Analysis on the motion of nonlinear vibration with fractional order and time variable mass

2022 ◽  
Vol 124 ◽  
pp. 107621
Author(s):  
Yue Yu ◽  
Wenyao Zhou ◽  
Zhengdi Zhang ◽  
Qinsheng Bi
Keyword(s):  
Nonlinear Vibration ◽  
Fractional Order ◽  
Variable Mass ◽  
Time Variable

Nonlinear Vibration Analysis of Viscoelastic Smart Sandwich Plates Through the use of Fractional Derivative Zener Model

2021 ◽  
pp. 2150061
Author(s):  
Hamid Reza Talebi Amanieh ◽  
Seyed Alireza Seyed Roknizadeh ◽  
Arash Reza
Keyword(s):  
Differential Equations ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Sandwich Plate ◽  
Functionally Graded ◽  
Viscoelastic Layer ◽  
Sandwich Plates ◽  
Multiple Time ◽  
Nonlinear Frequency

In this paper, the nonlinear vibrational behavior of a sandwich plate with embedded viscoelastic material is studied through the use of constitutive equations with fractional derivatives. The studied sandwich structure is consisted of a viscoelastic core that is located between the faces of functionally graded magneto-electro-elastic (FG-MEE). In order to determine the frequency-dependent feature of the viscoelastic layer, four-parameter fractional derivative model is utilized. The material properties of FG-MEE face sheets have been distributed considering the power law scheme along the thickness. In addition, for derivation of the governing equations on the sandwich plate, first-order shear deformation plate theory along with von Karman-type of kinematic nonlinearity are implemented. The derived partial differential equations (PDEs) have been transformed to the ordinary differential equations (ODEs) through the Galerkin method. After that, the nonlinear vibration equations for the sandwich plate have been solved by multiple time scale perturbation technique. Moreover, for evaluating the effect of different parameters such as electric and magnetic fields, fractional order, the ratio of the core-to-face thickness and the power low index on the nonlinear vibration characteristics of sandwich plates with FG-MEE face sheets, the parametric analysis has been performed. The obtained results revealed the enhanced nonlinear natural frequency through an increment in the fractional order. Furthermore, the prominent influence of fractional order on the nonlinear frequency of sandwich plate was declared at the negative electric potential and positive magnetic potential.

scholarly journals Feedback control for two-degree-of-freedom vibration system with fractional-order derivative damping

2017 ◽  
Vol 37 (3) ◽  
pp. 554-564
Author(s):  
Canchang Liu ◽  
Chicheng Ma ◽  
Jilei Zhou ◽  
Lu Liu ◽  
Shuchang Yue ◽  
...  
Keyword(s):  
Feedback Control ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Suspension System ◽  
Degree Of Freedom ◽  
Vehicle Suspension ◽  
Vibration System ◽  
Fractional Order Derivative ◽  
Vehicle Suspension System ◽  
Two Degree Of Freedom

A two-degree-of-freedom nonlinear vibration system of a quarter vehicle suspension system is studied by using the feedback control method considered the fractional-order derivative damping. The nonlinear dynamic model of two-degree-of-freedom vehicle suspension system is built and linear velocity and displacement controllers are used to control the nonlinear vibration of the vehicle suspension system. A case of the 1:1 internal resonance is considered. The amplitude–frequency response is obtained with the multiscale method. The asymptotic stability conditions of the nonlinear system can be gotten by using the Routh–Hurwitz criterion and the ranges of control parameters are gained in the condition of stable solutions to the system. The simulation results show that the feedback control can effectively reduce the amplitude of primary resonance, weaken or even eliminate the nonlinear vibration characteristics of the suspension system. Fractional orders have an impact on control performance, which should be considered in the control problem. The study will provide a theoretical basis and reference for the optimal design of the vehicle suspension system.

scholarly journals Nonlinear Vibration of a Nonlocal Nanobeam Resting on Fractional-Order Viscoelastic Pasternak Foundations

2018 ◽  
Vol 2 (3) ◽  
pp. 21 ◽  
Author(s):  
Guy Eyebe ◽  
Gambo Betchewe ◽  
Alidou Mohamadou ◽  
Timoleon Kofane
Keyword(s):  
Analytical Solution ◽  
Fractional Derivative ◽  
Nonlinear Vibration ◽  
Fractional Order ◽  
Nonlocal Elasticity ◽  
Multiple Scales ◽  
Approximate Analytical Solution ◽  
Nonlocal Elasticity Theory ◽  
Pasternak Foundation ◽  
D’Alembert Principle

In the present study, the nonlinear vibration of a nanobeam resting on the fractional order viscoelastic Winkler–Pasternak foundation is studied using nonlocal elasticity theory. The D’Alembert principle is used to derive the governing equation and the associated boundary conditions. The approximate analytical solution is obtained by applying the multiple scales method. A detailed parametric study is conducted, and the effects of the variation of different parameters belonging to the application problems on the system are calculated numerically and depicted. We remark that the order and the coefficient of the fractional derivative have a significant effect on the natural frequency and the amplitude of vibrations.

A priori estimate for the solution of a nonlocal boundary value problem for the McKendrick - von Foerster equation of fractional order

2020 ◽  
Vol 20 (1) ◽  
pp. 9-14
Author(s):  
R.Z. Berezgova ◽  
Keyword(s):  
Boundary Value Problem ◽  
Fractional Order ◽  
Boundary Value ◽  
A Priori ◽  
Nonlocal Boundary ◽  
A Priori Estimate ◽  
Time Variable ◽  
Nonlocal Boundary Value Problem ◽  
Priori Estimate

In this paper, by the method of energy inequalities, an a priori estimate for the solution of the nonlocal boundary value problem is obtained for the generalized Mackendrick - von Foerster equation with the Caputo operator with respect to the time variable.

Free Vibration of MDOF Systems with Nonperiodically Time-Varying Mass

2018 ◽  
Vol 18 (06) ◽  
pp. 1850077
Author(s):  
Seyed Mojtaba Hozhabrossadati ◽  
Ahmad Aftabi Sani
Keyword(s):  
Free Vibration ◽  
Variable Mass ◽  
Coupled System ◽  
Variable Coefficients ◽  
Time Variable ◽  
Viscous Damping ◽  
Transform Method ◽  
Constant Stiffness ◽  
Mdof Systems ◽  
Mass Spring

This paper deals with the free vibration response of MDOF mass-spring systems with time-variable mass and constant stiffness. To show the necessity of this study, a review on the related published articles is presented. After formulating the governing initial value problem which is a coupled system of differential equations with variable coefficients, the differential transform method (DTM) is employed to obtain an analytical solution. The proposed solutions are verified against exact results available in the literature. It is demonstrated that the effect of time-variable mass is equivalent to viscous damping. This viscous damping can be positive or negative depending on the sign of the mass change rate. This role is thoroughly investigated via numerical examples.

Sign in / Sign up

Export Citation Format

Share Document