共查询到20条相似文献,搜索用时 15 毫秒
1.
Utz von Wagner 《International Journal of Non》2004,39(4):673-688
Characteristic non-linear effects can be observed, when piezoceramics are excited using weak electric fields. In experiments with longitudinal vibrations of piezoceramic rods, the behavior of a softening Duffing-oscillator including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage is observed. Another phenomenon is the decrease of normalized amplitude responses with increasing excitation voltages. For such small stresses and weak electric fields as applied in the experiments, piezoceramics are usually described by linear constitutive equations around an operating point in the butterfly hysteresis curve. The non-linear effects under consideration were, e.g. observed and described by Beige and Schmidt [1,2], who investigated longitudinal plate vibrations using the piezoelectric 31-effect. They modeled these non-linearities using higher order quadratic and cubic elastic and electric terms. Typical non-linear effects, e.g. dependence of the resonance frequency on the amplitude, superharmonics in spectra and a non-linear relation between excitation voltage and vibration amplitude were also observed e.g. by von Wagner et al. [3] in piezo-beam systems. In the present paper, the work is extended to longitudinal vibrations of non-slender piezoceramic rods using the piezoelectric 33-effect. The non-linearities are modeled using an extended electric enthalpy density including non-linear quadratic and cubic elastic terms, coupling terms and electric terms. The equations of motion for the system under consideration are derived via the Ritz method using Hamilton's principle. An extended kinetic energy taking into consideration the transverse velocity is used to model the non-slender rods. The equations of motion are solved using perturbation techniques. In a second step, additional dissipative linear and non-linear terms are used in the model. The non-linear effects described in this paper may have strong influence on the relation between excitation voltage and response amplitude whenever piezoceramic actuators and structures are excited at resonance. 相似文献
2.
Khaled A. Alhazza Mohammed F. Daqaq Ali H. Nayfeh Daniel J. Inman 《International Journal of Non》2008,43(8):801-812
Non-linear feedback control provides an effective methodology for vibration mitigation in non-linear dynamic systems. However, within digital circuits, actuation mechanisms, filters, and controller processing time, intrinsic time-delays unavoidably bring an unacceptable and possibly detrimental delay period between the controller input and real-time system actuation. If not well-studied, these inherent and compounding delays may inadvertently channel energy into or out of a system at incorrect time intervals, producing instabilities and rendering controllers’ performance ineffective. In this work, we present a comprehensive investigation of the effect of time delays on the non-linear control of parametrically excited cantilever beams. More specifically, we examine three non-linear cubic delayed-feedback control methodologies: position, velocity, and acceleration delayed feedback. Utilizing the method of multiple scales, we derive the modulation equations that govern the non-linear dynamics of the beam. These equations are then utilized to investigate the effect of time delays on the stability, amplitude, and frequency–response behavior. We show that, when manifested in the feedback, even the minute amount of delays can completely alter the behavior and stability of the parametrically excited beam, leading to unexpected behavior and responses that could puzzle researchers if not well-understood and documented. 相似文献
3.
S. Nima Mahmoodi 《International Journal of Non》2007,42(4):577-587
Microcantilevers have recently received widespread attentions due to their extreme applicability and versatility in both biological and non-biological applications. Along this line, this paper undertakes the non-linear vibrations of a piezoelectrically driven microcantilever beam as a common configuration in many scanning probe microscopy and nanomechanical cantilever biosensor systems. A part of the microcantilever beam surface is covered by a piezoelectric layer (typically ZnO), which acts both as an actuator and sensor. The bending vibrations of the microcantilever beam are studied considering the inextensibility condition and the coupling between electrical and mechanical properties in the piezoelectric materials. The non-linear terms appear in the form of quadratic expression due to presence of piezoelectric layer, and cubic form due to geometrical non-linearities. The Galerkin approximation is then utilized to discretize the equations of motion. In addition, the method of multiple scales is applied to arrive at the closed form solution for the fundamental natural frequency of the system. An experimental setup consisting of a commercial piezoelectric microcantilever attached on the stand of a state-of-the-art microsystem analyzer for non-contact vibration measurement is utilized to verify the theoretical developments. It is found that the experimental results and theoretical findings are in good agreement, which demonstrates that the non-linear modeling framework could provide a better dynamic representation of the microcantilever than the previous linear models. Due to microscale nature of the system, excitation amplitude plays an important role since even a small change in the amplitude of excitation can lead to significant vibrations and frequency shift. 相似文献
4.
