On large deflections of viscoelastic plates

Bock, Igor

doi:10.1016/s0378-4754(99)00066-x

Cited by 7 publications

(6 citation statements)

References 10 publications

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“…, k, which will enable us to obtain less restrictive conditions for the existence of a solution. In the special case k = 1 the originally long memory integro-differential stress-strain relations can be transformed to a first-order differential system with respect to time [1]. In both cases a weak formulation of the problem can be expressed as one canonical nonstationary variational inequality with respect to admissible deflections.…”

Section: Introductionmentioning

confidence: 99%

On a contact problem for a viscoelastic von Karman plate and its semidiscretization

Bock

Lovíšek

2005

Appl Math

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Section: Introductionmentioning

confidence: 99%

On a contact problem for a viscoelastic von Karman plate and its semidiscretization

Bock

Lovíšek

2005

Appl Math

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“…(24) with parameters ξ 01 = ξ 11 = 0, and ξ 02 = ξ 03 = ξ 12 = ξ 13 = 1, in terms of Eqs. (20) and (21). Substitute Eq.…”

Section: Equivalent Transverse Forcementioning

confidence: 96%

“…(72). We shall use the Coiflets with N = 6 and M 1 = 7 [13,20] and scaling parameters n = m = 3. For the solution of the dynamic Eq.…”

Section: Equivalent Transverse Forcementioning

confidence: 99%

A wavelet approach for active-passive vibration control of laminated plates

Wang

Zhou

2012

Acta Mech Sin

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As an extension of the wavelet approach to vibration control of piezoelectric beam-type plates developed earlier by the authors, this paper proposes a hybrid activepassive control strategy for suppressing vibrations of laminated rectangular plates bonded with distributed piezoelectric sensors and actuators via thin viscoelastic bonding layers. Owing to the low-pass filtering property of scaling function transform in orthogonal wavelet theory, this waveletbased control method has the ability to automatically filter out noise-like signal in the feedback control loop, hence reducing the risk of residual coupling effects which are usually the source of spillover instability. Moreover, the existence of thin viscoelastic bonding layers can further improve robustness and reliability of the system through dissipating the energy of any other possible noise induced partially by numerical errors during the control process. A simulation procedure based on an advanced wavelet-Galerkin technique is suggested to realize the hybrid active-passive control process. Numerical results demonstrate the efficiency of the proposed approach.

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“…The system can be transformed into one nonlinear Volterra type integral equation in the Hilbert space of deflection functions. The conditions for solving it were derived in [2]. This approach cannot be applied in the anisotropic case.…”

Section: Introductionmentioning

confidence: 99%

On a von Kármán System for Anisotropic Viscoelastic Plates

Bock

2005

Proc Appl Math and Mech

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We deal with a nonlinear system of equations describing the in-plane displacements and the deflection of the anisotropic viscoelastic plate made of a long memory material acting under the perpendicular load. We derive the full von Kármán system for the in-plane displacements and the deflection of the middle surface of the plate. The system contains the nonlinear integropartial differential operators applied to the in-plain strain tensor and to the tensor product of the displacement gradients. If the right-hand side of the system fulfils some estimate then the existence of a weak solution can be derived using the Rothe's method.

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On large deflections of viscoelastic plates

Cited by 7 publications

References 10 publications

On a contact problem for a viscoelastic von Karman plate and its semidiscretization

On a contact problem for a viscoelastic von Karman plate and its semidiscretization

A wavelet approach for active-passive vibration control of laminated plates

On a von Kármán System for Anisotropic Viscoelastic Plates

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