Size-Dependent Nonlinear Free and Forced Vibration Analyses of a Functionally Graded Microplate Subjected to Transverse Patch Loading
Publication: Journal of Engineering Mechanics
Volume 149, Issue 10
Abstract
This paper presents a semianalytical methodology for the nonlinear vibration of a functionally graded microplate under transverse patch loadings. The higher-order shear deformation theory (HSDT) is combined with the modified strain gradient theory (MSGT) to model the microplate. The power-law function is used to model the functionally graded material. Hamilton’s principle is used to obtain the governing partial differential equations of motion, which are then solved using Galerkin’s method. The nonlinear free and forced vibration responses are obtained using the incremental harmonic balance (IHB) method, where the incremental part is performed using the arc-length continuation methods. The dependence of the steady-state amplitude on the amplitude of initial perturbation is studied using time history plots. These are plotted using the Newmark- method. The effects of various parameters such as the power-law index, thickness of plate, thickness to material length scale parameter ratio, damping coefficient, different boundary conditions, and different positions of patch loading and its concentrations on the nonlinear free and forced vibration characteristics are examined in detail.
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Data Availability Statement
All data, models, or code that support the findings of this study are available from the corresponding author upon reasonable request.
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Information
Published In
Journal of Engineering Mechanics
Volume 149 • Issue 10 • October 2023
Copyright
© 2023 American Society of Civil Engineers.
History
Received: Feb 28, 2023
Accepted: Jun 23, 2023
Published online: Aug 10, 2023
Published in print: Oct 1, 2023
Discussion open until: Jan 10, 2024
ASCE Technical Topics:
- Continuum mechanics
- Deformation (mechanics)
- Design (by type)
- Dynamics (solid mechanics)
- Engineering fundamentals
- Engineering mechanics
- Equations of motion
- Load factors
- Material mechanics
- Materials engineering
- Mathematics
- Motion (dynamics)
- Nonlinear analysis
- Parameters (statistics)
- Shear deformation
- Solid mechanics
- Static loads
- Statics (mechanics)
- Statistics
- Strain
- Structural analysis
- Structural design
- Structural engineering
- Structural mechanics
- Transverse loads
- Vibration
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