Equivalent micropolar beam model for spatial vibration analysis of planar repetitive truss structure with flexible joints

The flapwise bending free vibration analysis of isotropic rotating Timoshenko microbeams, including the size effects, is presented in this paper. A nonclassical theory, i.e. the Modified Couple Stress theory, has been employed to include the size effect in the presented formulation. By consideration of the Timoshenko beam assumptions the shear deformation and the rotary inertia effects are taken into account. The Hamilton’s principle is applied to the obtained strain and kinetic energy relations to derive the nonlinear equations of motion and the associated boundary conditions. After nondimensionalization of the equations of motion and the corresponding boundary conditions, the linearized form of the equations of motion and the accompanied boundary conditions are developed. A semi-analytical approach, i.e. the differential transform method, is implemented to achieve the flapping and axial frequencies. The achieved results are validated via comparison with the available results in the literature. The material length scale, shear deformation consideration, rotating speed and the slenderness ratio influences on the natural frequencies are examined. The results demonstrate that the slenderness ratio and the thickness to the material length scale parameter quotient are the dominant indicators in determining the usage of the nonclassical theories against classical theories. On the other hand, the precision in determination of the higher modes frequencies motivates us to implement the Timoshenko beam model instead of the Euler–Bernoulli beam model.

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Transversal Vibration Analysis of Vehicle Track System

Volume 6: 15th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2019-98331 ◽

2019 ◽

Author(s):

Pingxin Wang ◽

Xiaoting Rui ◽

Jianshu Zhang ◽

Hailong Yu

Keyword(s):

Natural Frequency ◽

Vibration Analysis ◽

Stability Control ◽

Axially Moving Beam ◽

Natural State ◽

Beam Model ◽

Tracked Vehicle ◽

Transversal Vibration ◽

Rubber Bushing ◽

Axially Moving

Abstract The track is mainly composed of track shoes, track pins and rubber bushing elements. In order to suppress the transversal vibration of the upper track during the smooth running process of the tracked vehicle, it is necessary to study the important factors affecting the frequency characteristics of the kinematic chain and their interaction. Unlike the conventional chain drive system, the track in the natural state has a bending rigidity due to the action of the rubber bushing. Based on the dynamic theory of axially moving beam, the differential equation of transversal vibration of a beam element is established. The entire upper track is assumed to be a continuous multi-span axially moving Euler-Bernoulli beam with an axial tension. Based on the Transfer Matrix Method of Multibody System, the transfer equation is obtained. According to the boundary conditions, the natural frequency of the system is solved. The correctness of the beam model hypothesis is verified by experiments. The results show that the first-order natural frequency of the upper track increases with the increase of the tension and the decrease of the vehicle speed. Through frequency analysis, the main excitation source for the transversal vibration of the track is the polygon effect produced by the meshing of the track and the sprocket. This study provides a theoretical basis for the vibration analysis and stability control of the upper track on the tracked vehicle.

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Aeroelastic vibration analysis of wind turbine blade with Gurney flap

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406220977881 ◽

2020 ◽

pp. 095440622097788

Author(s):

Lin Chang ◽

Yingjie Yu ◽

Tingrui Liu

Keyword(s):

Cross Section ◽

Vibration Analysis ◽

Natural Frequencies ◽

Parametric Design ◽

Trust Region ◽

Aerodynamic Performance ◽

Least Square ◽

Equivalent Model ◽

Beam Model ◽

Gurney Flap

In this paper, based on the parametric design of 3 D blades including typical cross-section and natural frequency calculation of the equivalent model, an integral method for aerodynamic performance and aeroelastic vibration analysis of blade with Gurney flap is proposed. Parametric design and unstructured grid are used to pre-process the blades with/without the Gurney flap. The discrete aerodynamic performance parameters distribution including the lift, drag, and torsion coefficients calculated by Fluent is fitted by the nonlinear least square method based on the trust-region algorithm, and the natural frequencies of the rotating blade are accurately solved by the equivalent thin-walled beam model and Green’s functions. Based on the aerodynamic performance coefficients and natural frequencies obtained by the accurate calculation above, the aeroelastic response equation of typical cross-section considering local aerodynamic damping matrix is established, and the vibration response of blade in flap and torsion direction is further described. From the analysis results, it can be seen that the Gurney flap structure can not only bring higher lift performance to the blade, but also can reduce the amplitude and vibration range of aeroelastic vibration, improve the aeroelastic stability of the blade, and prove the effectiveness of Gurney flap.

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Four-beam model for vibration analysis of a cantilever beam with an embedded horizontal crack

Chinese Journal of Mechanical Engineering ◽

10.3901/cjme.2015.0901.108 ◽

2015 ◽

Vol 29 (1) ◽

pp. 163-179 ◽

Cited By ~ 3

Author(s):

Jing Liu ◽

Weidong Zhu ◽

Panos G. Charalambides ◽

Yimin Shao ◽

Yongfeng Xu ◽

...

Keyword(s):

Cantilever Beam ◽

Vibration Analysis ◽

Beam Model ◽

Horizontal Crack

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Nonlinear static and vibration analysis of Euler-Bernoulli composite beam model reinforced by FG-SWCNT with initial geometrical imperfection using FEM

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2016.59.3.431 ◽

2016 ◽

Vol 59 (3) ◽

pp. 431-454 ◽

Cited By ~ 11

Author(s):

M. Mohammadimehr ◽

S. Alimirzaei

Keyword(s):

Composite Beam ◽

Vibration Analysis ◽

Beam Model ◽

Geometrical Imperfection ◽

Nonlinear Static

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Control of the Continuum Model of a Large Flexible Space Structure

Aerospace ◽

10.1115/imece2006-13362 ◽

2006 ◽

Author(s):

Armaghan Salehian ◽

T. Michael Seigler ◽

Daniel J. Inman

Keyword(s):

Continuum Model ◽

Vibration Suppression ◽

Space Structure ◽

Truss Structure ◽

Distributed Parameter ◽

Beam Model ◽

Control Force ◽

Linear Quadratic ◽

Distributed Parameter Model ◽

Lqr Problem

An analytical approach is presented here to develop a continuum model of a space radar antenna and the truss structure for the purpose of the control and vibration suppression. Kinetic and potential energy expressions are given for the equivalent homogenized 1-D model. Hamilton's principle is applied to find the governing partial differential equations for this structure. The equations for bending are similar to an extended Timoshenko beam model. A Linear, Quadratic, Regulator (LQR) problem is solved to find the optimal solution for feedback control design of the distributed parameter model. The control force designed this way is applied to a Finite Element Model (FEM) of the truss structure for the purpose of validation. Results from the FEM are shown to be in good agreement with the distributed parameter model.

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