Nonlinear Response of an Inextensible, Free–Free Beam Subjected to a Nonconservative Follower Force

2019 ◽  
Vol 15 (2) ◽  
Author(s):  
Kevin A. McHugh ◽  
Earl H. Dowell
Keyword(s):  
Stability Boundary ◽  
Expansion Method ◽  
Follower Force ◽  
Limit Cycle Oscillation ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Time Histories ◽  
Cycle Oscillation ◽  
The Stability ◽  
Free Beam

Abstract A free–free beam with a compressive follower force applied to one end exhibits interesting flutter and limit cycle oscillation (LCO) responses. Here, the derivation from Lagrange's equations is given for the nonlinear inextensible beam with such a force applied. The inextensibility constraint is met with a Lagrange multiplier added to the Lagrangian, and the beam allowed three rigid body modes in planar motion in addition to its elastic deformation. The Rayleigh–Ritz modal expansion method and the Runge–Kutta method are used to calculate time histories of the forced beam response. This new model is validated against classical results for the stability boundary and new LCO bifurcation diagrams are computed.

Analytic solutions of the scattering by two multilayered dielectric spheres

1992 ◽  
Vol 70 (9) ◽  
pp. 696-705 ◽  
Author(s):  
A-K. Hamid ◽  
I. R. Ciric ◽  
M. Hamid
Keyword(s):  
Boundary Conditions ◽  
Cross Sections ◽  
Plane Electromagnetic Wave ◽  
Expansion Method ◽  
Analytic Solutions ◽  
Addition Theorem ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Dielectric Spheres ◽  
Scattered Fields

The problem of plane electromagnetic wave scattering by two concentrically layered dielectric spheres is investigated analytically using the modal expansion method. Two different solutions to this problem are obtained. In the first solution the boundary conditions are satisfied simultaneously at all spherical interfaces, while in the second solution an iterative approach is used and the boundary conditions are satisfied successively for each iteration. To impose the boundary conditions at the outer surface of the spheres, the translation addition theorem of the spherical vector wave functions is employed to express the scattered fields by one sphere in the coordiante system of the other sphere. Numerical results for the bistatic and back-scattering cross sections are presented graphically for various sphere sizes, layer thicknesses and permittivities, and angles of incidence.

Instability of Heated Panels in Supersonic Air Flow

2008 ◽  
Vol 33-37 ◽  
pp. 1101-1108
Author(s):  
Zhi Chun Yang ◽  
Wei Xia
Keyword(s):  
Stability Analysis ◽  
Stability Boundary ◽  
Boundary Curve ◽  
Static Stability ◽  
Static Deformation ◽  
Limit Cycle Oscillation ◽  
Aerodynamic Load ◽  
Aeroelastic System ◽  
Aerodynamic Pressure ◽  
The Stability

An investigation on the stability of heated panels in supersonic airflow is performed. The nonlinear aeroelastic model for a two-dimensional panel is established using Galerkin method and the thermal effect on the panel stiffness is also considered. The quasi-steady piston theory is employed to calculate the aerodynamic load on the panel. The static and dynamic stabilities for flat panels are studied using Lyapunov indirect method and the stability boundary curve is obtained. The static deformation of a post-buckled panel is then calculated and the local stability of the post-buckling equilibrium is analyzed. The limit cycle oscillation of the post-buckled panel is simulated in time domain. The results show that a two-mode model is suitable for panel static stability analysis and static deformation calculation; but more than four modes are required for dynamic stability analysis. The effects of temperature elevation and dimensionless parameters related to panel length/thickness ratio, material density and Mach number on the stability of heated panel are studied. It is found that panel flutter may occur at relatively low aerodynamic pressure when several stable equilibria exist for the aeroelastic system of heated panel.

Vibration Control of a Multi-Layer Piezoelectric Cylindrical Shell

1997 ◽  
Author(s):  
Jinhao Qiu ◽  
Junji Tani
Keyword(s):  
Cylindrical Shell ◽  
Feedforward Control ◽  
Equations Of Motion ◽  
Good Control ◽  
Expansion Method ◽  
Piezoelectric Sensor ◽  
State Equation ◽  
Integrated Sensor ◽  
Modal Expansion ◽  
Modal Expansion Method

Abstract Equations of motion for multi-layer piezoelectric cylindrical shells and the equations of the integrated piezoelectric sensors are derived. The state equation is obtained by solving the equations of motion with modal expansion method. The feedback control, feedforward control, and their combination are applied in the control of forced vibration of the piezoelectric cylindrical shell with integrated sensor and actuators. The simulation and experimental results show that good control effectiveness can be obtained by using the integrated piezoelectric sensor and actuators in conjunction with the combination of feedback and feedforward control methods.

