Analytical solution on dynamic response of airport rigid pavements

Dynamic response of an electro-rheological sandwich beam subjected to simultaneous Impact loads will be considered. Analytical solution will be used to draw FRF diagram of the beam for different electric field. Upper and lower layers of the beam have different material properties. Coupled governing equations derived from Hamilton Principle will be solved in frequency domain to find transverse vibration of the beam.

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A Theory Research of Asphalt Pavement Dynamic Response under Vehicle Random Stimulation

Applied Mechanics and Materials ◽

10.4028/www.scientific.net/amm.105-107.13 ◽

2011 ◽

Vol 105-107 ◽

pp. 13-19

Author(s):

Xiao Yun Liu ◽

Chun Juan Shi ◽

Shui Jing Chen

Keyword(s):

Correlation Function ◽

Analytical Solution ◽

Dynamic Response ◽

Asphalt Pavement ◽

Mathematic Model ◽

Square Function ◽

Random Response ◽

Space Correlation ◽

Time Space ◽

Function Time

In order to study the dynamic response of the asphalt pavement under vehicle random stimulation, the random vibration model of vehicles and the mathematic model of pavement dynamic response in which the base and surface are all viscoelasticity are established respectively. The analytical solution of the stochastic response for the pavement is deduced. The stochastic load acted on the pavement can be gotten by the mathematic model of the vehicle vibration. The numeral feature functions of the random response, such as even function, time-space correlation function, time correlation function and mean square function, are obtained by the analytical solution. The paper provides a theory method for studying the random response of the asphalt pavement.

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Torsional Vibration of a Pile in Transversely Isotropic Saturated Soil Considering Its Construction Disturbance Effect

International Journal of Structural Stability and Dynamics ◽

10.1142/s0219455422500444 ◽

2021 ◽

Author(s):

Wenjie Ma ◽

Yao Shan ◽

Binglong Wang ◽

Shunhua Zhou

Keyword(s):

Analytical Solution ◽

Dynamic Response ◽

Twist Angle ◽

Complex Impedance ◽

Closed Form Solution ◽

Transversely Isotropic ◽

Saturated Soil ◽

Parameter Study ◽

Present Solution ◽

Transversely Isotropic Saturated Soil

The torsional dynamic response of a pile embedded in transversely isotropic saturated soil is investigated while allowing for the construction of disturbance effect. The dynamic governing equations of soil are established based on Biot’s poroelastic theory. By virtue of the continuous conditions of stress and displacement of adjacent disturbance circle and the boundary conditions of pile-soil coupling system, the circumferential displacement of soil and the shear stress on pile-soil contact surface are derived. Subsequently, a closed-form solution for the torsional dynamic response of a pile is derived in the frequency domain. By using inverse Fourier transform and the convolution theorem, a quasi-analytical solution for the velocity response of the pile head subjected to a semi-sine excitation torque is derived in the time domain. The proposed analytical solution is verified by comparing with the two existing solutions available in literature. Following the present solution, a parameter study is undertaken to portray the influence on the complex impedance, twist angle and torque of pile.

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Analytical modal analysis of thin-film flat lenses

Proceedings of the Institution of Mechanical Engineers Part K Journal of Multi-body Dynamics ◽

10.1243/146441905x9999 ◽

2005 ◽

Vol 219 (1) ◽

pp. 55-59 ◽

Cited By ~ 1

Author(s):

H R Hamidzadeh ◽

L Moxey

Keyword(s):

Thin Film ◽

Analytical Solution ◽

Dynamic Response ◽

Modal Analysis ◽

Closed Form ◽

Material Properties ◽

Mathieu Equation ◽

Free Vibrations ◽

Mode Shapes ◽

Closed Form Solutions

The free vibrations of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin-film membranes were mathematically modelled using the Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case, when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters, such as material properties, membrane pre-strain rate, and the geometry, on natural frequency and mode shapes of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin-film lenses.

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Analytical Modal Analysis of Thin-Film Flat Lenses

Design Engineering, Volumes 1 and 2 ◽

10.1115/imece2003-42493 ◽

2003 ◽

Author(s):

L. Moxey ◽

H. Hamidzadeh

Keyword(s):

Thin Film ◽

Analytical Solution ◽

Dynamic Response ◽

Modal Analysis ◽

Closed Form ◽

Material Properties ◽

Mathieu Equation ◽

Free Vibrations ◽

Vibration Response ◽

Closed Form Solutions

Dynamics of circular and elliptical thin-film lens are investigated. In particular, linear closed-form solutions for free vibrations of these structures were achieved and modal analysis was performed. The vibration response of the thin film membranes were mathematically modeled using Mathieu equation. Numerical results for various nodal diameters were computed. For the limited case when an elliptical lens becomes circular, an excellent comparison was established with the available analytical solution. Experimental analyses were conducted to determine the effects of various parameters such as material properties, membrane pre strain and the geometry on the dynamic response of these structures. The comparison verified the adequacy of linear solutions to predict the dynamic response of thin film lenses.

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