scholarly journals Dynamic Modeling and Response of a Rotating Cantilever Beam with a Concentrated Mass

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Yang Yong-feng ◽  
Wang Yan-lin ◽  
Chen Hu ◽  
Wu Min-juan
Keyword(s):  
Natural Frequency ◽  
Lagrange Equation ◽  
Concentrated Mass ◽  
Assumed Mode Method ◽  
Damping Characteristics ◽  
Coupling System ◽  
Mode Method ◽  
Position Parameter ◽  
Mass Position ◽  
Assumed Mode

The rigid-flexible coupling system with a hub and concentrated mass is studied in this paper. Considering the second-order coupling of axial displacement which is caused by transverse deformation of the beam, the dynamic equations of the system are established using the second Lagrange equation and the assumed mode method. The simulation results show that the concentrated mass mainly suppresses the vibration and exhibits damping characteristics. When the nondimensional mass position parameterβ>0.67, the first natural frequency is reduced as the concentrated mass increases. Whenβ<0.67, the first natural frequency is increased as the concentrated mass increases. We also find the maximum first natural frequency nondimensional position for the concentrated mass.

Study on the Iced Quad-Bundle Transmission Lines Incorporated With Viscoelastic Antigalloping Devices

2015 ◽  
Vol 137 (6) ◽  
Author(s):  
Zhao-Dong Xu ◽  
Ling-Zhi Xu ◽  
Fei-Hong Xu
Keyword(s):  
Transmission Lines ◽  
Lagrange Equation ◽  
Dynamic Responses ◽  
Strong Wind ◽  
Viscoelastic Damper ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Energy Dissipation Capacity ◽  
Experimental And Theoretical Studies ◽  
Assumed Mode

The viscoelastic damper is one of the most promising devices for vibration mitigation. In order to reduce dynamic responses of iced transmission lines due to strong wind, a new kind of viscoelastic antigalloping device (VEAGD) is developed. Experimental and theoretical studies indicate that the device has fine energy dissipation capacity and high damping characteristic. Then, the motion equations of the iced quad-bundle transmission lines incorporated with VEAGDs are established by employing Lagrange equation based on the assumed mode method. At the same time, the parameters and positions of the VEAGDs are determined optimally by the genetic algorithm. Numerical analysis results show that VEAGDs have excellent antigalloping effect, and the dynamic responses of the transmission lines with optimally designed VEAGDs are mitigated more effectively.

scholarly journals Vibration analysis and pull-in instability behavior in a multiwalled piezoelectric nanosensor with fluid flow conveyance

2020 ◽  
Vol 11 ◽  
pp. 1072-1081
Author(s):  
Sayyid H Hashemi Kachapi
Keyword(s):  
Differential Equations ◽  
Viscous Fluid ◽  
Natural Frequency ◽  
Mass Density ◽  
Fluid Velocity ◽  
Assumed Mode Method ◽  
Interface Theory ◽  
Mode Method ◽  
Assumed Mode ◽  
Piezoelectric Constants

In this work, surface/interface effects for pull-in voltage and viscous fluid velocity effects on the dimensionless natural frequency of fluid-conveying multiwalled piezoelectric nanosensors (FC-MWPENSs) based on cylindrical nanoshells is investigated using the Gurtin–Murdoch surface/interface theory. The nanosensor is embedded in a viscoelastic foundation and subjected to nonlinear van der Waals and electrostatic forces. Hamilton’s principle is used to derive the governing and boundary conditions and is also the assumed mode method used for changing the partial differential equations into ordinary differential equations. The influences of the surface/interface effect, such as Lame’s constants, residual stress, piezoelectric constants and mass density, are considered for analysis of the dimensionless natural frequency with respect to the viscous fluid velocity and pull-in voltage of the FC-MWPENSs.

Numerical Analysis of the Iced Transmission Line Galloping

2014 ◽  
Vol 607 ◽  
pp. 894-900
Author(s):  
Li Qin ◽  
Tian Yuan Xu
Keyword(s):  
Wind Speed ◽  
Transmission Line ◽  
Lagrange Equation ◽  
Equations Of Motion ◽  
Lyapunov Stability Theory ◽  
Assumed Mode Method ◽  
Torsional Response ◽  
Critical Wind Speed ◽  
Mode Method ◽  
Assumed Mode

By used the assumed mode method to simulate the iced transmission line galloping,with three generalized coordinates to represent the iced transmission line galloping. In order to avoid the complicated calculation of vector,used the Lagrange equation to build the nonlinear equations of iced transmission line from the perspective of energy,used the Runge-Kutta numerical calculation to solve the equations of motion and get the iced transmission line’s across-wind,along-wind and the torsional response. Based on Lyapunov stability theory to deduce the critical wind speed of the iced transmission line galloping. And had used a test iced transmission line to verify the feasibility of the numerical solution and the critical wind speed.

scholarly journals Vibration analysis and pull-in instability behavior in multi walled piezoelectric nano-sensor with fluid flow conveyance: influences of surface/interface energy

2019 ◽  
Author(s):  
Sayyid H Hashemi Kachapi
Keyword(s):  
Viscous Fluid ◽  
Natural Frequency ◽  
Mass Density ◽  
Fluid Velocity ◽  
Interface Energy ◽  
Assumed Mode Method ◽  
Interface Theory ◽  
Mode Method ◽  
Assumed Mode ◽  
Piezoelectric Constants

In this work, surface/interface effects for pull-in voltage and viscous fluid velocity effects on dimensionless natural frequency (DNF) of fluid-conveying multi walled piezoelectric nanoresonator (FC-MWPENS) based on cylindrical nanoshell is investigated using the Gurtin–Murdoch surface/interface theory. The nano-sensor is embedded in viscoelastic foundation, nonlinear van der Waals and electrostatic forces. Hamilton’s principle is used for deriving of the governing equations and boundary conditions and also the assumed mode method is used for changing the partial differential equations into ordinary differential equation. The influences of the surface/interface effect such as Lame’s constants, residual stress, piezoelectric constants and mass density are considered for analysis of dimensionless natural frequency respect to viscous fluid velocity and pull-in voltage of FC-MWPENS.

