Analytical approximate solutions to large amplitude vibration of a spring-hinged beam

Yu, Yongping; Wu, Baisheng; Sun, Youhong; Zhang, Lin

doi:10.1007/s11012-013-9782-z

Cited by 5 publications

(3 citation statements)

References 14 publications

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“…where 2 0 =1.0745, 1 = −8.1836 1 , and 2 = −53.5149 1 . In order to compare the large curvature vibration with the small amplitude vibration, for the linear equation in (13), the classic mode shape function sin( ) is adopted; thus the classic the dimensionless ODE can degenerate tö+ = 0. Then one can obtain the theoretical solution easily, which is named as theoretical solution of the linear equation throughout the paper.…”

Section: Mode Discretization With Exact Mode Shapementioning

confidence: 99%

“…In their model, the von Karman type nonlinear strain-displacement relationship is employed, and the effects of transverse shear deformation are included based upon the Timoshenko beam theory. Similarly, to further seek the nonlinear frequencies, Gunda and Gupta [11] investigated the vibration of a composite beam, Nikkar and Bagheri [12] explored the cantilever beam with an intermediate lumped mass, and Yu and Wu et al [13] studied the beam with immovable spring-hinged ends. More related works include that Raju and Rao [14] formulated the nonlinear vibration of the beam using multiterm admissible 2 Mathematical Problems in Engineering functions for the first mode.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

Zhao

Zhang

et al. 2018

Mathematical Problems in Engineering

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Mechanical nonlinear vibration of slender structures, such as beams, strings, rods, plates, and even shells occurs extensively in a variety of areas, spanning from aerospace, automobile, cranes, ships, offshore platforms, and bridges to MEMS/NEMS. In the present study, the nonlinear vibration of an elastic string with large amplitude and large curvature has been systematically investigated. Firstly, the mechanics model of the string undergoing strong geometric deformation is built based on the Hamilton principle. The nonlinear mode shape function was used to discretize the partial differential equation into ordinary differential equation. The modified complex normal form method (CNFM) and the finite difference scheme are used to calculate the critical parameters of the string vibration, including the time history diagram, configuration, total length, and fundamental frequency. It is shown that the calculation results from these two methods are close, which are different with those from the linear equation model. The numerical results are also validated by our experiment, and they take excellent agreement. These analyses may be helpful to engineer some soft materials and can also provide insight into the design of elementary structures in sensors, actuators and resonators, etc.

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Section: Mode Discretization With Exact Mode Shapementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

Zhao

Zhang

et al. 2018

Mathematical Problems in Engineering

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show abstract

“…Besides, this method is also algebraically much simpler and it avoids solving a set of complex nonlinear algebraic equations. In the previous studies, the NHB method was applied to solve various engineering problems, including analogy to double sine-Gordon equation [28], large post-buckling deformation of elastic rings [29], large amplitude vibration of spring-hinged beam [30], hydrothermal buckling deformation of beams [31], large-amplitude vibration of simply-supported laminated plates [32], and oscillation of current-carrying wires [33].…”

Section: Introductionmentioning

confidence: 99%

Analytical asymptotic approximations for large amplitude nonlinear free vibration of a dielectric elastomer balloon

et al. 2017

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Dielectric elastomer is a prosperous material in electromechanical systems because it can effectively transform electrical energy to mechanical work. In this paper, the period and periodic solution for a spherical dielectric elastomer balloon subjected to static pressure and voltage are derived through an analytical method, called the Newton-harmonic balance (NHB) method. The elastomeric spherical balloon is modeled as an autonomous nonlinear differential equation with general and negatively powered nonlinearities. The NHB method enables to linearize the governing equation prior to applying the harmonic balance method. Even for such a nonlinear system with negatively powered variable and non-classical non-odd nonlinearity, the NHB method is capable of deriving highly accurate approximate solutions. Several practical examples with different initial stretch ratios are solved to illustrate the dynamic inflation of elastomeric spherical balloons. When the initial amplitude is sufficiently large, the system will lose its stability. Comparison with Runge-Kutta numerical integration solutions is also presented and excellent agreement has been observed.

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Analytical approximations to resonance response of harmonically forced strongly odd nonlinear oscillators

Zhou

Lim

et al. 2018

Arch Appl Mech

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Analytical approximate solutions to large amplitude vibration of a spring-hinged beam

Cited by 5 publications

References 14 publications

Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

Nonlinear Vibration of an Elastic Soft String: Large Amplitude and Large Curvature

Analytical asymptotic approximations for large amplitude nonlinear free vibration of a dielectric elastomer balloon

Analytical approximations to resonance response of harmonically forced strongly odd nonlinear oscillators

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