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1.
The paper is concerned with the forced nonlinear multimode vibrations of thin cylindrical shells fully filled with a perfect
incompressible fluid. The frequency response characteristics of shells undergoing steady-state vibration as simple (standing
wave) and compound (traveling wave) deformation modes are plotted and examined
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 8, pp. 97–106, August 2006. 相似文献
2.
Nonlinear vibration analysis of viscoelastic plates based on a refined Timoshenko theory 总被引:2,自引:0,他引:2
B. Kh. Éshmatov 《International Applied Mechanics》2006,42(5):596-605
Nonlinear vibrations of viscoelastic orthotropic and isotropic shells are mathematically modeled using a geometrically nonlinear
Timoshenko theory. Nonlinear problems are solved by using the Bubnov-Galerkin method and a numerical method based on quadrature
formulas. Results obtained from different theories are compared and analyzed. For each problem, the Bubnov-Galerkin method
is tested for convergence. The influence of the viscoelasticity and inhomogeneity of materials on the vibrations of plates
is demonstrated
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 5, pp. 120–131, May 2006. 相似文献
3.
K. V. Avramov 《International Applied Mechanics》2008,44(10):1173-1179
The forced vibrations of an impact Duffing oscillator with one degree of freedom are studied using Zhuravlev's nonsmooth transformation
and the multiple-scales method. Detailed consideration is given to the forced vibrations in the domain of resonance family.
The stability and bifurcations of periodic vibrations are analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 114–121, October 2008. 相似文献
4.
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 相似文献
5.
Flexural vibrations and vibrational heating of a ring plate with thin piezoceramic pads under single-frequency electromechanical loading 总被引:1,自引:1,他引:0
I. F. Kirichok 《International Applied Mechanics》2008,44(2):200-207
The paper deals with the coupled problem of flexural vibrations and dissipative heating of a viscoelastic ring plate with
piezoceramic actuators under monoharmonic electromechanical loading. The temperature dependence of the complex characteristics
of passive and piezoactive materials is taken into account. The coupled nonlinear problem of thermoviscoelasticity is solved
by an iterative method. At each iteration, orthogonal discretization is used to integrate the equations of elasticity and
an explicit finite-difference scheme is used to solve the heat-conduction equation with a nonlinear heat source. The effect
of the dissipative heating temperature, boundary conditions, and the thickness and area of the actuator on the active damping
of the forced vibrations of the plate under uniform transverse harmonic pressure is examined
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 99–108, February 2008. 相似文献
6.
D. A. Khodzhaev B. Kh. Éshmatov 《Journal of Applied Mechanics and Technical Physics》2007,48(6):905-914
The problem of vibrations of a viscoelastic plate with concentrated masses is studied in a geometrically nonlinear formulation.
In the equation of motion of the plate, the action of the concentrated masses is taken into account using Dirac δ-functions.
The problem is reduced to solving a system of Volterra type ordinary nonlinear integrodifferential equations using the Bubnov-Galerkin
method. The resulting system with a singular Koltunov-Rzhanitsyn kernel is solved using a numerical method based on quadrature
formulas. The effect of the viscoelastic properties of the plate material and the location and amount of concentrated masses
on the vibration amplitude and frequency characteristics is studied. A comparison is made of numerical calculation results
obtained using various theories.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007. 相似文献
7.
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
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Translated from Prikladnaya Mekhanika, Vol. 44, No. 4, pp. 101–106, April 2008. 相似文献
8.
The nonlinear parametric vibrations of cylindrical shell are described by the Donnell–Mushtari–Vlasov equations. The motions
are represented as a mode expansion. Discretization is performed using the Bubnov–Galerkin method. The describing-function
method is used to study traveling waves and nonlinear normal modes in systems with and without dissipation 相似文献
9.
Theoretical and experimental investigations of the nonlinear vibrations and dynamic stability of thin shells partially filled
with a liquid are reviewed. The paper deals with the basic laws governing the dynamic high-deflection deformation of carrying
shell structures and the considerable vibrations of the free liquid surface due to the natural, forced, and parametrically
excited vibrations of the combined system and also due to impulse loads acting on the carrying object. The nonlinear dynamic
interaction of shells with a liquid filler is analyzed with allowance for the wave motions of the free liquid surface.
S.P. Timoshenko Institute of Mechanics, National Academy of Sciences of Ukraine, Kiev. Translated from Prikladnaya Mekhanika,
Vol. 36, No. 4, pp. 3–34, April, 2000. 相似文献
10.
