Applications of He’s Amplitude-Frequency Formulation to the Free Vibration of Strongly Nonlinear Oscillators
نویسندگان
چکیده
In this paper, He's amplitude-frequency formulation is used to obtain a periodic solution of a nonlinear oscillator. We illustrate that He's amplitude-frequency formulation is very effective and convenient and does not require linearization or small perturbation. The obtained results are valid for the whole solution domain with high accuracy.
منابع مشابه
Assessing different nonlinear analysis methods for free vibrations of initially stressed composite laminated plates
In this paper, the nonlinear free vibrations of thin symmetric and non-symmetric cross-ply composite plates subjected to biaxial initial stresses are investigated. Because of their excellent properties such as specific strength and specific stiffness, composite plates have wide applications in aerospace and mechanical structures. Based on Von-Karman's strain-displacement relations and using Gal...
متن کاملSize-Dependent Large Amplitude Vibration Analysis of Nanoshells Using the Gurtin-Murdoch Model
Shell-type nanostructures have recently attracted a lot of attention due to their several applications. The surface stress effect plays an important role in the mechanical behavior of such structures because of their large surface-to-volume ratio. In this paper, an analytical approach is presented for analyzing the geometrically nonlinear free vibrations of cylindrical nanoshells. In order ...
متن کاملPeriodic solutions for some strongly nonlinear oscillations by He's energy balance method
In this paper, applying He’s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy. Keywords—He’s energy balance method; Periodic solution; Nonlinear oscillator; Discontinuous; Fracti...
متن کاملNonlinear Vibration of Functionally Graded Cylindrical Shells under Radial Harmonic Load
In this paper, the nonlinear vibration of functionally graded (FGM) cylindrical shells subjected to radial harmonic excitation is investigated. The nonlinear formulation is based on a Donnell’s nonlinear shallow-shell theory, in which the geometric nonlinearity takes the form of von Karman strains. The Lagrange equations of motion were obtained by an energy approach. In order to reduce the syst...
متن کاملA Note on Free Vibration of a Double-beam System with Nonlinear Elastic Inner Layer
In this note, small amplitude free vibration of a double-beam system in presence of inner layer nonlinearity is investigated. The nonlinearity is due to inner layer material and is not related to large amplitude vibration. At first, frequencies of a double-beam system with linear inner layer are studied and categorized as synchronous and asynchronous frequencies. It is revealed that the inner l...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2012