Solution of regular beam equations in arbitrary emission conditions on a curvilinear surface

1969 ◽  
Vol 7 (3) ◽  
pp. 31-35
Author(s):  
V. A. Syrovoi
Keyword(s):  
Curvilinear Surface ◽  
Beam Equations

scholarly journals Aeroelastic Stability Analysis of Electric Aircraft Wings with Distributed Electric Propulsors

Aerospace ◽  
2021 ◽  
Vol 8 (4) ◽  
pp. 100
Author(s):  
Mohammadreza Amoozgar ◽  
Michael I. Friswell ◽  
Seyed Ahmad Fazelzadeh ◽  
Hamed Haddad Khodaparast ◽  
Abbas Mazidi ◽  
...  
Keyword(s):  
Angular Momentum ◽  
Electric Propulsion ◽  
Aeroelastic Stability ◽  
Concentrated Mass ◽  
High Lift ◽  
Aircraft Wings ◽  
Time Space ◽  
Beam Equations ◽  
Geometrically Exact Beam ◽  
Electric Aircraft

In this paper, the effect of distributed electric propulsion on the aeroelastic stability of an electric aircraft wing was investigated. All the electric propulsors, which are of different properties, are attached to the wing of the aircraft in different positions. The wing structural dynamics was modelled by using geometrically exact beam equations, while the aerodynamic loads were simulated by using an unsteady aerodynamic theory. The electric propulsors were modelled by using a concentrated mass attached to the wing, and the motor’s thrust and angular momentum were taken into account. The thrust of each propulsor was modelled as a follower force acting exactly at the centre of gravity of the propulsor. The nonlinear aeroelastic governing equations were discretised using a time–space scheme, and the obtained results were verified against available results and very good agreement was observed. Two case studies were considered throughout the paper, resembling two flight conditions of the electric aircraft. The numerical results show that the tip propulsor thrust, mass, and angular momentum had the most impact on the aeroelastic stability of the wing. In addition, it was observed that the high-lift motors had a minimal effect on the aeroelastic stability of the wing.

scholarly journals Long-Time Existence for Semi-linear Beam Equations on Irrational Tori

2021 ◽  
Author(s):  
Joackim Bernier ◽  
Roberto Feola ◽  
Benoît Grébert ◽  
Felice Iandoli
Keyword(s):  
Long Time Existence ◽  
Beam Equations ◽  
Long Time ◽  
Time Existence

Asymptotic derivation of a refined equation for an elastic beam resting on a Winkler foundation

2021 ◽  
pp. 108128652110238
Author(s):  
Barış Erbaş ◽  
Julius Kaplunov ◽  
Isaac Elishakoff
Keyword(s):  
Ad Hoc ◽  
Moving Load ◽  
Low Frequency ◽  
Elastic Beam ◽  
Winkler Foundation ◽  
One Dimensional ◽  
Beam Equations ◽  
Dimensional Equation ◽  
Phase And Group Velocities ◽  
Group Velocities

A two-dimensional mixed problem for a thin elastic strip resting on a Winkler foundation is considered within the framework of plane stress setup. The relative stiffness of the foundation is supposed to be small to ensure low-frequency vibrations. Asymptotic analysis at a higher order results in a one-dimensional equation of bending motion refining numerous ad hoc developments starting from Timoshenko-type beam equations. Two-term expansions through the foundation stiffness are presented for phase and group velocities, as well as for the critical velocity of a moving load. In addition, the formula for the longitudinal displacements of the beam due to its transverse compression is derived.

Exponential attractors for extensible beam equations

Nonlinearity ◽  
1993 ◽  
Vol 6 (3) ◽  
pp. 457-479 ◽  
Author(s):  
A Eden ◽  
A J Milani
Keyword(s):  
Exponential Attractors ◽  
Beam Equations

scholarly journals Two solutions to Kirchhoff-type fourth-order implusive elastic beam equations

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Jian Liu ◽  
Wenguang Yu
Keyword(s):  
Iterative Method ◽  
Variational Methods ◽  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Kirchhoff Type ◽  
Newton Iterative Method ◽  
Beam Equations ◽  
Critical Point Theorems ◽  
Elastic Beam Equations

AbstractIn this paper, the existence of two solutions for superlinear fourth-order impulsive elastic beam equations is obtained. We get two theorems via variational methods and corresponding two-critical-point theorems. Combining with the Newton-iterative method, an example is presented to illustrate the value of the obtained theorems.

Variational approaches to impulsive elastic beam equations of Kirchhoff type

2016 ◽  
Vol 61 (7) ◽  
pp. 931-968 ◽  
Author(s):  
Shapour Heidarkhani ◽  
Ghasem A. Afrouzi ◽  
Massimiliano Ferrara ◽  
Shahin Moradi
Keyword(s):  
Elastic Beam ◽  
Kirchhoff Type ◽  
Beam Equations ◽  
Variational Approaches ◽  
Elastic Beam Equations
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