The problem of forced nonaxisymmetric vibrations of reinforced ellipsoidal shells under nonstationary loads is formulated.
A numerical algorithm of solving it is developed and the results obtained are analyzed
Translated from Prikladnaya Mekhanika, Vol. 44, No. 10, pp. 63–73, October 2008. 相似文献
11.
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
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Translated from Prikladnaya Mekhanika, Vol. 41, No. 6, pp. 56–71, June 2005. 相似文献
12.
Katica? Hedrih 《Archive of Applied Mechanics (Ingenieur Archiv)》2008,78(9):725-735
Based on the author’s previously published results for transversal free vibrations of axially moving sandwich belts described
by coupled partial differential equations, which are derived and analytically solved, this paper contains new analytical results,
for forced vibrations of the same system excited by transversal external excitation. The transversal forced vibrations of
the axially moving sandwich belts are described by the coupled partial nonhomogeneous differential equations. The partial
differential equations are analytically solved. Bernoulli’s method of particular integrals and Lagrange’s method of the variations
of the constants are used. 相似文献
13.
The Hamilton–Ostrogradsky principle is used to substantiate the statement of initial–boundary-value problems of electroelasticity.
The free vibrations of a piezoceramic layer are used as an example to illustrate some features of solving nonstationary problems
of electroelasticity
Translated from Prikladnaya Mekhanika, Vol. 44, No. 12, pp. 62–69, December 2008. 相似文献
14.
Yaroslav Alexander Zhuk I. A. Guz C. M. Sands 《Archive of Applied Mechanics (Ingenieur Archiv)》2011,81(2):215-227
A coupled dynamic problem of electromechanics for thin wall multilayer elements is formulated based on the Kirchhoff–Love
hypotheses. In the case of harmonic loading, a simplified formulation is given using the monoharmonic approach and the concept
of complex moduli to characterize the cyclic properties of the material. The problem of forced vibrations of three-layer beam,
whose outer layers are made of a viscoelastic piezoactive material, and, the inner layer of a passive physically nonlinear
material, is considered as an example to demonstrate the possibility of the technique elaborated. The possibility of damping
the forced vibrations of a structure with the help of harmonic voltages applied to the external piezoactive layers is studied.
Results obtained for the transient response of the beam using the complete model are compared with data found using the simplified
model. Limitations on the simplified model application are specified. 相似文献
15.
水轮发电机转子偏心引起的非线性电磁振动 总被引:5,自引:0,他引:5
由于机械和电磁相互耦合,水轮发电机的电磁振动具有强非线性特征。根据不平衡磁拉力与转子偏心的非线性函数关系,通过简化的各向同性的单圆盘转子系统,建立了水轮发电机转子电磁振动的非线性系统。利用非线性振动理论的多尺度方法,从理论上分析了该系统强迫振动的稳态响应,进而研究了水轮发电机转子偏心引起的电磁振动。研究发现不平衡磁拉力使系统的涡动频率下降,使运动的中心发生变化;并且会引起两倍转频的振动。最后用模型转子仿真试验的结果验证了这些理论分析的结论。 相似文献
16.
Studies on Bifurcation and Chaos of a String-Beam Coupled System with Two Degrees-of-Freedom 总被引:1,自引:0,他引:1
In this paper, research on nonlinear dynamic behavior of a string-beam coupled system subjected to parametric and external
excitations is presented. The governing equations of motion are obtained for the nonlinear transverse vibrations of the string-beam
coupled system. The Galerkin's method is employed to simplify the governing equations to a set of ordinary differential equations
with two degrees-of-freedom. The case of 1:2 internal resonance between the modes of the beam and string, principal parametric
resonance for the beam, and primary resonance for the string is considered. The method of multiple scales is utilized to analyze
the nonlinear responses of the string-beam coupled system. Based on the averaged equation obtained here, the techniques of
phase portrait, waveform, and Poincare map are applied to analyze the periodic and chaotic motions. It is found from numerical
simulations that there are obvious jumping phenomena in the resonant response–frequency curves. It is indicated from the phase
portrait and Poincare map that period-4, period-2, and periodic solutions and chaotic motions occur in the transverse nonlinear
vibrations of the string-beam coupled system under certain conditions.
An erratum to this article is available at . 相似文献
17.