Modal expansion method of analysis for slot-coupled microstrip antenna

1989 ◽  
Vol 25 (20) ◽  
pp. 1338 ◽  
Author(s):  
A. Ittipiboon ◽  
R. Oostlander ◽  
Y.M.M. Antar
Keyword(s):  
Microstrip Antenna ◽  
Expansion Method ◽  
Modal Expansion ◽  
Modal Expansion Method

Evaluating actuator distributions in simply supported truncated thin conical shell with embedded piezoelectric layers

2018 ◽  
Vol 29 (12) ◽  
pp. 2641-2659 ◽  
Author(s):  
Rasa Jamshidi ◽  
Ali A Jafari
Keyword(s):  
Conical Shell ◽  
Piezoelectric Layer ◽  
Cone Angle ◽  
Expansion Method ◽  
Longitudinal Direction ◽  
Modal Expansion ◽  
Simply Supported ◽  
Modal Expansion Method ◽  
Layer Segmentation ◽  
Distributed Actuator

In this investigation, distributed modal actuator forces of simply supported truncated conical shell embedded by a piezoelectric layer are studied. Piezoelectric layer is distributed on the conical shell surface as actuators. Three types of distributions are considered: longitudinal, circumferential, and diagonal distributions. First, electromechanical equations of the conical shell with embedded piezoelectric actuator layer are extracted. Then modal expansion method is used to define independent modal characteristics of the conical shell. For each kind of distribution, three case studies are considered and evaluated. Results showed that in the longitudinal and diagonal distributed actuator, membrane force in the longitudinal direction is the dominant force and in the circumferential distributed actuator, the membrane force in the circumferential direction is the dominant force. The effects of cone angle, piezoelectric thickness, and piezoelectric layer segmentation on modal forces of each distributed actuator are also studied. In circumferential distributed actuator, modal forces increase as the cone angle increases. This phenomenon in the longitudinal and diagonal distributed actuator is almost reversed. The piezoelectric layer segmentation effect on the modal forces distribution is also evaluated, and it showed that this phenomenon has a critical effect on the modal forces distribution.

Aeroelastic analysis of pre-stressed variable stiffness composite panels

2019 ◽  
Vol 26 (9-10) ◽  
pp. 724-734 ◽  
Author(s):  
Mehnaz Rasool ◽  
Maloy K Singha
Keyword(s):  
Dynamic Pressure ◽  
Variable Stiffness ◽  
Limit Cycle Oscillation ◽  
Composite Panels ◽  
Constant Stiffness ◽  
Aerodynamic Pressure ◽  
Aeroelastic Analysis ◽  
Divergence Type ◽  
Cycle Oscillation ◽  
The Stability

The effect of in-plane stresses on the stability behaviors of constant stiffness and variable stiffness composite panels, exposed to aerodynamic pressure, is studied using the finite element method. The dynamic pressure from the high velocity airflow is evaluated from the first-order piston theory, and the eigenvalue analysis is performed to investigate the flutter or divergence type of instabilities in such composite panels under combined mechanical and aerodynamic loads. Attempt is made to understand the effect of the lamination parameter on the stability characteristics of edge-supported and cantilever composite trapezoidal panels. Finally, the limit cycle oscillation of variable stiffness plates subjected to aerodynamic pressure is investigated.

Hybrid finite-element-modal-expansion method for matched magic T-junction

2002 ◽  
Vol 38 (2) ◽  
pp. 385-388 ◽  
Author(s):  
Zhongxiang Shen ◽  
Choi Look Law ◽  
Cheng Qian
Keyword(s):  
Finite Element ◽  
Expansion Method ◽  
Modal Expansion ◽  
Hybrid Finite Element ◽  
Modal Expansion Method

Modelling of a single-link flexible manipulator system: theoretical and practical investigations

Robotica ◽  
1996 ◽  
Vol 14 (1) ◽  
pp. 91-102 ◽  
Author(s):  
M. O. Tokhi ◽  
A. K. M. Azad
Keyword(s):  
Expansion Method ◽  
Practical Investigations ◽  
Flexible Manipulator ◽  
Experimental Investigations ◽  
Model Parameters ◽  
Modal Expansion ◽  
Modal Expansion Method ◽  
Lagrange’S Equation ◽  
Equivalent Time ◽  
Single Link

SummaryThis paper presents theoretical and experimental investigations into modelling a single-link flexible manipulator system. An analytical model of the manipulator, characterised by an infinite number of modes, is developed using the Lagrange's equation and modal expansion method. This is used to develop equivalent time-domain and frequency-domain working models of the system in state-space and transfer function forms respectively. The model parameters are then estimated experimentally using system's measured input/output data. The model thus obtained is validated through experimentation and results including the effect of payload on system characteristics presented and discussed.

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