Applicability of the method of averaging for investigations of nonlinear vibrations of rectangular plates

1971 ◽  
Vol 22 (5) ◽  
pp. 575-578
Author(s):  
P. A. Bondarev
Keyword(s):  
Nonlinear Vibrations ◽  
Rectangular Plates ◽  
Method Of Averaging

Nonlinear vibrations and damping of fractional viscoelastic rectangular plates

2020 ◽  
Author(s):  
Marco Amabili ◽  
Prabakaran Balasubramanian ◽  
Giovanni Ferrari
Keyword(s):  
Nonlinear Vibrations ◽  
Rectangular Plates

Nonlinear Vibrations of Plates in Axial Pulsating Flow

2014 ◽  
Author(s):  
E. Tubaldi ◽  
M. Amabili ◽  
F. Alijani
Keyword(s):  
Flow Velocity ◽  
Nonlinear Vibrations ◽  
Plate Theory ◽  
Fluid Model ◽  
Equations Of Motion ◽  
Transmural Pressure ◽  
Pulsating Flow ◽  
Pulsation Frequency ◽  
Rectangular Plates ◽  
Flow Perturbation

A theoretical approach is presented to study nonlinear vibrations of thin infinitely long rectangular plates subjected to pulsatile axial inviscid flow. The case of plates in axial uniform flow under the action of constant transmural pressure is also addressed for different flow velocities. The equations of motion are obtained based on the von Karman nonlinear plate theory retaining in-plane inertia via Lagrangian approach. The fluid model is based on potential flow theory and the Galerkin method is applied to determine the expression of the flow perturbation potential. The effect of different system parameters such as flow velocity, pulsation amplitude, pulsation frequency, and channel pressurization on the stability of the plate and its geometrically nonlinear response to pulsating flow are fully discussed. In case of zero uniform transmural pressure numerical results show hardening type behavior for the entire flow velocity range when the pulsation frequency is spanned in the neighbourhood of the plate’s fundamental frequency. Conversely, a softening type behavior is presented when a uniform transmural pressure is introduced.

Nonlinear Vibrations of Pressurized Functionally Graded Plates Using Higher-Order Thickness Stretching Theory

2014 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Continuation ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Functionally Graded Plates

Nonlinear vibrations of moderately thick functionally graded (FG) rectangular plates are investigated by considering a higher-order shear deformation theory that takes into account the thickness deformation effect. The geometrically nonlinear strain-displacement relationships are derived retaining full non-linear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain. The plate is assumed to have immovable boundary conditions at the edges. The equations of motion are obtained by using multi-modal energy approach. A code based on pseudo arc-length continuation and collocation scheme is utilized for numerical continuation and bifurcation analysis. Results show that higher-order thickness deformation theories yield a significant accuracy improvement for nonlinear vibrations of highly pressurized functionally graded plates.

Nonlinear vibrations of FGM rectangular plates in thermal environments

2011 ◽  
Vol 66 (3) ◽  
pp. 251-270 ◽  
Author(s):  
F. Alijani ◽  
F. Bakhtiari-Nejad ◽  
M. Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Rectangular Plates ◽  
Thermal Environments

Nonlinear Vibrations of Rectangular Plates

1973 ◽  
Vol 99 (5) ◽  
pp. 853-864
Author(s):  
D. Jack Bayles ◽  
Richard L. Lowery ◽  
Donald E. Boyd
Keyword(s):  
Nonlinear Vibrations ◽  
Rectangular Plates
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