Complex Parametric Vibrations of Flexible Rectangular Plates

Experiments have been conducted to investigate the transition mechanisms attendant to the parametric vibrations of a simply supported rectangular plate subjected to a periodic load of the form P = P0 + P1 cos γt. It is found that the transition mechanisms, such as “jumps” within the zone and “dropout” from the zone, are influenced by the initial curvature of the plate and by interactions with the source of energy. Due to the possibility of transitions between the parametric oscillations and forced vibrations of the plate, “splitting” of the zone may occur. Preliminary experiments indicate that the transition mechanisms have a strong influence on the response of the plate to stochastic loading.

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On Dynamic Stability and Nonlinear Modal Interaction of Parametrically-Excited Rectangular Plates

14th Biennial Conference on Mechanical Vibration and Noise: Dynamics and Vibration of Time-Varying Systems and Structures ◽

10.1115/detc1993-0136 ◽

1993 ◽

Author(s):

Germain L. Ostiguy ◽

Ross M. Evan-Iwanowski

Keyword(s):

Dynamic Stability ◽

Rectangular Plates ◽

Modal Interaction ◽

Parametric Vibrations ◽

Geometric Imperfections ◽

Qualitative And Quantitative ◽

Recent Developments ◽

Quantitative Verification ◽

Nonlinear Modal Interaction ◽

Initial Geometric Imperfections

Abstract The authors review recent developments on the dynamic stability and nonlinear parametric vibrations of general rectangular plates. Emphasis is placed on nonlinear modal interaction in parametncally excited plates and various types of resonances are investigated. Analytical predictions are compared to experimental data to form a qualitative and quantitative verification of the solutions. Experimental results indicate that the presence of initial geometric imperfections can modify considerably the dynamic behavior of the plate and produce various types of resonances highly unpredictable beforehand and differing from those generally assumed in analytical studies.

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DYNAMIC STABILITY AND NONLINEAR PARAMETRIC VIBRATIONS OF RECTANGULAR PLATES

Dynamics with Friction: Modeling, Analysis and Experiment - Series on Stability, Vibration and Control of Systems, Series B ◽

10.1142/9789812811271_0007 ◽

2001 ◽

pp. 191-225

Author(s):

G. L. OSTIGUY

Keyword(s):

Dynamic Stability ◽

Rectangular Plates ◽

Parametric Vibrations

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Experimental Investigation and Dimensionless Analysis of Forming of Rectangular Plates Subjected to Hydrodynamic Loading

Прикладная механика и техническая физика ◽

10.15372/pmtf20170115 ◽

2017 ◽

Keyword(s):

Experimental Investigation ◽

Rectangular Plates ◽

Dimensionless Analysis ◽

Hydrodynamic Loading

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Using phase field and third-order shear deformation theory to study the effect of cracks on free vibration of rectangular plates with varying thickness

Transport and Communication Science Journal ◽

10.25073/tcsj.71.7.10 ◽

2020 ◽

Vol 71 (7) ◽

pp. 853-867

Author(s):

Phuc Pham Minh

Keyword(s):

Free Vibration ◽

Shear Deformation ◽

Phase Field ◽

Deformation Theory ◽

Plate Thickness ◽

Shear Deformation Theory ◽

Rectangular Plates ◽

Equilibrium Equations ◽

Third Order ◽

Free Vibration Frequency

The paper researches the free vibration of a rectangular plate with one or more cracks. The plate thickness varies along the x-axis with linear rules. Using Shi's third-order shear deformation theory and phase field theory to set up the equilibrium equations, which are solved by finite element methods. The frequency of free vibration plates is calculated and compared with the published articles, the agreement between the results is good. Then, the paper will examine the free vibration frequency of plate depending on the change of the plate thickness ratio, the length of cracks, the number of cracks, the location of cracks and different boundary conditions

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