Basic equations for thermoviscoelastic plates with distributed actuators under monoharmonic loading

The basic equations for thin-walled thermoviscoelastic plates with distributed piezoelectric actuators under monoharmonic mechanical and electric loads are derived. The thermomechanical behavior of materials is described using the concept of complex characteristics. Variational methods of solving nonlinear problems of active damping of the bending vibrations of plates are considered. The effect of dissipative heating on the damping of the axisymmetric bending vibrations of a circular plate is examined as an example Translated from Prikladnaya Mekhanika, Vol. 45, No. 2, pp. 107–123, February 2009.     

Active damping of vibrations of plates subject to unknown pressure

An approach to the active damping of the forced resonant vibrations of orthotropic thermoviscoelastic plates with distributed sensors and actuators is proposed. The mechanical load is assumed unknown and is determined from the sensors’ indications. The problem of active damping of an isotropic thermoviscoelastic rectangular plate with hinged edges is solved as an example. A formula for the voltage to be applied to the actuator to damp the forced vibrations in the first mode is derived. The effect of the dimensions of the sensor and actuator and the dissipative properties of the materials on the effectiveness of active damping is studied     

Active damping of the vibrations of a plate using sensor data: effect of boundary conditions

A new approach is followed to study the effect of mixed mechanical boundary conditions on the effectiveness of active damping of the forced resonant vibrations of thermoviscoelastic orthotropic plates. The problem is solved by the Bubnov–Galerkin method. Formulas for the voltage that should be applied to the actuator to damp the first vibration mode are derived. It is shown that the mechanical boundary conditions, the dissipative properties of the material, and the dimenstions of the sensors and actuators have a strong effect on the effectiveness of active damping of the vibrations of plates     

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     

Active damping of the resonant vibrations of a flexible viscoelastic rectangular plate

The active damping of the resonant vibrations of a hinged flexible viscoelastic rectangular plate with distributed piezoelectric sensors and actuators is considered. It is shown that it is possible to considerably decrease the amplitude of resonant vibrations by choosing the appropriate feedback factor. The collective effect of geometrical nonlinearity and dissipative properties of the material on the effectiveness of active damping of the resonance vibrations of rectangular plates with sensors and actuators is analyzed     

Forced Vibration and Self-Heating of a Thermoviscoelastic Cylindrical Shear Compliant Shell with Piezoelectric Actuators and Sensors*

International Applied Mechanics - The problem of the forced resonant vibrations and dissipative heating of a hinged thermoviscoelastic cylindrical shell with piezoelectric actuators and sensors is...     

Basic relations of the theory of thermoviscoelastic plates with distributed sensors

The basic relations of the thermomechanics of thin-walled viscoelastic plates with distributed piezoelectric sensors under monogarmonic mechanical loading are presented. To describe the thermomechanical behavior of materials, the concept of complex characteristics is used. Numerical and variational methods are used to study the forced resonant vibrations of viscoelastic plates with distributed piezoelectric sensors. The effect of dissipative heating on the readings of the sensors of a circular viscoelastic plate undergoing axisymmetric resonant bending vibrations is analyzed as an example     

Active damping of the resonant vibrations of a flexible cylindrical panel with sensors and actuators

The active damping of the resonant vibrations of a flexible cylindrical panel with rectangular planform and clamped edges is considered. The damping is done with distributed piezoelectric sensors and actuators. It is shown that the amplitude of the resonant vibrations can be substantially decreased by choosing the appropriate feedback factors. The combined effect of geometrical nonlinearity and dissipative properties of the material on the effectiveness of damping is analyzed     

Forced axisymmetric vibrations and self-heating of a circular viscoelastic plate,controlled with piezoelectric sensors and actuators

The forced monoharmonic vibrations and self-heating of a circular thermoviscoelastic plate with piezoelectric sensor and actuator are studied. The viscoelastic behavior of the passive (without piezoeffect) and piezoactive materials is described using the concept of complex moduli. The problems of electroelasticity and heat conduction are solved numerically, assuming that the mechanical load is unknown. The effect of self-heating on the active damping of the vibrations of the plate is analyzed     

Damping the resonant flexural vibration of a hinged plate with actuators

The paper addresses the active damping of the resonant flexural vibration of a hinged viscoelastic rectangular plate with distributed piezoelectric actuators. The thermomechanical behavior of passive and active materials is described using the concept of complex characteristics. The interaction of the mechanical and temperature fields is taken into account. To solve the problem, the variational and Bubnov–Galerkin methods are used. The effect of the temperature of dissipative heating on the effectiveness of the active damping of resonant vibration is studied     

Damping the flexural vibration of a clamped viscoelastic rectangular plate with piezoelectric actuators

The paper addresses the active damping of the resonant flexural vibration of a clamped viscoelastic rectangular plate with distributed piezoelectric actuators. The thermomechanical behavior of passive and active materials is described using the concept of complex characteristics. The interaction of the mechanical and thermal fields is taken into account. To solve the problem, the variational and Bubnov–Galerkin methods are used. The effect of the temperature of dissipative heating on the effectiveness of the active damping of resonant vibration is studied     

超弹性NiTi合金丝动力特性试验及本构模型研究

形状记忆合金(SMA)是一种兼具感知和驱动功能的功能材料,因其独特的形状记忆效应、超弹性和高阻尼等特性,成为土木工程结构振动控制的理想材料.论文研究了超弹性NiTi丝的动力特性和应变率相关的本构模型.试验测试了NiTi丝在不同应变率下的力学性能,建立了应力增量与应变率的关系方程.在试验的基础上,提出了改进的SMA本构模...     

