周期荷载作用下的稳态响应问题,导出了板中位移、电场、载流子等物理量的解析表达式,并数值分析了周期荷载的幅值、激励频率和初始载流子浓度对结构宏观力学响应的影响.数值结果表明:在一阶固有频率下,结构内部各物理量响应幅值较大;在高阶固有频率下,各物理量响应出现多个局部峰值区域,其幅值相对减小,载流子会朝局部极值区域“聚集”或“离开”局部极值区域.初始载流子浓度在一定范围内对结构各物理量(如固有频率和电势)的稳态响应有显著的调控作用.     

Forced Vibrations and Nonstationary Heating of a Rectangular Viscoelastic Plate with Prestresses*

International Applied Mechanics - The problem of forced resonant vibrations and stationary, as well as nonstationary dissipative heating of a prestressed viscoelastic elastomeric rectangular plate...