Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

Cao, Dongxing; Zhang, Wei; Yao, Minghui

doi:10.1007/s10409-010-0385-9

Cited by 25 publications

(4 citation statements)

References 33 publications

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“…It shows that the resonance curve is extremely complicated with multiple branches and interactions between the first four modes. Cao et al [31] explored the dynamical behaviors of the internal resonance of an L-shape beam structure. The amplitude spectrum, Poincaré map, phase portraits and bifurcation diagram were presented to describe the nonlinear vibration phenomenon of the structure.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nie¹,

Gao²,

Wang³

et al. 2022

J. Stat. Mech.

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The nonlinear behaviors of the L-shaped beam structure based on 1:2 internal resonance are investigated. The governing equations considering quadratic and cubic nonlinearity of the L-shaped beam structure are verified by the transient dynamic analysis of the finite element model. The approximate analytical solution for this system is derived by the method of multiple scales, and verified by the numerical solution. The Jacobian matrix of the modulation equation is employed to determine the equilibrium stability of the vibration response. The effects of the excitation frequency, amplitude and cubic nonlinear terms on the nonlinear responses of the primary resonance of the first and second modes are discussed. The bifurcation diagram, spectrum, phase plane and Poincaré section are applied to investigate the nonlinear vibration response. The results reveal that many nonlinear phenomena are observed, such as double-jump, hysteresis, Hopf bifurcation, modal saturation, multiple solutions, multi-softening and so on. The influence of cubic nonlinear term on internal resonance response should be considered. The broadband characteristics of internal resonance system are broadened by the nonlinear softening and hardening in the frequency response curve. In the primary resonance of the second mode, the hardening region in the frequency response curve becomes the softening region with the increase of excitation amplitude. The double-jump phenomenon is found in this newly formed softening region, and up to five solutions are observed in this region, including three sink points and two saddle-nodes. The broadband characteristics of the system is of great benefit to the application of broadband piezoelectric vibration energy harvesting.

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Section: Introductionmentioning

confidence: 99%

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nie¹,

Gao²,

Wang³

et al. 2022

J. Stat. Mech.

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“…As a typical multi-beam structure, the research on the dynamics of L-shaped beam structures has received extensive attention in the past few decades [ 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 ]. Because of the inertial effect of the large motion, and the geometry of motion, the L-shaped beam structure is a typical quadratic nonlinearity system.…”

Section: Introductionmentioning

confidence: 99%

“…Warminski et al [ 8 ] formulated a detailed derivation of the nonlinear PDEs of motion for the L-shaped beam structure with different flexibilities in two orthogonal directions. Cao et al [ 9 ] conducted theoretical and experimental studies on the periodic and chaotic motion in the L-shaped beam structure under the one-to-one internal resonance. Onozato et al [ 10 ] investigated the chaotic responses of a post-buckled L-shaped beam with an axial constraint and examined the contribution ratio of the vibration mode to the chaotic responses by using the proper orthogonal decomposition.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

Jin

et al. 2021

Materials

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A dynamic model of an L-shaped multi-beam joint structure is presented to investigate the nonlinear dynamic behavior of the system. Firstly, the nonlinear partial differential equations (PDEs) of motion for the beams, the governing equations of the tip mass, and their matching conditions and boundary conditions are obtained. The natural frequencies and the global mode shapes of the linearized model of the system are determined, and the orthogonality relations of the global mode shapes are established. Then, the global mode shapes and their orthogonality relations are used to derive a set of nonlinear ordinary differential equations (ODEs) that govern the motion of the L-shaped multi-beam jointed structure. The accuracy of the model is verified by the comparison of the natural frequencies solved by the frequency equation and the ANSYS. Based on the nonlinear ODEs obtained in this model, the dynamic responses are worked out to investigate the effect of the tip mass and the joint on the nonlinear dynamic characteristic of the system. The results show that the inertia of the tip mass and the nonlinear stiffness of the joints have a great influence on the nonlinear response of the system.

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“…By introducing simple topological folds or creases in slender beams, we show, using the Euler-Bernoulli beam theory equations, that beam's natural frequencies can be tuned over a wide range by varying fold angles, fold locations, and number of folds. The dynamics of L-shaped [17,18] and Z-shaped [19] beams have been investigated for applications as robotic arms, swing-arm cranes and as morphing wing designs for aircrafts. We follow the mechanics of materials (MoM)-based discrete modeling approach proposed for stiffened plates [20,21] and sandwich panels [22][23][24].…”

Section: Introductionmentioning

confidence: 99%

Beam-Based Vibration Energy Harvesters Tunable Through Folding

Pydah

Batra

2018

Journal of Vibration and Acoustics

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We present a novel beam-based vibration energy harvester, and use a structural tailoring concept to tune its natural frequencies. Using a solution of the Euler–Bernoulli beam theory equations, verified with finite element (FE) solutions of shell theory equations, we show that introducing folds or creases along the span of a slender beam, varying the fold angle at a crease, and changing the crease location helps tune the beam natural frequencies to match an external excitation frequency and maximize the energy harvested. For a beam clamped at both ends, the first frequency can be increased by 175% with a single fold. With two folds, selective frequencies can be tuned, leaving others unchanged. The number of folds, their locations, and the fold angles act as tuning parameters that provide high sensitivity and controllability of the frequency response of the harvester. The analytical model can be used to quickly optimize designs with multiple folds for anticipated external frequencies.

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Analytical and experimental studies on nonlinear characteristics of an L-shape beam structure

Cited by 25 publications

References 33 publications

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nonlinear analysis of the internal resonance response of an L-shaped beam structure considering quadratic and cubic nonlinearity

Nonlinear Dynamic Modeling and Analysis of an L-Shaped Multi-Beam Jointed Structure with Tip Mass

Beam-Based Vibration Energy Harvesters Tunable Through Folding

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