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

2019 ◽  
Vol 14 (3) ◽  
Author(s):  
Kevin A. McHugh ◽  
Earl H. Dowell
Keyword(s):  
Linear Model ◽  
Critical Force ◽  
Follower Force ◽  
System Of Nonlinear Equations ◽  
Constraint Force ◽  
New Energy ◽  
Out Of Plane ◽  
Engineering Designs ◽  
Cantilevered Beam

The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers consider a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and the agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear postcritical limit cycle oscillations (LCO) are studied including a concentration on the force which enforces the inextensibility constraint.

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

2018 ◽  
Author(s):  
Kevin A. McHugh ◽  
Earl H. Dowell
Keyword(s):  
Linear Model ◽  
Critical Force ◽  
Follower Force ◽  
System Of Nonlinear Equations ◽  
Constraint Force ◽  
Critical Limit ◽  
New Energy ◽  
Out Of Plane ◽  
Engineering Designs ◽  
Cantilevered Beam

The dynamic stability of a cantilevered beam actuated by a nonconservative follower force has previously been studied for its interesting dynamical properties and its applications to engineering designs such as thrusters. However, most of the literature considers a linear model. A modest number of papers considers a nonlinear model. Here, a system of nonlinear equations is derived from a new energy approach for an inextensible cantilevered beam with a follower force acting upon it. The equations are solved in time, and agreement is shown with published results for the critical force including the effects of damping (as determined by a linear model). This model readily allows the determination of both in-plane and out-of-plane deflections as well as the constraint force. With this novel transparency into the system dynamics, the nonlinear post-critical limit cycle oscillations are studied including a concentration on the force which enforces the inextensibility constraint.

Plate subjected to an out-of-plane follower force

2002 ◽  
Vol 216 (9) ◽  
pp. 913-921
Author(s):  
J Genin ◽  
W Xu
Keyword(s):  
Dynamic Stability ◽  
Follower Force ◽  
Jet Engine ◽  
Engine Thrust ◽  
Out Of Plane ◽  
The Stability

The stability of bending-torsional equilibrium of a uniform plate subjected to an out-of-plane follower force is studied in this paper. The resulting system approximates to a wing subjected to the thrust of a jet engine. Attention is focused on the determination of the dynamic stability of the wing as a function of engine thrust. Criteria are established for the determination of the maximum allowable value of the engine thrust.

Anisotropy of Nanoindentation – a tool for the determination of nanocrystal orientation ?

2003 ◽  
Vol 779 ◽  
Author(s):  
David Christopher ◽  
Steven Kenny ◽  
Roger Smith ◽  
Asta Richter ◽  
Bodo Wolf ◽  
...  
Keyword(s):  
Crystal Surface ◽  
Scanning Force Microscopy ◽  
Depth Range ◽  
Dislocation Loops ◽  
Force Microscopy ◽  
Pile Up ◽  
Out Of Plane ◽  
Scanning Force ◽  
Dynamics Simulations

AbstractThe pile up patterns arising in nanoindentation are shown to be indicative of the sample crystal symmetry. To explain and interpret these patterns, complementary molecular dynamics simulations and experiments have been performed to determine the atomistic mechanisms of the nanoindentation process in single crystal Fe{110}. The simulations show that dislocation loops start from the tip and end on the crystal surface propagating outwards along the four in-plane <111> directions. These loops carry material away from the indenter and form bumps on the surface along these directions separated from the piled-up material around the indenter hole. Atoms also move in the two out-of-plane <111> directions causing propagation of subsurface defects and pile-up around the hole. This finding is confirmed by scanning force microscopy mapping of the imprint, the piling-up pattern proving a suitable indicator of the surface crystallography. Experimental force-depth curves over the depth range of a few nanometers do not appear smooth and show distinct pop-ins. On the sub-nanometer scale these pop-ins are also visible in the simulation curves and occur as a result of the initiation of the dislocation loops from the tip.

Statistical method of steepest improvement of response

2018 ◽  
Vol 84 (11) ◽  
pp. 74-87
Author(s):  
V. B. Bokov
Keyword(s):  
Statistical Method ◽  
Linear Model ◽  
Response Prediction ◽  
Initial Experiment ◽  
First Order ◽  
Prediction Response ◽  
Conditional Extremum ◽  
Order Polynomial ◽  
Limiting Values

A new statistical method for response steepest improvement is proposed. This method is based on an initial experiment performed on two-level factorial design and first-order statistical linear model with coded numerical factors and response variables. The factors for the runs of response steepest improvement are estimated from the data of initial experiment and determination of the conditional extremum. Confidence intervals are determined for those factors. The first-order polynomial response function fitted to the data of the initial experiment makes it possible to predict the response of the runs for response steepest improvement. The linear model of the response prediction, as well as the results of the estimation of the parameters of the linear model for the initial experiment and factors for the experiments of the steepest improvement of the response, are used when finding prediction response intervals in these experiments. Kknowledge of the prediction response intervals in the runs of steepest improvement of the response makes it possible to detect the results beyond their limits and to find the limiting values of the factors for which further runs of response steepest improvement become ineffective and a new initial experiment must be carried out.

Automatic 3-D Crack Propagation Calculations in Industrial Components: A Pure Hexahedral versus a Combined Hexahedral-Tetrahedral Approach

2007 ◽  
Vol 348-349 ◽  
pp. 45-48
Author(s):  
Guido Dhondt
Keyword(s):  
Crack Propagation ◽  
Computing Time ◽  
Propagation Direction ◽  
Hexahedral Elements ◽  
Crack Propagation Direction ◽  
Low Weight ◽  
Out Of Plane ◽  
Hexahedral Meshes ◽  
Crack Faces

In recent years, increased loading and low weight requirements have led to the need for automatic crack tracing software. At MTU a purely hexahedral code has been developed in the nineties for Mode-I applications. It has been used extensively for all kinds of components and has proven to be very flexible and reliable. Nevertheless, in transition regions between complex components curved cracks have been observed, necessitating the development of mixed-mode software. Due to the curvature of the crack faces, purely hexahedral meshes are not feasible, and therefore a mixture of hexahedral elements at the crack tip, combined with tetrahedral in the remaining structure has been selected. The intention of the present paper is to compare both methods and to point out the strength and weaknesses of each regarding accuracy, complexity, flexibility and computing time. Furthermore, difficulties arising from the out-of-plane growth of the crack such as the determination of the crack propagation direction are discussed.

Piezoelectric T-Beam Microactuators

2008 ◽  
Author(s):  
Hareesh K. R. Kommepalli ◽  
Andrew D. Hirsh ◽  
Christopher D. Rahn ◽  
Srinivas A. Tadigadapa
Keyword(s):  
Cross Section ◽  
Fabrication Process ◽  
Mems Fabrication ◽  
Out Of Plane ◽  
Cantilevered Beam ◽  
Piezoelectric Mems ◽  
The Cross ◽  
T Beam ◽  
Cross Section Geometry

This paper introduces a novel T-beam actuator fabricated by a piezoelectric MEMS fabrication process. ICP-RIE etching from the front and back of a bulk PZT chip is used to produce stair stepped structures through the thickness with complex inplane shapes. Masked electrode deposition creates active and passive regions in the PZT structure. With a T-shaped crosssection, and bottom and top flange and web electrodes, a cantilevered beam can bend in-plane and out-of-plane with bimorph actuation in both directions. One of these T-beam actuators is fabricated and experimentally tested. An experimentally validated model predicts that the cross-section geometry can be optimized to produce higher displacement and blocking force.

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