Related Experiment Video
Updated: Jan 4, 2026

Cutting Procedures, Tensile Testing, and Ageing of Flexible Unidirectional Composite Laminates
Published on: April 27, 2019
Free Vibration Analysis of Smart Laminated Functionally Graded CNT Reinforced Composite Plates via New Four-Variable
Tran Huu Quoc1, Tran Minh Tu1, Vu Van Tham1
1Faculty of Industrial and Civil Engineering, National University of Civil Engineering, Hanoi 100000, Vietnam.
Abstract:
This paper presents a new four-variable refined plate theory for free vibration analysis of laminated piezoelectric functionally graded carbon nanotube-reinforced composite plates (PFG-CNTRC). The present theory includes a parabolic distribution of transverse shear strain through the thickness and satisfies zero traction boundary conditions at both free surfaces of the plates. Thus, no shear correction factor is required. The distribution of carbon nanotubes across the thickness of each FG-CNT layer can be functionally graded or uniformly distributed. Additionally, the electric potential in piezoelectric layers is assumed to be quadratically distributed across the thickness. Equations of motion for PFG-CNTRC rectangular plates are derived using both Maxwell's equation and Hamilton's principle. Using the Navier technique, natural frequencies of the simply supported hybrid plate with closed circuit and open circuit of electrical boundary conditions are calculated. New parametric studies regarding the effect of the volume fraction, the CNTs distribution, the number of layers, CNT fiber orientation and thickness of the piezoelectric layer on the free vibration response of hybrid plates are performed.
Related Concept Videos
Bending of Members Made of Several Materials
Hooke's Law determines stress in each material, stating that stress is proportional to strain but varies due to each material's...
Fluid Pressure over Flat Plate of Variable Width
The pressure distribution on the plate can be calculated by determining the force that acts on a differential area strip of the plate. Thus, the magnitude of the force is equal to the...
Saint-Venant's Principle
Plastic Deformations of Members with a Single Plane of Symmetry
Fluid Pressure over Flat Plate of Constant Width
The resultant force...
Members Made of Elastoplastic Material
As the bending moment...

