Dynamic response analysis of Euler–Bernoulli beam on spatially random transversely isotropic viscoelastic soil

2022 ◽  
pp. 146442072110674
Author(s):  
Zele Li ◽  
Decheng Feng ◽  
Mohammad Noori ◽  
Dipanjan Basu ◽  
Wael A. Altabey
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Transversely Isotropic ◽  
Response Analysis ◽  
Bernoulli Beam ◽  
Partial Differential ◽  
Soil System ◽  
Present Solution ◽  
Foundation Model ◽  
Euler Bernoulli Beam

A novel dynamic soil-structure interaction model is developed for analysis for Euler–Bernoulli beam rests on a spatially random transversely isotropic viscoelastic foundation subjected to moving and oscillating loads. The dynamic equilibrium equation of beam-soil system is established using the extended Hamilton's principle, and the corresponding partial differential equations describing the displacement of beam and soil and boundary conditions are further obtained by the variational principles. These partial differential equations are discretized in spatial and time domains and solved by the finite difference (FD) method. After the differential equations of beam and soil are discretized in the spatial domain, the implicit iterative scheme is used to solve the equations in the time domain. The solving result shows the FD method is effective and convenient for solving the differential equations of beam-soil system. The spring foundation model adopted the modified Vlasov model, which is a two-parameter model considering the compression and shear of soil. The advantage of the present foundation model is avoided estimating input parameters of the modified Vlasov model using prior knowledge. The present solution is verified by publishing solution and equivalent three-dimensional FE analysis. The present model produced an accurate, faster, and effective displacement response. A few examples are carried out to analyze the parameter variation influence for beam on spatially random transversely isotropic viscoelastic soil under moving loads.

scholarly journals Effects of Hall current on unsteady hydromagnetic free convection flow past an impulsively moving vertical plate with Newtonian heating

2016 ◽  
Vol 21 (1) ◽  
pp. 187-203 ◽  
Author(s):  
G.S. Seth ◽  
S. Sarkar ◽  
R. Sharma
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Free Convection ◽  
Vertical Plate ◽  
Numerical Solutions ◽  
Hall Current ◽  
Convection Flow ◽  
Free Convection Flow ◽  
Partial Differential ◽  
Present Solution

Abstract An investigation of unsteady hydromagnetic free convection flow of a viscous, incompressible and electrically conducting fluid past an impulsively moving vertical plate with Newtonian surface heating embedded in a porous medium taking into account the effects of Hall current is carried out. The governing partial differential equations are first subjected to the Laplace transformation and then inverted numerically using INVLAP routine of Matlab. The governing partial differential equations are also solved numerically by the Crank-Nicolson implicit finite difference scheme and a comparison has been provided between the two solutions. The numerical solutions for velocity and temperature are plotted graphically whereas the numerical results of skin friction and the Nusselt number are presented in tabular form for various parameters of interest. The present solution in special case is compared with a previously obtained solution and is found to be in excellent agreement.

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

Symmetry ◽  
2021 ◽  
Vol 13 (12) ◽  
pp. 2234
Author(s):  
Zu-Guang Ying ◽  
Yi-Qing Ni
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Periodic Structures ◽  
Response Analysis ◽  
Periodic Part ◽  
Spatial Mode ◽  
Partial Differential ◽  
Vibration Localization ◽  
Linear Partial Differential Equations ◽  
Distribution Parameters

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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