Nonlinear vibration analysis of a membrane based on large deflection theory

2017 ◽  
Vol 24 (12) ◽  
pp. 2418-2429 ◽  
Author(s):  
Xiang Liu ◽  
Guo-ping Cai ◽  
Fu-jun Peng ◽  
Hua Zhang ◽  
Liang-liang Lv
Keyword(s):  
Nonlinear Vibration ◽  
Natural Frequency ◽  
Large Deflection ◽  
Nonlinear Fem ◽  
Assumed Mode Method ◽  
Discretization Methods ◽  
Mode Method ◽  
Deflection Theory ◽  
Large Deflection Theory ◽  
Assumed Mode

This paper investigates nonlinear vibration of a simply supported rectangular membrane based on large deflection theory. Dynamic stress caused by transverse displacement of the membrane is considered in modeling the membrane. The assumed mode method and the nonlinear finite element method (FEM) are both used as discretization methods for the membrane. In the assumed mode method, an approximate analytical formula of the natural frequency is derived. In the nonlinear FEM, a three-node triangular membrane element is proposed. The difference between the membrane’s dynamical characteristics obtained by these two discretization methods is revealed. Simulation results indicate that natural frequency of the membrane will rise along with the increasing of the vibration amplitude of the membrane, and the natural frequency obtained by the nonlinear FEM is larger than that obtained by the assumed mode method. When the membrane vibration is small, the assumed mode method may achieve a reasonable result, but it may lead to a big error when the membrane vibration is large.

The Squeeze Film Damping Effect on Dynamic Responses of Micro-Electromechanical Resonators

2013 ◽  
Vol 284-287 ◽  
pp. 1961-1965 ◽  
Author(s):  
Shih Chieh Sun ◽  
Chi Wei Chung ◽  
Chao Ming Hsu ◽  
Jao Hwa Kuang
Keyword(s):  
Dynamic Responses ◽  
Squeeze Film ◽  
Assumed Mode Method ◽  
Damping Effect ◽  
Lagrange’S Equation ◽  
Damping Characteristics ◽  
Squeeze Film Damping ◽  
Mode Method ◽  
Eigen Solutions ◽  
Assumed Mode

The air squeeze film damping effect on the dynamic responses of clamped micro- electromechanical resonators is investigated in this study. A dynamic model for a clamped micro- electromechanical resonator with the damping consideration is derived using Lagrange’s equation. The corresponding resonator eigen solutions are formulated and solved by employing the assumed-mode method. The effect of different parameters; i.e. the resonator size, ambient temperature and pressure on the squeeze film damping characteristics were simulated and investigated. The results indicate that the squeeze film damping effect may significantly affect the dynamic responses of micro-scale electromechanical resonator.

A Method to Improve the Modal Convergence for Structures With External Forcing

1987 ◽  
Vol 54 (4) ◽  
pp. 904-909 ◽  
Author(s):  
Keqin Gu ◽  
Benson H. Tongue
Keyword(s):  
Spatial Distribution ◽  
Free Vibration ◽  
Convergence Rate ◽  
Traditional Approach ◽  
Vibration Modes ◽  
External Forcing ◽  
Slow Convergence ◽  
Assumed Mode Method ◽  
Mode Method ◽  
Assumed Mode

The traditional approach of using free vibration modes in the assumed mode method often leads to an extremely slow convergence rate, especially when discete interactive forces are involved. By introducing a number of forced modes, significant improvements can be achieved. These forced modes are intrinsic to the structure and the spatial distribution of forces. The motion of the structure can be described exactly by these forced modes and a few free vibration modes provided that certain conditions are satisfied. The forced modes can be viewed as an extension of static modes. The development of a forced mode formulation is outlined and a numerical example is presented.

scholarly journals Nonlinear Controller Design for a Flexible Spacecraft

2020 ◽  
Vol 67 (4) ◽  
pp. 1500-1520
Author(s):  
Jose Luis Redondo Gutiérrez ◽  
Ansgar Heidecker
Keyword(s):  
Controller Design ◽  
Flexible Structures ◽  
Rigid Motion ◽  
Nonlinear Controller ◽  
Assumed Mode Method ◽  
Control Approach ◽  
Mode Method ◽  
Study Case ◽  
Nonlinear Controller Design ◽  
Assumed Mode

AbstractThis paper combines the nonlinear Udwadia-Kalaba control approach with the Assumed Mode Method to model flexible structures and derives an attitude controller for a spacecraft. The study case of this paper is a satellite with four flexible cantilever beams attached to a rigid central hub. Two main topics are covered in this paper. The first one is the formulation of the equation of motion and the second one is the nonlinear controller design. The combination of these two techniques is able to provide a controller that damps the vibration of a flexible structure while achieving the desired rigid-motion state.

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