Influences of two-parameter elastic foundations on nonlinear free vibration of anisotropic shallow shell structures with variable parameters

The p-version of the finite element method is used in conjunction with the blending function method to investigate the nonlinear free vibration of a doubly curved shallow shell of elliptical plan-form. The effects of transverse shear deformations, rotary inertia, and geometrical nonlinearity are taken into account. The harmonic balance method is used to derive the equations of free motion. The resultant nonlinear equations are solved iteratively using the linearized updated mode method. The efficiency of the method is demonstrated through convergence study and comparison with published results. The effects of geometric parameters such as thickness, ellipse aspects, and curvatures on the backbone curves of a clamped doubly curved shallow shell of elliptical plan-form are studied. It is shown that the increase or decrease of the hardening behavior is dependent upon these parameters.

Download Full-text

Adaptive Control of Nonlinear Free Vibration of Shallow Shell Using Piezoelectric Actuators

AIAA Journal ◽

10.2514/1.38520 ◽

2011 ◽

Vol 49 (3) ◽

pp. 472-488 ◽

Cited By ~ 7

Author(s):

Minseock Park ◽

Adam Przekop ◽

Thongchai Phairoh ◽

Jen-Kuang Huang ◽

Chuh Mei

Keyword(s):

Adaptive Control ◽

Free Vibration ◽

Shallow Shell ◽

Piezoelectric Actuators ◽

Nonlinear Free Vibration

Download Full-text

Analytical free vibration solutions of fully free orthotropic rectangular thin plates on two-parameter elastic foundations by the symplectic superposition method

Journal of Vibration and Control ◽

10.1177/1077546320967823 ◽

2020 ◽

pp. 107754632096782

Author(s):

Xin Su ◽

Eburilitu Bai

Keyword(s):

Free Vibration ◽

Fundamental Solutions ◽

Thin Plates ◽

Superposition Method ◽

Elastic Foundations ◽

Vibration Problem ◽

Separation Variable ◽

Vibration Problems ◽

Two Parameter ◽

Free Edges

The free vibration of orthotropic rectangular thin plates with four free edges on two-parameter elastic foundations is studied by the symplectic superposition method. Firstly, by analyzing the boundary conditions, the original vibration problem is converted into two sub-vibration problems of the plates slidingly clamped at two opposite edges. Based on slidingly clamped at two opposite edges, the fundamental solutions of these two sub-vibration problems are respectively derived by the separation variable method of the corresponding Hamiltonian system, and then the symplectic superposition solution of the original vibration problem is obtained by superimposing the fundamental solutions of the two sub-problems. Finally, the symplectic superposition solution obtained in this study is verified by calculating the frequencies and mode functions of several concrete rectangular thin plates with four free edges.

Download Full-text