Vertical nonlinear response of single and 2 × 2 group pile under strong harmonic excitation

Abstract This study presents an investigation of the coupled longitudinal-transverse waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathematical model is presented that describes the three-dimensional nonlinear response of a long elastic cable. An asymptotic form of this model is derived for the linear response of cables having small equilibrium curvature. Linear in-plane response is described by coupled longitudinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing propagating waves is derived using transform methods. In the spectral relation, three qualitatively distinct frequency regimes exist that are separated by two cut-off frequencies. This relation is employed in deriving a Green’s function which is then used to construct solutions for in-plane response under arbitrarily distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves which propagate through the cable, one characterizing extension-compressive deformations (rod-type) and the other characterizing transverse deformations (string-type). These waves may propagate or attenuate depending on wave frequency. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated harmonic excitation source.

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Harmonically Forced Wave Propagation in Elastic Cables With Small Curvature

Journal of Vibration and Acoustics ◽

10.1115/1.2889735 ◽

1997 ◽

Vol 119 (3) ◽

pp. 390-397 ◽

Cited By ~ 2

Author(s):

M. Behbahani-Nejad ◽

N. C. Perkins

Keyword(s):

Nonlinear Response ◽

Asymptotic Form ◽

Equations Of Motion ◽

Three Dimensional ◽

Harmonic Excitation ◽

Forced Response ◽

Periodic Waves ◽

Transverse Waves ◽

Propagating Waves ◽

Elastic Cables

This study presents an investigation of coupled longitudinal-transverse waves that propagate along an elastic cable. The coupling considered derives from the equilibrium curvature (sag) of the cable. A mathematical model is presented that describes the three-dimensional nonlinear response of an extended elastic cable. An asymptotic form of this model is derived for the linear response of cables having small equilibrium curvature. Linear, in-plane response is described by coupled longitudinal-transverse partial differential equations of motion, which are comprehensively evaluated herein. The spectral relation governing propagating waves is derived using transform methods. In the spectral relation, three qualitatively distinct regimes exist that are separated by two cut-off frequencies which are strongly influenced by cable curvature. This relation is employed in deriving a Green’s function which is then used to construct solutions for in-plane response under arbitrarily distributed harmonic excitation. Analysis of forced response reveals the existence of two types of periodic waves which propagate through the cable, one characterizing extension-compressive deformations (rod-type) and the other characterizing transverse deformations (string-type). These waves may propagate or attenuate depending on wave frequency. The propagation and attenuation of both wave types are highlighted through solutions for an infinite cable subjected to a concentrated harmonic excitation source.

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The Nonlinear Response of a Simply Supported Rectangular Metallic Plate to Transverse Harmonic Excitation

Journal of Applied Mechanics ◽

10.1115/1.1308579 ◽

2000 ◽

Vol 67 (3) ◽

pp. 621-626 ◽

Cited By ~ 6

Author(s):

O. Elbeyli and ◽

G. Anlas

Keyword(s):

Critical Points ◽

Internal Resonance ◽

Nonlinear Response ◽

Multiple Scales ◽

Method Of Multiple Scales ◽

Primary Resonance ◽

Harmonic Excitation ◽

Stability Of Solutions ◽

Metallic Plate ◽

Simply Supported

In this study, the nonlinear response of a simply supported metallic rectangular plate subject to transverse harmonic excitations is analyzed using the method of multiple scales. Stability of solutions, critical points, types of bifurcation in the presence of a one-to-one internal resonance, together with primary resonance, are determined. [S0021-8936(00)00603-6]

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Frequency-Domain-Based Nonlinear Response Analysis of Stationary Ring Displacement of Noncontact Mechanical Seal

Shock and Vibration ◽

10.1155/2019/7082538 ◽

2019 ◽

Vol 2019 ◽

pp. 1-8 ◽

Cited By ~ 2

Author(s):

Dian Feng Sun ◽

Jian Jun Sun ◽

Chen Bo Ma ◽

Qiu Ping Yu

Keyword(s):

Nonlinear Response ◽

Volterra Series ◽

Operational Reliability ◽

Harmonic Excitation ◽

System Stability ◽

Response Analysis ◽

Mechanical Seals ◽

Low Frequencies ◽

Selection Scheme ◽

The Time Domain

Dynamic characteristics affect the operational reliability of noncontacting mechanical seals, which involves the complex relationship between the system of noncontact mechanical seals, excitation, and response. Hence, it is one of the hot topics of current research. However, domestic and foreign scholars mainly calculate the response in the time domain by establishing a linear dynamic model so that the response results can be used for system stability and tracking analysis. In this study, according to the harmonic excitation, the stationary ring’s output response was expressed via the famous Volterra series and solved with a new method, which can be used to analyze the frequency response and to calculate the displacement response of the stationary ring with single and double harmonic excitation. Based on the analysis of the response results, the parameter (stationary ring mass, axial damping, stiffness, etc.) selection scheme of noncontact mechanical seals at high and low frequencies was obtained.