Resonant vibrations of a clamped viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a viscoelastic rectangular plate undergoing resonant vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the Bubnov–Galerkin method. The effect of the mechanical boundary conditions and dissipative-heating temperature on the performance of the sensors is analyzed     

Influence of shear strains on damping the vibrations of a rectangular plate with piezoelectric actuators

The problem of active damping of the nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators is solved using Timoshenko’s hypotheses. To this end, two methods are employed: (i) a classical method of balancing the principal vibration modes by applying the appropriate potential difference to the actuator and (ii) the dynamical-programming method that reduces the problem to the matrix algebraic Riccati equation. The results obtained by both approaches are compared. The effect of the shear modulus on the amplitude of the damping potential difference and the deflection of the plate is analyzed     

Resonant vibrations of a hinged viscoelastic rectangular plate

The paper examines the effect of dissipative heating on the performance of a sensor in a hinged thermoviscoelastic rectangular plate undergoing resonant flexural vibrations. The thermoviscoelastic behavior of materials is described using the concept of complex characteristics. The coupling of the electromechanical and thermal fields is taken into account. The nonlinear problem is solved by the variational and Bubnov–Galerkin methods. The effect of the dissipative-heating temperature and the dimensions of the sensor on its performance during resonant vibrations of the plate is analyzed.     

Damping for large-amplitude vibrations of plates and curved panels,Part 1: Modeling and experiments

Theoretical and experimental non-linear vibrations of thin rectangular plates and curved panels subjected to out-of-plane harmonic excitation are investigated. Experiments have been performed on isotropic and laminated sandwich plates and panels with supported and free boundary conditions. A sophisticated measuring technique has been developed to characterize the non-linear behavior experimentally by using a Laser Doppler Vibrometer and a stepped-sine testing procedure. The theoretical approach is based on Donnell's non-linear shell theory (since the tested plates are very thin) but retaining in-plane inertia, taking into account the effect of geometric imperfections. A unified energy approach has been utilized to obtain the discretized non-linear equations of motion by using the linear natural modes of vibration. Moreover, a pseudo arc-length continuation and collocation scheme has been used to obtain the periodic solutions and perform bifurcation analysis. Comparisons between numerical simulations and the experiments show good qualitative and quantitative agreement. It is found that, in order to simulate large-amplitude vibrations, a damping value much larger than the linear modal damping should be considered. This indicates a very large and non-linear increase of damping with the increase of the excitation and vibration amplitude for plates and curved panels with different shape, boundary conditions and materials.     

Experimental and theoretical study on large amplitude vibrations of clamped rubber plates

In this paper, the large amplitude forced vibrations of thin rectangular plates made of different types of rubbers are investigated both experimentally and theoretically. The excitation is provided by a concentrated transversal harmonic load. Clamped boundary conditions at the edges are considered, while rotary inertia, geometric imperfections and shear deformation are neglected since they are negligible for the studied cases. The von Kármán nonlinear strain-displacement relationships are used in the theoretical study; the viscoelastic behaviour of the material is modelled using the Kelvin-Voigt model, which introduces nonlinear damping. An equivalent viscous damping model has also been created for comparison. In-plane pre-loads applied during the assembly of the plate to the frame are taken into account. In the experimental study, two rubber plates with different material and thicknesses have been considered; a silicone plate and a neoprene plate. The plates have been fixed to a heavy rectangular metal frame with an initial stretching. The large amplitude vibrations of the plates in the spectral neighbourhood of the first resonance have been measured at various harmonic force levels. A laser Doppler vibrometer has been used to measure the plate response. Maximum vibration amplitude larger than three times the thickness of the plate has been achieved, corresponding to a hardening type nonlinear response. Experimental frequency-response curves have been very satisfactorily compared to numerical results. Results show that the identified retardation time increases when the excitation level is increased, similar to the equivalent viscous damping but to a lesser extent due to its nonlinear nature. The nonlinearity introduced by the Kelvin-Voigt viscoelasticity model is found to be not sufficient to capture the dissipation present in the rubber plates during large amplitude vibrations.     

采用压电机敏元件进行结构振动控制Ⅲ：控制系统设计与实验研究

采用作者在上篇导出的压电耦合体动力学模型，给出了压电主动阻尼控制系统的设计方法；导出了压电耦合梁系统的作动方程和检测方程的显式表达式。以此为基础，以简单梁为对象，对压电检测器和作动器的性能、粘结层的影响、压电主动阻尼控制及压电主、被动阻尼双控制进行了实验研究     

Thermoviscoelastic deformations of functionally graded thin plates

By considering the influence of the mid-plane strains due to the inhomogeneous property of FGMs across the thickness, a constitutive equation of thermoviscoelastic functionally graded thin plates is reduced on the basis of the Kirchhoff's hypothesis for the classical plate theory. The corresponding simplified Gurtin's type variational principle of functionally graded thin plates is presented by means of the modern convolution bilinear forms. By using the Navier analytic method or combining the Ritz method in the spatial domain and the Legendre interpolation method in the temporal domain, the static thermoelastic deformations or quasi-static thermoviscoelastic deformations of functionally graded thin plates under mechanical or thermal loads are studied.