Nonlinear response of elastic plates to pulse excitations

Chandrasekharappa, G.; Srirangarajan, H.R.

doi:10.1016/0045-7949(87)90061-7

Cited by 13 publications

(15 citation statements)

References 7 publications

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“…At this point, we mention that we consider the response of the elastic plate to be linear, while the propagation in the waveguide weakly nonlinear. This is a reasonable approximation, since the pressure amplitudes used in this work are not sufficiently strong to excite nonlinear vibrations of the elastic plate 31 . On the other hand, it is well known that due to the compressibility of air the wave celerity is nonlinear, c N L .…”

Section: Electro-acoustic Analogue Modeling a Setup And Modelmentioning

confidence: 99%

Bright and gap solitons in membrane-type acoustic metamaterials

et al. 2017

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We study analytically and numerically envelope solitons (bright and gap solitons) in a onedimensional, nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear, dispersive and dissipative wave equation. Applying the multiple scales perturbation method, we derive an effective lossy nonlinear Schrödinger equation and obtain analytical expressions for bright and gap solitons. We also perform direct numerical simulations to study the dissipation-induced dynamics of the bright and gap solitons. Numerical and analytical results, relying on the analytical approximations and perturbation theory for solions, are found to be in good agreement.

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Section: Electro-acoustic Analogue Modeling a Setup And Modelmentioning

confidence: 99%

Bright and gap solitons in membrane-type acoustic metamaterials

et al. 2017

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“…This is a reasonable approximation, since the amplitudes used in this work are not sufficient to excite nonlinear vibrations of the elastic plate [9,20]. Due to the compressibility of the air, the wave celerity is a nonlinear term, c NL .…”

Section: Electro-acoustic Analogue Modelingmentioning

confidence: 99%

“…It is clear that Equation (20) suggests the existence of a gap at low frequencies, i.e., for 0 ≤ ω < m, with the cut-off frequency defined by the parameter m. For m < ω < ω B , there exists a band, with the dispersion curve ω(k) having the form of hyperbola, which asymptotes (according to Equation (20)) to unity, which is the normalized velocity associated with the wave equation p ττ − p χχ = 0. The term γk 4 accounts for the influence of the periodicity of the lattice (originating from the termδ 2 p n ) to the dispersion relation.…”

Section: The Linear Dispersion Relationmentioning

confidence: 99%

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Second-Harmonic Generation in Membrane-Type Nonlinear Acoustic Metamaterials

et al. 2016

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Abstract:We study analytically and numerically the second-harmonic generation in a one-dimensional nonlinear acoustic metamaterial, composed of an air-filled waveguide periodically loaded by clamped elastic plates. Based on the transmission line approach, we derive a nonlinear dynamical lattice model which, in the continuum approximation, leads to a nonlinear dispersive wave equation. By applying the perturbation method to the latter, we derive the analytical expressions for the first-and second-harmonics, which are in excellent agreement with the numerical simulations of the nonlinear dynamical lattice model. Apart from the case of dispersionless nonlinear propagation and the Fubini solution, special attention is payed to the role of dispersion. In that regard, it is found that, once dispersion comes into play, second-harmonic beatings in space due to phase-mismatch can be identified. Our results provide many opportunities for the development of new periodic acoustic structures featuring both nonlinearity and dispersion.

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“…Theoretical and experimental results are compared for geometrically nonlinear vibrations of rectangular plates with different boundary conditions [9,10]. The effect of the boundary conditions on the dynamic response of the elastic plates subjected to blast loading is also investigated [11]. In another study, the response of simply supported anti-symmetrically laminated angle-ply plates to explosive blast loading is considered [12].…”

Section: Introductionmentioning

confidence: 99%

The Nonlinear Dynamic Behaviour of Tapered Laminated Plates Subjected to Blast Loading

Süsler

Türkmen

Kazancı

2012

Shock and Vibration

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Abstract. In this study, the geometrically nonlinear dynamic behaviour of simply supported tapered laminated composite plates subjected to the air blast loading is investigated numerically. In-plane stiffness, inertia and the geometric nonlinearity effects are considered in the formulation of the problem. The equations of motion for the tapered laminated plate are derived by the use of the virtual work principle. Approximate solution functions are assumed for the space domain and substituted into the equations of motion. Then, the Galerkin method is used to obtain the nonlinear algebraic differential equations in the time domain. The resulting equations are solved by using the finite difference approximation over the time. The effects of the taper ratio, the stacking sequence and the fiber orientation angle on the dynamic response are investigated. The displacement-time and strain-time histories are obtained on certain points in the tapered direction. The results obtained by using the present method are compared with the ones obtained by using a commercial finite element software ANSYS. The results are found to be in an agreement. The method presented here is able to determine the nonlinear dynamic response of simply supported tapered laminated plates to the air blast loading accurately.

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Nonlinear response of elastic plates to pulse excitations

Cited by 13 publications

References 7 publications

Bright and gap solitons in membrane-type acoustic metamaterials

Bright and gap solitons in membrane-type acoustic metamaterials

Second-Harmonic Generation in Membrane-Type Nonlinear Acoustic Metamaterials

The Nonlinear Dynamic Behaviour of Tapered Laminated Plates Subjected to Blast Loading

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