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.

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.

Elastodynamic Modeling and Simulation of an Axially Accelerating Beam

2015 ◽  
Author(s):  
Fadi A. Ghaith ◽  
Ahmad Ayub
Keyword(s):  
Differential Equations ◽  
Plane Motion ◽  
Force Frequency ◽  
Major Focus ◽  
Assumed Mode Method ◽  
Vibrational Response ◽  
Runge Kutta Method ◽  
Mode Method ◽  
Elastodynamic Modeling ◽  
Assumed Mode

This paper aims to develop an accurate nonlinear mathematical model which may describe the coupled in-plane motion of an axially accelerating beam. The Extended Hamilton’s Principle was utilized to derive the partial differential equations governing the motion of a simply supported beam. The set of the ordinary differential equations were obtained by means of the assumed mode method. The derived elastodynamic model took into account the geometric non-linearity, the time-dependent axial velocity and the coupling between the transverse and longitudinal vibrations. The developed equations were solved numerically using the Runge-Kutta method and the obtained results were presented in terms of the vibrational response graphs and the system natural frequencies. The system dynamic characteristics were explored with a major focus on the influence of the velocity, acceleration and the excitation force frequency. The obtained results showed that the natural frequency decreased significantly at high axial velocities. Also it was found that the system may exhibit unstable behavior at high accelerations.

Effects of surface energy on vibration characteristics of double-walled piezo-viscoelastic cylindrical nanoshell

2019 ◽  
Vol 233 (15) ◽  
pp. 5264-5279 ◽  
Author(s):  
Sayyid H Hashemi Kachapi ◽  
Morteza Dardel ◽  
Hamidreza Mohamadi Daniali ◽  
Alireza Fathi
Keyword(s):  
Surface Energy ◽  
Governing Equations ◽  
Assumed Mode Method ◽  
Remarkable Effect ◽  
Nanoscale System ◽  
Interface Theory ◽  
Piezoelectric Layers ◽  
Mode Method ◽  
Pasternak Model ◽  
Assumed Mode

In this paper, vibration analysis of double-walled piezo-viscoelastic cylindrical nanoshell integrated with piezoelectric layers is investigated using Gurtin–Murdoch surface/interface theory and Donnell's theory. Three parameters namely, shear modulus, damp coefficient, and Winkler modulus are used for simulation of visco-Pasternak model. Hamilton's principle is used for deriving 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 effects of the surface energy, length and thickness of nanoshell and piezoelectric layer, boundary condition, van der Waals force, and visco-Pasternak effects on the undamped and damped natural frequencies of piezo-viscoelastic cylindrical nanoshell is studied. Also, the results show that on considering surface effects in the nanoscale system without considering the surface density, the maximum frequency will be obtained and this case will be considered as the critical state of the system. As a result, controlling the frequency of the system in this case is essential and it is quite clear that considering the effects of the surface energy will have a remarkable effect on the natural frequency of the piezo-viscoelastic nanoshell.

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.

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.

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.

Squeal Analysis of a Disc Brake Considering Damping between a Disc and a Pad Lining

2012 ◽  
Vol 157-158 ◽  
pp. 1000-1003
Author(s):  
Ke Wei Zhou ◽  
Cheol Kim ◽  
Min Ok Yun ◽  
Ju Young Kim
Keyword(s):  
Finite Element ◽  
Equations Of Motion ◽  
Element Model ◽  
Disc Brake ◽  
Vibration Modes ◽  
Assumed Mode Method ◽  
Frictional Damping ◽  
System Components ◽  
Mode Method ◽  
Assumed Mode

The improved equations of motion for a friction-engaged brake system have been newly derived on the basis of the assumed mode method and frictional damping. The equations of motion with a finite element model were constructed by a set of vibration modes found from FE modal analysis on all system components. Consequently, the modal information of system components are combined with equations of motion derived from the analytical model. Numerical analysis showed the mode which was unstable in an undamped case became stable in a damped case.

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