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.

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.

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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