The Nature of Solutions of a Rayleigh‐Type Forced Vibration Equation with a Large Coefficient of Damping

1953 ◽  
Vol 24 (8) ◽  
pp. 1004-1007 ◽  
Author(s):  
Paul Brock
Keyword(s):  
Forced Vibration ◽  
Vibration Equation ◽  
Large Coefficient

scholarly journals Vibration Equation of Fractional Order Describing Viscoelasticity and Viscous Inertia

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 850-856 ◽  
Author(s):  
Jun-Sheng Duan ◽  
Yun-Yun Xu
Keyword(s):  
Fractional Derivative ◽  
Fractional Order ◽  
Fractional Derivatives ◽  
Harmonic Excitation ◽  
Steady State Response ◽  
Vibration System ◽  
Derivative Operator ◽  
Vibration Equation ◽  
State Response ◽  
Frequency Relation

Abstract The steady state response of a fractional order vibration system subject to harmonic excitation was studied by using the fractional derivative operator ${}_{-\infty} D_t^\beta,$where the order β is a real number satisfying 0 ≤ β ≤ 2. We derived that the fractional derivative contributes to the viscoelasticity if 0 < β < 1, while it contributes to the viscous inertia if 1 < β < 2. Thus the fractional derivative can represent the “spring-pot” element and also the “inerterpot” element proposed in the present article. The viscosity contribution coefficient, elasticity contribution coefficient, inertia contribution coefficient, amplitude-frequency relation, phase-frequency relation, and influence of the order are discussed in detail. The results show that fractional derivatives are applicable for characterizing the viscoelasticity and viscous inertia of materials.

scholarly journals Forced Vibration Analysis of Laminated Composite Shells Reinforced with Graphene Nanoplatelets Using Finite Element Method

2020 ◽  
Vol 2020 ◽  
pp. 1-17 ◽  
Author(s):  
Trung Thanh Tran ◽  
Van Ke Tran ◽  
Pham Binh Le ◽  
Van Minh Phung ◽  
Van Thom Do ◽  
...  
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Forced Vibration ◽  
Vibration Analysis ◽  
Shear Deformation Theory ◽  
Laminated Composite ◽  
Thermal Environments ◽  
Forced Vibration Analysis ◽  
Laminated Composite Shells ◽  
Element Method

This paper carries out forced vibration analysis of graphene nanoplatelet-reinforced composite laminated shells in thermal environments by employing the finite element method (FEM). Material properties including elastic modulus, specific gravity, and Poisson’s ratio are determined according to the Halpin–Tsai model. The first-order shear deformation theory (FSDT), which is based on the 8-node isoparametric element to establish the oscillation equation of shell structure, is employed in this work. We then code the computing program in the MATLAB application and examine the verification of convergence rate and reliability of the program by comparing the data of present work with those of other exact solutions. The effects of both geometric parameters and mechanical properties of materials on the forced vibration of the structure are investigated.

Integral terminal sliding-mode robust vibration control of large space intelligent truss structures using a disturbance observer

2021 ◽  
pp. 095441002110290
Author(s):  
Dalong Tian ◽  
Jianguo Guo
Keyword(s):  
Robust Control ◽  
Forced Vibration ◽  
Disturbance Observer ◽  
Sliding Mode ◽  
External Disturbance ◽  
Truss Structures ◽  
Model Parameters ◽  
Large Space ◽  
Terminal Sliding Mode ◽  
Piezoelectric Stack Actuator

This study aims to develop an advanced integral terminal sliding-mode robust control method using a disturbance observer (DO) to suppress the forced vibration of a large space intelligent truss structure (LSITS). First, the dynamics of the electromechanical coupling of the piezoelectric stack actuator and the LSITS, based on finite element and Lagrangian methods, are established. Subsequently, to constrict the vibration of the structure, a novel integral terminal sliding-mode control (ITSMC) law for the DO is used to estimate the parameter perturbation of the LSITS based on a continuous external disturbance. Simulation results show that, under a forced vibration and compared with the ITSMC system without a DO, the displacement amplitude of the ITSMC system with the DO is effectively reduced. In the case where the model parameters of the LSITS deviate by ±50%, and an unknown continuous external disturbance exists, the control system with the DO can adequately attenuate the structural vibration and realize robust control. Concurrently, the voltage of the employed piezoelectric stack actuator is reduced, and voltage jitter is alleviated.

Acoustically Forced Vibration of Greenhouse Tomato Blossoms to Induce Pollination

1968 ◽  
Vol 11 (5) ◽  
pp. 0731-0735 ◽  
Author(s):  
W. R. DeTar ◽  
C. G. Haugh and J. F. Hamilton
Keyword(s):  
Forced Vibration ◽  
Greenhouse Tomato

Forced vibration analysis of blade after selective laser shock processing based on Timoshenko’s beam theory

2020 ◽  
Vol 243 ◽  
pp. 112249 ◽  
Author(s):  
Peilin Fu ◽  
Jianghong Yuan ◽  
Xu Zhang ◽  
Guozheng Kang ◽  
Ping Wang ◽  
...  
Keyword(s):  
Forced Vibration ◽  
Vibration Analysis ◽  
Beam Theory ◽  
Laser Shock ◽  
Laser Shock Processing ◽  
Forced Vibration Analysis ◽  
Shock Processing
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