Non-linear vibrations of cantilever beams with feedback delays 总被引:1,自引:0,他引:1
A comprehensive investigation of the effect of feedback delays on the non-linear vibrations of a piezoelectrically actuated cantilever beam is presented. In the first part of this work, we examine the linear and non-linear free responses of a beam subjected to a delayed-acceleration feedback. We show that the trivial solution loses stability via a Hopf bifurcation leading to limit-cycle oscillations. We analyze the stability of the dynamic response in the postbifurcation, close to the stability boundaries by examining the nature of the Hopf bifurcation and away from the stability boundaries by using the method of harmonic balance and Floquet theory. We find that, increasing the gain for certain feedback delays may culminate in quasiperiodic and chaotic oscillations of the beam.In the second part, we analyze the effect of feedback delays on a beam subjected to a harmonic base excitations. We find that the nature of the forced response is largely defined by the stability of the trivial solutions of the unforced response. For stable trivial solutions (i.e., inside the stability boundaries of the trivial solutions), the homogeneous response emanating from the feedback diminishes, leaving only the particular solution resulting from the external excitation. In this case, delayed feedback acts as a vibration absorber. On the other hand, for unstable trivial solutions, the response contains two co-existing frequencies. Depending on the excitation amplitude and the commensurability of the delayed-response frequency to the excitation frequency, the response is either periodic or quasiperiodic. 相似文献
5.
The paper addresses the forced flexural vibrations and dissipative heating of a circular viscoelastic plate with piezoactive
actuators under axisymmetric loading. A refined formulation of this coupled problem is considered. The viscoelastic behavior
of materials is described using the concept of complex moduli dependent on the temperature of dissipative heating. The electromechanical
behavior of the plate is modeled based on the Timoshenko hypotheses for the mechanical variables and analogous hypotheses
for the electric-field variables in the piezoactive layers of the actuator. The temperature is assumed constant throughout
the thickness. The nonlinear problem is solved by a time stepping method using, at each step, the discrete-orthogonalization
and finite-difference methods to solve the elastic and heat-conduction equations, respectively. A numerical study is made
of the effect of the shear strain, the temperature dependence of the material properties, fixation conditions, and geometrical
parameters of the plate on the vibrational characteristics and the electric potential applied to the actuator electrodes to
balance the mechanical load
Translated from Prikladnaya Mekhanika, Vol. 44, No. 9, pp. 104–114, September 2008. 相似文献
6.
L. O. Grigor’eva 《International Applied Mechanics》2007,43(3):303-308
The paper proposes a method to solve the problem of vibrations of a radially polarized piezoelectric cylinder subject to nonstationary
electric excitation. The dynamic electromechanical state of the cylinder is analyzed. The time-dependences of electric and
mechanical characteristics are plotted. The distribution of these characteristics over the cross section of a short cylinder
is examined. The region of end disturbances in a long cylinder is identified
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 3, pp. 73–79, March 2007. 相似文献
7.
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
8.
V. L. Karlash 《International Applied Mechanics》2007,43(7):786-793
The evolution of the planar vibrations of a rectangular piezoceramic plate as its aspect ratio is changed starting with 1
is studied. Experimental data are obtained using an integrated technique based on Meson’s circuit, Onoe’s circuit, and a piezotransformer
transducer. As the aspect ratio increases (square plate becomes rectangular), the intensity of electromagnetic vibrations
rapidly increases at the first longitudinal resonance and gradually decreases in the first radial mode. When the aspect ratio
is changed so that the length of one of the plate sides remains constant, the resonant frequencies of all vibration modes
change too
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 7, pp. 98–106, July 2007. 相似文献
9.
Nonlinear Longitudinal Vibrations of Transversally Polarized Piezoceramics: Experiments and Modeling 总被引:1,自引:0,他引:1
Nonlinear behavior of piezoceramics at strong electric fields is a well-known phenomenon and is described by various hysteresis curves. On the other hand, nonlinear vibration behavior of piezoceramics at weak electric fields has recently been attracting considerable attention. Ultrasonic motors (USM) utilize the piezoceramics at relatively weak electric fields near the resonance. The consistent efforts to improve the performance of these motors has led to a detailed investigation of their nonlinear behavior. Typical nonlinear dynamic effects can be observed, even if only the stator is experimentally investigated. At weak electric fields, the vibration behavior of piezoceramics is usually described by constitutive relations linearized around an operating point. However, in experiments at weak electric fields with longitudinal vibrations of piezoceramic rods, a typical nonlinear vibration behavior similar to that of the USM-stator is observed at near-resonance frequency excitations. The observed behavior is that of a softening Duffing-oscillator, including jump phenomena and multiple stable amplitude responses at the same excitation frequency and voltage. Other observed phenomena are the decrease of normalized amplitude responses with increasing excitation voltage and the presence of superharmonics in spectra. In this paper, we have attempted to model the nonlinear behavior using higher order (quadratic and cubic) conservative and dissipative terms in the constitutive equations. Hamilton's principle and the Ritz method is used to obtain the equation of motion that is solved using perturbation techniques. Using this solution, nonlinear parameters can be fitted from the experimental data. As an alternative approach, the partial differential equation is directly solved using perturbation techniques. The results of these two different approaches are compared. 相似文献
10.
