Linear modal analysis of L-shaped beam structures

In this article a theoretical linear modal analysis of Euler-Bernoulli L-shaped beam structures is performed by solving two sets of coupled partial differential equations of motion. The first set, with two equations, corresponds to in-plane bending motions whilst the second set with four equations corresponds to out-of-plane motions with bending and torsion. The case is also shown of a single cantilever beam taking into account rotary inertia terms. At first for the case of examination of the results for the L-shaped beam structure, an individual modal analysis is presented for four selected beams which will be used for modelling an L-shaped beam structure; in order to investigate the influence of rotary inertia terms and shear effects. Then, a theoretical and numerical modal analysis is performed for four models of the L-shaped beam structure consisting of two sets of beams, in order to examine the effect of the orientation of the secondary beam (oriented in two ways) and also shear effects. The comparison of theoretical and finite element simulations shows a good agreement for both in-plane and out-of-plane motions, which validates the theoretical analysis. This work is essential to make progress with new investigations into the nonlinear equations for the L-shaped beam structures within Nonlinear Normal Mode theory

Linear modal analysis of L-shaped beam structures: parametric studies

Linear modal analysis of L-shaped beam structures indicates that there are two independent motions, these are in-plane bending and out of plane motions including bending and torsion. Natural frequencies of the structure can be determined by finding the roots of two transcendental equations which correspond to in-plane and out-of-plane motions. Due to the complexity of the equations of motion the natural frequencies cannot be determined explicitly. In this article we nondimensionalise the equations of motion in the space and time domains, and then we solve the transcendental equations for selected values of the L-shaped beam parameters in order to determine their natural frequencies. We use a numerical continuation scheme to perform the parametric solutions of the considered transcendental equations. Using plots of the solutions we can determine the natural frequencies for a specific L-shape beam configuration

Mode shapes variation of a composite beam with piezoelectric patches

In this paper the modal shapes of a light, thin laminate beam with active elements were evaluated. Cases with one or two Macro Fiber Composite (MFC) active elements adhered onto a glass-epoxy cantilever beam were analyzed. The systems under consideration were modeled in ABAQUS finite element software to derive mode shapes numerically. Next, the modes were compared to each other to estimate the influence of PZT patches. First 20 modes of natural vibrations were examined including bending, torsion and axial ones. The comparisons of mode shapes were performed according to Modal Assurance Criterion (MAC) analysis. The examination of changes of mode shapes of the original beam with placement of active elements is the starting point in prior of optimal placements of PZTs with final goal the control of dynamics of helicopter blades

Rational placement of a macro fibre composite actuator in composite rotating beams

In the presented research the dynamics of a thin rotating composite beam with surface bonded MFC actuator are considered. A parametric analysis aimed at finding the most efficient location of the actuator on the beam is presented. Gyroscopic effects resulting in the beam’s initial strain and therefore non-zero voltage in PZT are taken into account. Within the frame of the study maximising the system's response observed in vibration modes for uncoupled and coupled motions is examined. The results are compared to the case of a nonrotating beam and also to the maximum response of the beam with the actuator placed at different positions. To perform the analysis an ABAQUS finite element model of an electromechanical system under consideration is developed. The multi-layer composite beam structure is modelled by shell elements according to a layup-ply technique; the MFC actuator is modelled by 3D coupled field piezoelectric elements. Both modal analysis and frequency response spectra are performed to obtain the structural modal parameters and response amplitude, respectively. The analysis is repeated for three different orientations of the beam's cross-section with respect to the plane of rotation (i.e. arbitrary assumed pitch angles); in all cases the condition constant angular speed is preserved. This work is fundamental for continuing the research for control of dynamics of rotating composite beams with active elements

Nonlinear modal analysis of an L-shape beam structure

In this work it is derived the nonlinear equations of motion of L-shaped beam structure considering rotary inertia terms for out-of-plane motion in order to be used for nonlinear modal analysis of the structure. The dynamics has been projected in the infinite mode shapes space and it is derived the equations of motion in generalized coordinates. The nonlinear equations of motion indicates that there is coupling between in-plane and out-of-plane motions which in linear case is not the case

Towards linear modal analysis for an L-shaped beam: equations of motion

We consider an L-shaped beam structure and derive all the equations of motion considering also the rotary inertia terms. We show that the equations are decoupled in two motions, namely the in-plane bending and out-of-plane bending with torsion. In neglecting the rotary inertia terms the torsional equation for the secondary beam is fully decoupled from the other equations for out-of-plane motion. A numerical modal analysis was undertaken for two models of the L-shaped beam, considering two different orientations of the secondary beam, and it was shown that the mode shapes can be grouped into these two motions: in-plane bending and out-of-plane motion. We compared the theoretical natural frequencies of the secondary beam in torsion with finite element results which showed some disagreement, and also it was shown that the torsional mode shapes of the secondary beam are coupled with the other out-of-plane motions. These findings confirm that it is necessary to take rotary inertia terms into account for out-of-plane bending. This work is essential in order to perform accurate linear modal analysis on the L-shaped beam structure

<Contributed Talk 12>Regular and Chaotic Vibrations of Self-Excited Oscillators Driven by Parametric and External Excitations

[Date] November 28 (Mon) - December 2 (Fri), 2011: [Place] Kyoto University Clock Tower Centennial Hall, Kyoto, JAPA

An Analysis of the EQIP program for Lesser Prairie Chickens in the Northern Texas Panhandle

The Environmental Quality Incentives Program (EQIP) for the Lesser Prairie Chicken provides monetary compensation to agricultural producers for species habitat development. The advantages and disadvantages of program enrollment, as well as the overall economic impact are evaluated for a typical ranch operation in the Northern Texas Panhandle from 2009-2013.Prairie Chicken, FARM Assistance, EQIP, Environmental Economics and Policy,

Nonlinear vibrations of a rotating thin-walled composite piezo-beam with circumferentially uniform stiffness (CUS)

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Economic Considerations for Playa Management Alternatives

Playa lakes are very important to the Texas High Plains. They provide habitat for a wide variety of wildlife, and are the Ogallala Aquifer’s primary recharge source. Plowing and sedimentation have caused substantial damage to the overall health of many playas. A need exists to protect this resource for future generations. Several government programs are available to assist landowners with playa preservation including CP23A, the Wetlands Reserve Program, and the Wildlife Habitat Incentive Program. This study evaluates each conservation program and weighs the economic benefits and costs of program implementation.Southern Great Plains, Playa Lakes, CP23A, Conservation Reserve Program, Wetlands Reserve Program, Wildlife Habitat Incentive Program, Environmental Economics and Policy,