Electromagnetic excitation in high power density permanent magnet synchronous motors (PMSMs) due to eccentricity is a significant concern in industry; however, the treatment of lateral and torsional coupled vibrations caused by electromagnetic excitation is rarely addressed, yet it is very important for evaluating the stability of dynamic rotor vibrations. This study focuses on an analytical method for analyzing the stability of coupled lateral/torsional vibrations in rotor systems caused by electromagnetic excitation in a PMSM. An electromechanically coupled lateral/torsional dynamic model of a PMSM Jeffcott rotor is derived using a Lagrange–Maxwell approach. Equilibrium stability was analyzed using a linearized matrix of the equation describing the system. The stability criteria of coupled torsional–lateral motions are provided, and the influences of the electromagnetic and mechanical parameters on mechanical vibration stability and nonlinear behavior were investigated. These results provide better understanding of the nonlinear response of an eccentric PMSM rotor system and are beneficial for controlling and diagnosing eccentricity. 相似文献
18.
I. F. Kirichok 《International Applied Mechanics》2006,42(3):336-341
The forced flexural vibrations and dissipative heating of a bimorph ring plate are studied. The plate is made of viscoelastic
piezoceramics and is polarized across the thickness. The outer surfaces of the plate are nonuniformly electroded, and harmonic
electric excitation is applied to the electrodes. The viscoelastic behavior of the material is described using the concept
of temperature-dependent complex moduli. The coupled nonlinear problem of thermoviscoelasticity is solved by time iteration
using, at each iteration, the discrete-orthogonalization method to integrate the mechanics equations and the explicit finite-difference
method to solve the heat-conduction equation with a nonlinear heat source. Numerical calculations demonstrate that by changing
the size of the ring electrode we can influence the natural frequency, stress and displacement distributions, dissipative-heating
temperature, and amplitude-and temperature-frequency characteristics. With certain boundary conditions, there is an optimal
electrode configuration that produces deflections of maximum amplitudes when an electric excitation is applied
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Translated from Prikladnaya Mekhanika, Vol. 42, No. 3, pp. 102–109, March 2006. 相似文献
19.
C. W. Lim S. K. Lai B. S. Wu W. P. Sun Y. Yang C. Wang 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(5):411-431
An analytical approach is developed for the nonlinear oscillation of a conservative, two-degree-of-freedom (TDOF) mass-spring
system with serial combined linear–nonlinear stiffness excited by a constant external force. The main idea of the proposed
approach lies in two categories, the first one is the transformation of two nonlinear differential equations of a two-mass
system using suitable intermediate variables into a single nonlinear differential equation. Another is the treatment a quadratic
nonlinear oscillator (QNO) by the modified Lindstedt–Poincaré (L-P) method presented recently by the authors. The first-order
and second-order analytical approximations for the modified L-P method are established for the QNOs with satisfactory results.
After solving the nonlinear differential equation, the displacements of two-mass system can be obtained directly from the
governing linear second-order differential equation. Unlike the common perturbation method, the modified L-P method is valid
for weak as well as strong nonlinear oscillation systems. On the other hand, the new approach yields simple approximate analytical
expressions valid for small as well as large amplitudes of oscillation. In short, this new approach yields extended scope
of applicability, simplicity, flexibility in application, and avoidance of complicated numerical integration as compared to
the previous approaches such as the perturbation and classical harmonic balance methods. Two examples of nonlinear TDOF mass-spring
systems excited by a constant external force are selected and the approximate solutions are verified with the exact solutions
derived from the Jacobi elliptic function and also the numerical fourth-order Runge–Kutta solutions. 相似文献
20.
The nonlinear modes of essentially nonlinear piecewise-linear finite degrees of freedom systems are calculated by the numerical methods, which are suggested in this paper. The basis of these methods is numerical solutions of the equations of the systems motions in configuration space. The numerical method for the nonlinear modes of essentially nonlinear piecewise-linear systems forced vibrations is suggested. The basis of this approach is the combination of the Rauscher method and the calculations of the autonomous system nonlinear modes. The nonlinear modes of the diesel engine transmission torsional vibrations are analyzed numerically. The vibrations are described by essentially nonlinear piecewise-linear system with fifteen degrees of freedom. The NNMs of this system forced vibrations are observed in the resonance regions. Both NNMs and the motions, which are essentially differ from NNMs, are observed in the distance from the resonances. NNMs of the forced vibrations of the systems with dissipation are close to NNMs of the system without dissipation. 相似文献