This study is devoted to the experimental validation of a theoretical model of large amplitude vibrations of thin spherical
shells described in a previous study by the same authors. A modal analysis of the structure is first detailed. Then, a specific
mode coupling due to a 1:1:2 internal resonance between an axisymmetric mode and two companion asymmetric modes is especially
addressed. The structure is forced with a simple-harmonic signal of frequency close to the natural frequency of the axisymmetric
mode. The experimental setup, which allows precise measurements of the vibration amplitudes of the three involved modes, is
presented. Experimental frequency response curves showing the amplitude of the modes as functions of the driving frequency
are compared to the theoretical ones. A good qualitative agreement is obtained with the predictions given by in the model.
Some quantitative discrepancies are observed and discussed, and improvements of the model are proposed. 相似文献
11.
Coupled extension and thickness-twist vibrations of lateral field excited AT-cut quartz plates简 总被引:1,自引:0,他引:1
Ting-Feng Ma Rong-Xing Wu Ji Wang Jian-Ke Du Li-Li Yuan Fa-Peng Yu Chao Xie 《Acta Mechanica Sinica》2014,30(1):67-72
In this paper, the coupled extension and thickness- twist vibrations are studied for AT-cut quartz plates under Lateral Field Excitation (LFE) with variations along the x1- direction. Mindlin's two-dimensional equations are used for anisotropic crystal plates. Both free and electrically forced vibrations are considered. Important vibration characteristics are obtained, including dispersion relations, frequency spectra, and motional capacitances. It is shown that, to avoid the effects of the couplings between extension and thickness-twist vibrations, a series of discrete values of the length/thickness ratio of the crystal plate need to be excluded. The results are of fundamental significance for the design of LFE resonators and sensors. 相似文献
12.
V. L. Karlash 《International Applied Mechanics》2007,43(5):547-553
An attempt is made to systematize experimental data for a rectangular piezoceramic plate and to compare them with those on
planar vibrations of a thin piezoceramic half-disk. Experimental data on planar vibrations of a half-disk are discussed for
the first time. Neighboring vibration modes of a rectangular plate with solid electrodes demonstrate strong superposition
and coupling
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Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 89–96, May 2007. 相似文献
13.
Non-linear vibrations of doubly curved shallow shells 总被引:1,自引:0,他引:1
M. Amabili 《International Journal of Non》2005,40(5):683-710
Large amplitude (geometrically non-linear) vibrations of doubly curved shallow shells with rectangular base, simply supported at the four edges and subjected to harmonic excitation normal to the surface in the spectral neighbourhood of the fundamental mode are investigated. Two different non-linear strain-displacement relationships, from the Donnell's and Novozhilov's shell theories, are used to calculate the elastic strain energy. In-plane inertia and geometric imperfections are taken into account. The solution is obtained by Lagrangian approach. The non-linear equations of motion are studied by using (i) a code based on arclength continuation method that allows bifurcation analysis and (ii) direct time integration. Numerical results are compared to those available in the literature and convergence of the solution is shown. Interaction of modes having integer ratio among their natural frequencies, giving rise to internal resonances, is discussed. Shell stability under static and dynamic load is also investigated by using continuation method, bifurcation diagram from direct time integration and calculation of the Lyapunov exponents and Lyapunov dimension. Interesting phenomena such as (i) snap-through instability, (ii) subharmonic response, (iii) period doubling bifurcations and (iv) chaotic behaviour have been observed. 相似文献
14.
Mehmet Çevik 《International Journal of Non》2005,40(6):901-923
Non-linear coupled vertical and torsional vibrations of suspension bridges are investigated. Method of Multiple Scales, a perturbation technique, is applied to the equations to find approximate analytical solutions. The equations are not discretized as usually done, rather the perturbation method is applied directly to the partial differential equations. Free and forced vibrations with damping are investigated in detail. Amplitude and phase modulation equations are obtained. The dependence of non-linear frequency on amplitude is described. Steady-state solutions are analyzed. Frequency-response equation is derived and the jump phenomenon in the frequency-response curves resulting from non-linearity is considered. Effects of initial amplitude and phase values, amplitude of excitation, and damping coefficient on modal amplitudes, are determined. 相似文献
15.
