1. Primary parametric resonance–primary resonance response of stiffened plates with moving boundary conditions
- Author
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Rong-Hui Wang, Qiang Han, and Niu-Jing Ma
- Subjects
Physics::Biological Physics ,business.industry ,Applied Mathematics ,Mechanical Engineering ,Aerospace Engineering ,Boundary (topology) ,Ocean Engineering ,Structural engineering ,Resonance (particle physics) ,Quantitative Biology::Cell Behavior ,Physics::Fluid Dynamics ,Condensed Matter::Soft Condensed Matter ,symbols.namesake ,Transverse plane ,Control and Systems Engineering ,Euler's formula ,symbols ,Boundary value problem ,Electrical and Electronic Engineering ,Parametric oscillator ,business ,Homotopy analysis method ,Mathematics ,Parametric statistics - Abstract
An approach is presented to investigate the nonlinear vibration of stiffened plates. A stiffened plate is divided into one plate and some stiffeners, with the plate considered to be geometrically nonlinear, and the stiffeners taken as geometrically nonlinear Euler beams. Lagrange equation and modal superposition method are used to derive the dynamic equilibrium equations of the stiffened plate according to the energy of the system. Besides, the effect caused by boundary movement is transformed into equivalent excitations. The primary parametric resonance–primary resonance of the stiffened plate is studied by using homotopy analysis method. Numerical examples for stiffened plates with different thicknesses of the plates are presented to discuss the amplitude–frequency and amplitude–excitation relationship of the primary parametric resonance–primary resonance. In addition, the analysis on how the damping coefficients and the transverse excitations influence amplitude–frequency curves is also carried out. Some nonlinear vibration characteristics of stiffened plates are obtained, which are useful for engineering design.
- Published
- 2014