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     

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.     

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     

Nonlinear vibrations and damping of fractional viscoelastic rectangular plates

Nonlinear Dynamics - A new model-free robust control scheme for payload swing angle attenuation of two-dimensional crane systems with varying rope length is introduced in this work. The proposed...     

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 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.     

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     

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.     

Nonlinear vibrations of a viscoelastic plate with concentrated masses

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. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007.     

Planar electroelastic vibrations of piezoceramic rectangular plate and half-disk

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 __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 5, pp. 89–96, May 2007.     

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     

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 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