Nonlinear vibrations of impacted rectangular plates. Comparison between numerical simulation and experiments

2008 ◽  
Vol 123 (5) ◽  
pp. 3665-3665
Author(s):  
Cédric Camier ◽  
Kevin Arcas ◽  
Stefan Bilbao
Keyword(s):  
Numerical Simulation ◽  
Nonlinear Vibrations ◽  
Rectangular Plates

Nonlinear Vibrations and Chaotic Dynamics of the Laminated Composite Piezoelectric Beam

2015 ◽  
Vol 137 (1) ◽  
Author(s):  
Minghui Yao ◽  
Wei Zhang ◽  
Zhigang Yao
Keyword(s):  
Numerical Simulation ◽  
Axial Load ◽  
Nonlinear Vibrations ◽  
Dynamical Behavior ◽  
Laminated Composite ◽  
Transverse Load ◽  
Nonlinear Phenomenon ◽  
Periodic Motions ◽  
Chaotic Motions ◽  
Piezoelectric Beam

This paper investigates the complicated dynamics behavior and the evolution law of the nonlinear vibrations of the simply supported laminated composite piezoelectric beam subjected to the axial load and the transverse load. Using the third-order shear deformation theory and the Hamilton's principle, the nonlinear governing equations of motion for the laminated composite piezoelectric beam are derived. Applying the method of multiple scales and Galerkin's approach to the partial differential governing equation, the four-dimensional averaged equation is obtained for the case of principal parametric resonance and 1:9 internal resonance. From the averaged equations obtained, numerical simulation is performed to study nonlinear vibrations of the laminated composite piezoelectric beam. The axial load, the transverse load, and the piezoelectric parameter are selected as the controlling parameters to analyze the law of complicated nonlinear dynamics of the laminated composite piezoelectric beam. Based on the results of numerical simulation, it is found that there exists the complex nonlinear phenomenon in motions of the laminated composite piezoelectric beam. In summary, numerical studies suggest that periodic motions and chaotic motions exist in nonlinear vibrations of the laminated composite piezoelectric beam. In addition, it is observed that the axial load, the transverse load and the piezoelectric parameter have significant influence on the nonlinear dynamical behavior of the beam. We can control the response of the system from chaotic motions to periodic motions by changing these parameters.

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
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