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     

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     

Damping the vibrations of a rectangular plate with piezoelectric actuators

The paper addresses the active damping of nonstationary vibrations of a hinged rectangular plate with distributed piezoelectric actuators. The problem is solved by two methods: (i) the classical method of balancing the fundamental vibration modes by applying the appropriate potential difference to the actuator and (ii) the dynamic-programming method that reduces the problem to an algebraic Riccati equation. The results produced by both approaches are presented and compared __________ Translated from Prikladnaya Mekhanika, Vol. 44, No. 2, pp. 78–84, February 2008.     

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 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     

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     

Bending of a partially clamped rectangular plate

Summary The present study deals with the bending of a rectangular plate with two opposite simply-supported edges and other two free edges having any portion, clamped in such a way that the slope is zero. The solution is obtained by means of a superposition proposed by Kurata and Hatano [3]. The case of a square plate under a uniform load or a point load has been studied in detail.

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Übersicht Es wird die Biegung einer rechteckigen Platte untersucht, von der zwei Ränder einfach unterstützt sind, während die anderen Ränder zum Teil frei sind, zum Teil so eingespannt, daß die Neigung verschwindet. Die Lösung wird mit Hilfe einer Superposition erhalten, die von Kurata und Hatano [3] vorgeschlagen wurde. Für den Fall einer quadratischen Platte unter einer gleichförmigen Last oder einer Einzellast werden die Berechnungen weiter ausgeführt.

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This paper is a part of author's Ph. D. thesis submitted to the Indian Institute of Technology, Kharagpur in 1965.     

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     

Forced axisymmetric vibrations and self-heating of thermoviscoelastic cylindrical shells with piezoelectric actuators

The coupled problem of the forced axisymmetric vibrations and self-heating of electrothermoviscoelastic cylindrical shells with piezoceramic actuators under monoharmonic electromechanical loading is solved. The temperature dependence of the complex characteristics of the passive and piezoactive materials is taken into account. The coupled nonlinear problem of electrothermoelasticity is solved by using a time-marching method with discrete orthogonalization at each time step (to integrate the equations of elasticity) and an explicit finite-difference method (to solve the heat-conduction equations). An analysis is made of the effect of the boundary conditions at the shell ends, the dimensions of the piezoactuator, and the self-heating temperature on the actuator voltage and the effectiveness of active damping of the forced vibrations of the shell under uniform transverse monoharmonic pressure     

Dynamic modelling and active vibration control of a submerged rectangular plate equipped with piezoelectric sensors and actuators

The active vibration control of a rectangular plate either partially or fully submerged in a fluid was investigated. Piezoelectric sensors and actuators were bonded to the plate, and the assumed mode method was used to derive a dynamic model for the submerged plate. The properties of the piezoelectric actuators and sensors, as well as their coupling to the structure, were used to derive the corresponding equations of their behaviour. The fluid effect was modelled according to the added virtual mass obtained by solving the Laplace equation. The natural vibration characteristics of the plate both in air and in water were obtained theoretically and were found to be consistent with the experimental results, and the changes in the natural frequencies resulting from submersion in fluid can be accurately predicted. A multi-input, multi-output positive position feedback controller was designed by taking the natural vibration characteristics into account and was then implemented by using a digital controller. The experimental results show that piezoelectric sensors and actuators along with the control algorithm can effectively suppress the vibration of a rectangular plate both in air and submerged in a fluid.     

A clamped rectangular plate containing a crack

In this paper the general problem of a rectangular plate clamped along two parallel sides and containing a crack parallel to the clamps is considered. The problem is formulated in terms of a system of singular integral equations and the asymptotic behaviour of the stress state near the corners is investigated. Numerical examples are considered for a clamped plate without a crack and with a centrally located crack, and the stress intensity factors and the stresses along the clamps are calculated.     

Free vibrations of a partially clamped trapezoidal plate

The natural frequencies and mode shapes of partially clamped trapezoidal cantilever plates having various swept-back angles are examined numerically and experimentally by a finite-element computer program, SAP6, and holographic interferometry, respectively. A good agreement is found between the numerical and the experimental results. The influence of the clamped position, the free-width ratio, and the swept-back angle on the vibratory behavior of the trapezoidal plates is investigated.Paper was presented at the 1990 SEM Spring Conference on Experimental Mechanics held in Albuquerque, NM on June 3–6.     

Basic equations of the theory of thermoviscoelastic plates with distributed sensors and actuators

The basic equations of the theory of thermoviscoelastic thin-walled plates with piezoelectric sensors and actuators under monoharmonic mechanical and electric loading are derived using the Kirchhoff–Love hypotheses. The thermomechanical behavior of passive and piezoactive materials is described using the concept of complex characteristics. Methods of solving nonlinear problems of active damping of thermomechanical vibrations of plates with sensors and actuators are considered. The effect of dissipative heating on the damping of axisymmetric vibrations of a thermoviscoelastic solid circular plate is analyzed as an example     

Bending vibrations of a rectangular poroelastic plate

This paper presents the equations of motion of an air saturated rectangular porous plate. The model is based on a mixed displacement–pressure formulation of the Biot–Allard theory [1]. We obtain a system of equations which describe the coupling beetween the solid and fluid phases of the plate. This system is solved by applying the Galerkin method.     

Free vibrations of a thin rectangular plate

An asympototic method developed by V.V. Kucherenko and the author is applied to the problem of free vibrations of a thin plate strip in a state of a plane strain. The first few terms of an asymptotic expansion of the natural frequencies are calculated. The results are compared with those obtained by using the classical and refined theories.     

Tension of a clamped rectangular plate containing a central crack

Using the fundamental solution of a single crack and the Fourier transform solution of an infinite strip, the tension problem of a clamped rectangular plate containing a central crack is reduced to solve a system of singular integral equations. Then, the normal stress on clamped side and the stress intensity factors of the central crack are carried out by means of Gauss-Jacobi integration formulas. The comparison of numerical results is shown in the “table of stress intensity factors”. This work was supported by the Science Fund of the Academy of Sciences of China.     

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     

A convergent method of solution for clamped rectangular plate

The conventional method of solution for clamped rectangular plate lies in releasing the constraints for rotation at the clamped sides and substituting them by equivalent distributed bending moments. This paper gives a general formulation of this method for arbitrary load with proof of the convergence, and discusses the rate of convergence for displacements and bending moments. The method and its convergence can be extended to the case of arbitrary boundary conditions and to plate on elastic foundation.The author expresses his sincere gratitude to Prof. Hu Hai-chang for guidance in this work.