On the free vibrations of a piezoceramic hollow sphere 总被引:1,自引:0,他引:1
The aim of the paper is to analyze the free vibrations of a piezoceramic hollow sphere with radial polarization. Using the cnoidal method and a genetic algorithm solves the equations of a radially inhomogeneous spherically isotropic piezoelastic medium. The Reddy and the cosine laws represent the functionally graded property of material. It is seen that for a piezoceramic hollow sphere, the piezoelectric effect consists in increasing the values for the natural frequencies in the specified classes of vibrations. 相似文献
16.
Lahcen Benchouaf El Hassan Boutyour El Mostafa Daya Michel Potier-Ferry 《Comptes Rendus Mecanique》2018,346(4):308-319
This paper deals with the non-linear vibration of sandwich viscoelastic shell structures. Coupling a harmonic balance method with the Galerkin's procedure, one obtains an amplitude equation depending on two complex coefficients. The latter are determined by solving a classical eigenvalue problem and two linear ones. This permits to get the non-linear frequency and the non-linear loss factor as functions of the displacement amplitude. To validate our approach, these relationships are illustrated in the case of a circular sandwich ring. 相似文献
17.
S. A. Q. Siddiqui M. F. Golnaraghi G. R. Heppler 《International Journal of Non》2003,38(10):1481-1493
The focus of this work is to develop a technique to obtain numerical solution over a long range of time for non-linear multi-body dynamic systems undergoing large amplitude motion. The system considered is an idealization of an important class of problems characterized by non-linear interaction between continuously distributed mass and stiffness and lumped mass and stiffness. This characteristic results in some distinctive features in the system response and also poses significant challenges in obtaining a solution.
In this paper, equations of motion are developed for large amplitude motion of a beam carrying a moving spring–mass. The equations of motion are solved using a new approach that uses average acceleration method to reduce non-linear ordinary differential equations to non-linear algebraic equations. The resulting non-linear algebraic equations are solved using an iterative method developed in this paper. Dynamics of the system is investigated using a time-frequency analysis technique. 相似文献
18.
Propagation of two-dimensional nonstationary vibrations in an electrically excited piezoceramic prismatic body 总被引:1,自引:1,他引:0
The paper outlines a numerical method to solve a plane problem for a piezoceramic prismatic body having rectangular cross-section
and undergoing mechanically excited nonstationary vibrations. The features of the onset and propagation of vibrations are
studied. The dynamic state of bodies with different widths is analyzed. The thickness and transverse displacements versus
time are plotted
Translated from Prikladnaya Mekhanika, Vol. 44, No. 11, pp. 71–78, November 2008. 相似文献
19.
We study the resonant dynamics of a two-degree-of-freedom system composed of a linear oscillator weakly coupled to a strongly non-linear one, with an essential (non-linearizable) cubic stiffness non-linearity. For the undamped system this leads to a series of internal resonances, depending on the level of (conserved) total energy of oscillation. We study in detail the 1:1 internal resonance, and show that the undamped system possesses stable and unstable synchronous periodic motions (non-linear normal modes—NNMs), as well as, asynchronous periodic motions (elliptic orbits—EOs). Furthermore, we show that when damping is introduced certain NNMs produce resonance capture phenomena, where a trajectory of the damped dynamics gets ‘captured’ in the neighborhood of a damped NNM before ‘escaping’ and becoming an oscillation with exponentially decaying amplitude. In turn, these resonance captures may lead to passive non-linear energy pumping phenomena from the linear to the non-linear oscillator. Thus, sustained resonance capture appears to provide a dynamical mechanism for passively transferring energy from one part of the system to another, in a one-way, irreversible fashion. Numerical integrations confirm the analytical predictions. 相似文献
20.
Linear and non-linear vibrations of a U-shaped hollow microcantilever beam filled with fluid and interacting with a small particle are investigated. The microfluidic device is assumed to be subjected to internal flowing fluid carrying a buoyant mass. The equations of motion are derived via extended Hamilton's principle and by using Euler-Bernoulli beam theory retaining geometric and inertial non-linearities. A reduced-order model is obtained applying Galerkin's method and solved by using a pseudo arc-length continuation and collocation scheme to perform bifurcation analysis and obtain frequency response curves. Direct time integration of the equations of motion has also been performed by using Adams-Moulton method to obtain time histories and analyze transient cantilever-particle interactions in depth. It is shown that exploiting near resonant non-linear behavior of the microcantilever could potentially yield enhanced sensor metrics. This is found to be due to the transitions that occur as a matter of particle movement near the saddle-node bifurcation points of the coupled system that lead to jumps between coexisting stable attractors. 相似文献