Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

Sun, Yuxin; Liu, Shoubin; Rao, Zhangheng; Li, Yuhang; Yang, Jialing

doi:10.3390/sym10080328

Cited by 10 publications

(5 citation statements)

References 29 publications

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“…In the future, the practical interest will be to investigate the behavior of a beam (thermodynamic response) with a variable foundation coefficient when the beam is irradiated by moving laser pulses. This issue was investigated in [32] for the constant coefficient. The results can be generalized to investigate the dynamic design of thin films on compliant substrates [33].…”

Section: Examplesmentioning

confidence: 99%

Symmetric Properties of Eigenvalues and Eigenfunctions of Uniform Beams

et al. 2020

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In this paper, the models of Euler–Bernoulli beams on the Winkler foundations are considered. The novelty of the research is in consideration of the models with an arbitrary variable coefficient of foundation. Qualitative results that influence the symmetry of the coefficient of foundation on the spectral properties of the corresponding problems are obtained, for which specific variable coefficients of foundation are tested using numerical calculations. Three types of fixing at the ends are studied: clamped-clamped, hinged-hinged and free-free. The conditions of the stiffness and types of beam fixing have been found for the set of eigenvalues of boundary value problems on a full segment and can be represented as two groups of the eigenvalues of certain problems on a half segment. Such qualitative spectral properties of a mechanical system can contribute to the creation of various algorithms for nondestructive testing, which are widely used in technical acoustics.

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Section: Examplesmentioning

confidence: 99%

Symmetric Properties of Eigenvalues and Eigenfunctions of Uniform Beams

et al. 2020

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“…Numerous studies have reported characteristic frequencies [1][2][3][4], modal localization and buckling [5][6][7][8][9][10][11][12][13][14], quasi-periodic distribution parameter effects [15][16][17][18] and application [19][20][21][22][23][24][25][26][27] based on transfer matrix method, spatial (Bloch) harmonic expansion method, (Floquet-Bloch and Galerkin) double expansion method and finite element method, etc. Waves and vibration in beams with non-uniform distribution parameters have also been pursued using a fundamental solution, semianalysis and finite element methods [28][29][30][31][32][33][34]. Perturbation and multiple scale methods were applied for weakly periodic parameter cases [35,36].…”

Section: Introductionmentioning

confidence: 99%

Vibration Localization and Anti-Localization of Nonlinear Multi-Support Beams with Support Periodicity Defect

Ying

2021

Symmetry

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A response analysis method for nonlinear beams with spatial distribution parameters and non-periodic supports was developed. The proposed method is implemented in four steps: first, the nonlinear partial differential equation of the beams is transformed into linear partial differential equations with space-varying parameters by using a perturbation method; second, the space-varying parameters are separated into a periodic part and a non-periodic part describing the periodicity defect, and the linear partial differential equations are separated into equations for the periodic and non-periodic parts; third, the equations are converted into ordinary differential equations with multiple modes coupling by using the Galerkin method; fourth, the equations are solved by using a harmonic balance method to obtain vibration responses, which are used to discover dynamic characteristics including the amplitude–frequency relation and spatial mode. The proposed method considers multiple vibration modes in the response analysis of nonlinear non-periodic structures and accounts for mode-coupling effects resulting from structural nonlinearity and parametric non-periodicity. Thus, it can handle nonlinear non-periodic structures with a high parameter-varying wave in wide frequency vibration. In numerical studies, a nonlinear beam with non-periodic supports (resulting in non-periodic distribution parameters or periodicity defect) under harmonic excitations was explored using the proposed method, which revealed some new dynamic response characteristics of this kind of structure and the influences of non-periodic parameters. The characteristics include remarkable variation in frequency response and spatial mode, and in particular, vibration localization and anti-localization. The results have potential applications in vibration control and the support damage detection of nonlinear structures with non-periodic supports.

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“…The most important physical quantity of interest for such practical applications is the temperature field of the medium, which is usually modeled by the heat conduction equation with time-dependent localized source terms for moving heat sources. Once the temperature field is obtained, many other thermophysical properties of material, including metallurgical microstructures, thermal stress, residual stress, and part distortion, could be subsequently determined [6][7][8][9][10]. It is therefore particularly important to precisely and efficiently predict the dynamic variation of the temperature field around the moving heat sources during these engineering processes.…”

Section: Introductionmentioning

confidence: 99%

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

Liu

2020

Advances in Mathematical Physics

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This paper focuses on efficiently numerical investigation of two-dimensional heat conduction problems of material subjected to multiple moving Gaussian point heat sources. All heat sources are imposed on the inside of material and assumed to move along some specified straight lines or curves with time-dependent velocities. A simple but efficient moving mesh method, which continuously adjusts the two-dimensional mesh dimension by dimension upon the one-dimensional moving mesh partial differential equation with an appropriate monitor function of the temperature field, has been developed. The physical model problem is then solved on this adaptive moving mesh. Numerical experiments are presented to exhibit the capability of the proposed moving mesh algorithm to efficiently and accurately simulate the moving heat source problems. The transient heat conduction phenomena due to various parameters of the moving heat sources, including the number of heat sources and the types of motion, are well simulated and investigated.

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Thermodynamic Response of Beams on Winkler Foundation Irradiated by Moving Laser Pulses

Cited by 10 publications

References 29 publications

Symmetric Properties of Eigenvalues and Eigenfunctions of Uniform Beams

Symmetric Properties of Eigenvalues and Eigenfunctions of Uniform Beams

Vibration Localization and Anti-Localization of Nonlinear Multi-Support Beams with Support Periodicity Defect

Heat Conduction Simulation of 2D Moving Heat Source Problems Using a Moving Mesh Method

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