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Exploitation of Nonlinear Dynamics of Buckled Beams

Volume 6: 12th International Conference on Multibody Systems, Nonlinear Dynamics, and Control ◽

10.1115/detc2016-59208 ◽

2016 ◽

Author(s):

James M. Wilson ◽

Amit Shukla ◽

William Olson

Keyword(s):

Nonlinear Dynamics ◽

Nonlinear Response ◽

Maximum Amplitude ◽

Harmonic Excitation ◽

System Response ◽

Optimization Approach ◽

Response Characteristics ◽

Buckled Beams ◽

Integral Role ◽

Loading Methods

Axially-loaded structures play an integral role in engineering design. Some of these structures exhibit a nonlinear response behavior under harmonic loading. Methods aimed at eliminating these behaviors are often employed in design of such structures. Our hypothesis is that the nonlinear dynamics can be used to optimize desired system response characteristics. In this paper, the dynamic response of a buckled beams under harmonic excitation is considered. An optimization approach is formulated that achieves maximum amplitude, periodic, and stable responses of the beam systems. Case studies are presented that demonstrate the utility of this optimization approach to exploit the nonlinear dynamics to achieve desired responses.

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Vibro-Impact Response of a Cracked Bar

Shock and Vibration ◽

10.1155/2011/134245 ◽

2011 ◽

Vol 18 (1-2) ◽

pp. 147-156 ◽

Cited By ~ 2

Author(s):

Vikrant R. Hiwarkar ◽

Vladimir I. Babitsky ◽

Vadim V. Silberschmidt

Keyword(s):

Nonlinear Response ◽

Dynamic Compliance ◽

Harmonic Excitation ◽

Impact Response ◽

Nonlinear Feedback ◽

One Dimensional ◽

Analytical Technique ◽

Structural Health ◽

Impact Interaction ◽

Contact Nonlinearity

The presence of a crack in a structure affects its dynamic behaviour under working conditions. Cracks introduce nonlinearities into the system; the use of such nonlinearities for damage detection should be investigated. A model of a one-dimensional cracked cantilever bar subjected to longitudinal harmonic excitation is used to analyse a vibro-impact response as a way to monitor structural health. The effect of contact nonlinearity due to crack's faces interaction is considered. This nonlinear information is obtained based on a combination of the analytical technique and the Matlab-Simulink computation. The procedure uses a numerical approximation for dynamic compliance operators and a nonlinear model of contact faces interaction implemented numerically as a nonlinear feedback. Nonlinear resonant phenomena due to vibro-impact interaction in the cracked bar are obtained and analysed. A distribution of the higher harmonics along the bar length, generated due to the nonlinear response of the crack, is revealed as a function of the distance from the crack. Recommendations on structural health monitoring of cracked bars due to contact nonlinearity are presented

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Large Amplitude Forced Vibrations of Simply Supported Thin Cylindrical Shells

Journal of Applied Mechanics ◽

10.1115/1.3423008 ◽

1973 ◽

Vol 40 (2) ◽

pp. 471-477 ◽

Cited By ~ 44

Author(s):

J. H. Ginsberg

Keyword(s):

Nonlinear Response ◽

Nonlinear Boundary ◽

Circular Cylindrical Shell ◽

Perturbation Technique ◽

Equations Of Motion ◽

Harmonic Excitation ◽

Inertia Effects ◽

Modal Expansion ◽

Wide Range ◽

Nonlinear Equations Of Motion

The response of a thin circular cylindrical shell to resonant harmonic excitation is examined by a modal expansion approach. The nonlinear strain-displacement relations lead to a nonlinear boundary condition, as well as nonlinear equations of motion. The solution, which retains tangential inertia effects, is obtained by a perturbation technique that yields a consistent first approximation of the nonlinear response. The results are applicable for a wide range of parameters and to cases of excitation near any of the three lowest natural frequencies corresponding to given axial and circumferential wavelengths. For situations where shallow shell theory is valid, the results of previous studies, which were based upon such a theory, are in close agreement.

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