Lumped‐Parameter Approach to Stability Analysis

Shah, Sudhir J.; Pilkey, Walter D.

doi:10.1061/(asce)0733-9399(1993)119:10(2109)

Cited by 2 publications

(2 citation statements)

References 9 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…6, where a constant axial force is applied to a simply supported deformed structure, leading to a spanwise bending moment distribution 𝑀 𝑋 . In their work, Shah and Pilkey [14] and Senjanovic et al [15] present expressions for the lumped geometric stiffness matrix, as a result of an applied axial force. In the former case, the moments are lumped at the rotational DoF, with the advantage of yielding symmetric matrices.…”

Section: Geometric Stiffnessmentioning

confidence: 99%

Design of Flexible Wind Tunnel Model of Yawed Wind Turbine Rotor with Teetering Hub

Georgopoulos

Sodja

Breuker

2023

AIAA SCITECH 2023 Forum

View full text Add to dashboard Cite

The present study regards a novel wind turbine design featuring a two-bladed rotor on a teetering hub and a yawed tower. A reduced order modelling methodology is proposed for the equation of motion, using a lumped parameter approximation to derive expressions for the structural, rotordynamic and geometric stiffness terms. The analytical expressions are validated numerically. In addition, a methodology is developed for aeroelastic scaling of the rotor for use in wind tunnel tests. This results in two blade design templates, a "stiff" and a "flexible" design focusing on the vibration behaviour and deflected shapes respectively. The templates are designed to be 3D-printable as a single part. Design optimisation was performed in MSC Nastran, yielding two rotor designs, each aiming to match the non-dimensional parameters of interest. The stiff rotor matches the flapwise and torsional natural frequencies within 2.7% error, but has a mismatch in the edgewise mode, as well as the modeshapes and anti-symmetric modes. The flexible rotor is capable of capturing the target normalised displacement profile, at reduced structural mass, partially alleviating the mismatch in Lock number.

show abstract

Section: Geometric Stiffnessmentioning

confidence: 99%

Design of Flexible Wind Tunnel Model of Yawed Wind Turbine Rotor with Teetering Hub

Georgopoulos

Sodja

Breuker

2023

AIAA SCITECH 2023 Forum

View full text Add to dashboard Cite

show abstract

“…The integration of equation (41) using the trapezoidal rule provides the same lumped force stiffness matrix as given by Shah and Pilkey. 49…”

Section: Preliminariesmentioning

confidence: 99%

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

Soleimani

Beni

Dehkordi

2019

Proceedings of the Institution of Mechanical Engineers, Part C:

View full text Add to dashboard Cite

In this paper, two-node size-dependent axisymmetric shell element formulation is developed by using thin conical shell model in the place of the beam model, which is used in previous research and using the modified couple stress theory in the place of the classical continuum theory. Since classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have become quite popular. The mass stiffness matrix and geometric stiffness matrix for axisymmetric shell element are developed in this paper, and by means of size-dependent finite element formulation it is extended to more precisely account for nanotube buckling. The results have indicated using the two-node axisymmetric shell element, where the rigidity of the nano-shell is greater than that in the classical, and the critical axial buckling loads obtained from couple stress theory are greater than that of classical, which is due to the presence of one size parameter in couple stress theory. The findings also indicate that the developed size-dependent axisymmetric shell element is able to analyze the buckling of cylindrical and conical shells and also circular plate, which is reliable for simulating micro/nanostructures and can be used for the analysis of size effect and has desirable convergence characteristic. Besides, in addition to reducing the number of elements required, using axisymmetric shell element also increases convergence speed and accuracy.

show abstract

Lumped‐Parameter Approach to Stability Analysis

Cited by 2 publications

References 9 publications

Design of Flexible Wind Tunnel Model of Yawed Wind Turbine Rotor with Teetering Hub

Design of Flexible Wind Tunnel Model of Yawed Wind Turbine Rotor with Teetering Hub

Size-dependent two-node axisymmetric shell element for buckling analysis with couple stress theory

Contact Info

Product

Resources

About