Parametric Resonance in Cantilever Beam with Feedback-Induced Base Excitation

Jani, Nikul; Chakraborty, Goutam

doi:10.1007/s42417-020-00226-1

Cited by 9 publications

(4 citation statements)

References 21 publications

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“…where a k and b k are constant coefficients. By substituting Equation (10) into Equation ( 9), a linear combination of trigonometric functions is obtained:…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

“…The stable regions correspond to finite solutions of the Mathieu–Hill equations, while the unstable regions correspond to solutions that increase indefinitely in time [ 3 ]. The stability charts of the Mathieu–Hill equations published in the literature are usually calculated using various methods, i.e., harmonic balance method [ 4 , 6 , 7 , 8 , 9 , 10 , 11 ], Galerkin method [ 11 , 12 ], multiscale methods [ 13 ], averaging method [ 14 , 15 ], discrete singular convolution [ 16 ], homotopy perturbation method [ 17 ], and small parameter method (Poincaré method) [ 3 , 11 ]. There is a wealth of literature available on parametric vibrations that comprehensively addresses all fundamental aspects of the subject [ 3 , 4 , 6 , 7 , 8 , 18 , 19 ].…”

Section: Introductionmentioning

confidence: 99%

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Dynamic Stability of Tensegrity Structures—Part II: The Periodic External Load

Obara

Tomasik

2023

Materials

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The paper contains a parametric analysis of tensegrity structures subjected to periodic loads. The analysis focuses on determining the main region of dynamic instability. When load parameters fall within this region, the resulting vibration amplitudes increase, posing a risk to the durability of structures. The study considers structures built using commonly used modules. The influence of the initial prestress on the distribution of the instability regions is examined. Additional prestress can significantly reduce the extent of instability regions, potentially narrowing them by up to 99%. A nondimensional parameter is introduced to accurately assess changes in the extent of the instability region. A geometrically non-linear model is employed to evaluate the behavior of the analyzed structures.

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“…where a k and b k are constant coefficients. By substituting Equation (10) into Equation ( 9), a linear combination of trigonometric functions is obtained:…”

Section: Harmonic Balance Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Dynamic Stability of Tensegrity Structures—Part II: The Periodic External Load

Obara

Tomasik

2023

Materials

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“…The discussion covered various major mechanisms of nonlinear VEH along with its operating principles, advantages, disadvantages and applications. Jani and Chakraborty 48 analysed the effect of parametric resonance on cantilever beam energized by base excitation. They developed an analytical model incorporating the concept of feedback-based excitation.…”

Section: Introductionmentioning

confidence: 99%

“…The study explored 44–48 the VEH using various nonlinear mechanisms such as bistability, duffing nonlinearity, parametric and stochastic oscillators. The EH adopting duffing oscillator principle based on the concept of amplitude dependant spring nonlinearity.…”

Section: Introductionmentioning

confidence: 99%

Energy harvesting from a cantilever beam with a spring-loaded oscillating mass system and base excitation

Mohanty

Behera

2022

Proceedings of the Institution of Mechanical Engineers, Part K:

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The present study deals with the mathematical modeling of a nonlinear energy harvester (EH) to analyze it's frequency bandwidth for optimal use. The exhibited unique piezoelectric energy harvester (PEH) contains a cantilever beam as resonator with a moving mass. To fulfill the mechanism, the mass needs to be connected to the fixed end of the beam with a spring that acts as a mechanical amplifier. A novel analytical approach with 1:2 internal resonance (IR) including kinematic nonlinearity is addressed for energy harvesting. The occurrence of strong nonlinear coupling is the result of constant interconnection between the beam and moving mass. A discrete electro-mechanical coupled equation is derived using Galerkin's method followed by Hamilton's energy method. To analyze the effect of input parameters on the frequency bandwidth, MATLAB code is improved by implementing the “Method of multiple scales” (MMS) for furthering the energy output of the system. Due to IR, the solution tilted to two branches in the designed EH, witnessing broader frequency bandwidth. The influence of different system parameters such as spring stiffness, mass, and velocity of moving mass changed the position of central frequency resulting in the change in symmetry of frequency response.

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