Dynamic stability of viscoelastic rectangular plates with concentrated masses

The focus of the present research is to eliminate the undesired steady-state vibrations at selected lines or locations in a vibrating plate by means of adding attachments at arbitrary selected locations. These attachments can be either added concentrated masses and/or translational or rotational springs which are connected to the plate at one end and grounded at the other. The case of attachment of translational and/or rotational oscillators systems is examined. In addition, imposing lines of zero displacements (nodal lines) at selected locations are also investigated. The dynamic Green's function method is employed. Several numerical examples are cited to verify the utility of the proposed method. In addition, sample experiments to measure the plate free and forced vibrations for the given boundary conditions are conducted and the experimental measurements are compared with the analytical results.

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Effect of concentrated masses with rotary inertia on vibrations of rectangular plates

Journal of Sound and Vibration ◽

10.1016/j.jsv.2005.11.035 ◽

2006 ◽

Vol 295 (1-2) ◽

pp. 1-12 ◽

Cited By ~ 14

Author(s):

M. Amabili ◽

M. Pellegrini ◽

F. Righi ◽

F. Vinci

Keyword(s):

Rotary Inertia ◽

Rectangular Plates ◽

Concentrated Masses

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Transverse Motions of Rectangular Plates Resting on Elastic Foundation and Under Concentrated Masses Moving at Varying Velocities

Latin American Journal of Solids and Structures ◽

10.1590/1679-78251429 ◽

2015 ◽

Vol 12 (7) ◽

pp. 1296-1318 ◽

Cited By ~ 1

Author(s):

Babatope Omolofe ◽

Sunday Tunbosun Oni

Keyword(s):

Elastic Foundation ◽

Rectangular Plates ◽

Concentrated Masses

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LATEST DEVELOPMENTS ON THE DYNAMIC STABILITY AND NONLINEAR PARAMETRIC RESPONSE OF GEOMETRICALLY IMPERFECT RECTANGULAR PLATES

Transactions of the Canadian Society for Mechanical Engineering ◽

10.1139/tcsme-1998-0029 ◽

1998 ◽

Vol 22 (4B) ◽

pp. 501-518 ◽

Cited By ~ 2

Author(s):

G.L. Ostiguy ◽

L. St-Georges ◽

S. Sassi

Keyword(s):

Dynamic Stability ◽

Asymptotic Method ◽

Plate Theory ◽

Lateral Displacement ◽

Equations Of Motion ◽

Rectangular Plates ◽

Rational Analysis ◽

Geometric Imperfection ◽

Direct Integration Method ◽

Parametric Response

The authors present a rational analysis of the effect of initial geometric imperfections on the dynamic stability and nonlinear parametric response of general rectangular plates, the plate theory used in the analysis may described as the dynamic analog of the von Kármán’s large deflection theory and is derived in terms of the stress function, the lateral displacement and the initial geometric imperfection. The governing equations are satisfied using the orthogonality properties of the assumed functions. The temporal response of the system is analyzed using a first-order asymptotic method and various types of resonances are investigated. The temporal equations of motion describing the nonlinear dynamic behaviour of the imperfect plates are also solved using a direct integration method and the results are compared with those obtained by the asymptotic method.

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Dynamic Stability of Nonlinear Antisymmetrically-Laminated Cross-Ply Rectangular Plates

Journal of Applied Mechanics ◽

10.1115/1.3176092 ◽

1989 ◽

Vol 56 (2) ◽

pp. 375-381 ◽

Cited By ~ 16

Author(s):

Andrzej Tylikowski

Keyword(s):

Asymptotic Stability ◽

Dynamic Stability ◽

Material Properties ◽

Stability Problem ◽

Large Deflection ◽

Direct Method ◽

Rectangular Plates ◽

Stability Criteria ◽

The Stability ◽

Liapunov's Direct Method

The dynamic stability problem is solved for rectangular plates that are laminated antisymmetrically about their middle plane and compressed by time-dependent deterministic or stochastic membrane forces. Moderately large deflection equations taking into account a coupling of in-plane and transverse motions are used. The asymptotic stability and almost-sure asymptotic stability criteria involving a damping coefficient and loading parameters are derived using Liapunov’s direct method. A relation between the stability of nonlinear equations and linearized ones is analyzed. An influence on the number of orthotropic layers, material properties for different classes of parametric excitation on stability domains is shown.

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