Dynamic Stability Analysis and Vibration Control of a Rotating Elastic Beam Connected With an End Mass

Abstract

In this paper, dynamic stability analysis and vibration control for a rotating elastic beam connected with an end mass driven by a direct current (DC) motor is considered. A complete strategy including mathematical modeling, dynamic analysis, vibration controller design and simulation for linear and nonlinear systems are presented. Once the rotating flexible physical system has been described by a set of governing partial differential equations, they are manipulated to achieve an appropriate mathematical format for vibration control system design and computer simulation, respectively. Hamilton principle, Lagrange's equation, assumed-modes and the fourth-order Runge–Kutta methods are applied in the system modeling derivation, descretization, and numerical analysis. The correctness of the numerical results and the characteristic property between mathematics and dynamics are demonstrated as well. Also, a realizable vibration control scheme is developed which not only can stabilize all the vibration modes but also make this rotating elastic beam system efficient for good transient response.

Design of a prototype generator based on piezoelectric power generation for vibration energy harvesting

“…A Puma vibration controller and analysis system captured the measurements. With scalable hardware and software, the vibration control and analysis system combine the simplicity of operation required for production screening with the power and versatility required for testing prototype generators [18]. The Puma vibration control and analysis system software incorporates high quality data acquisition and signal generation hardware designed with the latest floating-point digital signal-processing technology with patented digital vibration control methods [19].…”

Parametric Instability of Euler Beams under Random Wind Loads

“…The Euler beams, as common forms of members in modern structures, are significant research objects in the parametric instability field [1,2]. Modern civil structures are constructed with greater height or span, resulting in beam members of very small natural frequencies, so wind-induced parametric resonance has gradually become a remarkable problem.…”

Analytical Solution for Vibration of a Rotating Delaminated Composite Beam with End Mass

“…[1][2][3][4][5] Furthermore, the Poisson's e®ect, which is often neglected in 1D laminated beam analysis, has a signi¯cant e®ect in the analysis of angle-ply beams. [1][2][3][4][5] Free vibrations analysis of the intact rotating beams and delaminated nonrotating beams based on the classical beam theory (CBT) and shear deformation theory has been widely investigated in the literature, [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] whereas the dynamic analysis of the rotating delaminated beam has received relatively little attention. 25 The free vibration of an isotropic beam with a through-the-width delamination by using four Euler-Bernoulli sub-beams connected at the delamination boundaries was studied by Wang et al 6 According to this study, dramatic interpenetration of the delaminated sub-beams was observed, which was physically impossible to occur in the case of o®-mid-plane delamination.…”

“…[20][21][22][23][24] Kou et al 20 investigated the in°uence of taper ratio, elastic root restraints, tip mass and rotating speed on the vibration of rotating nonuniform beams based on the CBT. The natural frequencies of rotating tapered Timoshenko beams have been presented for di®erent combinations of¯xed, hinged and free end conditions by means of a new tapered¯nite beam element that accounts for the e®ect of shear deformation, rotary inertia, and centrifugal sti®ening due to beam rotation.…”