BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICAL RESPONSE OF VISCOELASTIC THIN PLATE(Ⅱ)──THEORETICAL ANALYSIS

In this paper, the necessary theoretical analysis for the approximation boundary element method to solve dynamical response of viscoelastic thin plate presented in [1] is.discussed. The theorem of existence and uniqueness of the approximate solution andthe error estimation are also obtained. Based on these conclusions , the principle forchoosing the mesh size and the number of truncated terms in the fundamental solution are given. It isshown that the theoretical ana analysis in this paper are consistent with thenumerical results in [1].

Dynamical Mechanical Properties for AD90 Alumina

The dynamic response of polycrystalline alumina was investigated in the pressure range of 0 - 13 GPa by planar impact experiments. Velocity interferometer system for any reflector（VISAR） was used to obtain free surface velocity profile and determine the Hugoniot elastic limit, and manganin gauges were employed to obtain the stress-time histories and determine Hugoniot curve. Both the free surface particle velocity profiles and Hugoniot curves indicate the dispersion of the ＂plastic＂ wave for alumina. With the measured stress histories, the complete histories of strain, particle velocity, specific volume and specific internal energy are gained by using path line principle of Lagrange analysis. The dynamic mechanical behaviors for alumina under impact loading are analyzed, such as nonlinear characteristic, strain rate dependence, dispersion and declination of shock wavein the material.

QUASI-STATIC AND DYNAMICAL ANALYSIS FOR VISCOELASTICTIMOSHENKO BEAM WITH FRACTIONAL DERIVATIVECONSTITUTIVE RELATION

The equations of motion governing the quasi-static and dynamical behavior of a viscoelastic Timoshenko beam are derived. The viscoelastic material is assumed to obey a three-dimensional fractional derivative constitutive relation. ne quasi-static behavior of the viscoelastic Timoshenko beam under step loading is analyzed and the analytical solution is obtained. The influence of material parameters on the deflection is investigated. The dynamical response of the viscoelastic Timoshenko beam subjected to a periodic excitation is studied by means of mode shape functions. And the effect of both transverse shear and rotational inertia on the vibration of the beam is discussed.

Analysis of dynamical response to large deformation of piles with initial displacements

In this paper, a nonlinear mathematical model for analyzing dynamical response to the large deformation of piles with initial displacements is firstly established with the arc-coordinate, and it is a set of nonlinear integral-differential equa- tions, in which, the Winkeler model is used to simulate the resistance of the soil to the pile. Secondly, a set of new auxiliary functions are introduced. The differential-integral equations are transformed into a set of nonlinear differential equations, and the differential quadrature method （DQM） and the finite difference method （FDM） are applied to discretize the set of nonlinear equations in the spatial and time domains, respectively. Then, the Newton-Raphson method is used to solve the set of discretization algebraic equations at each time step. Finally, numerical examples are presented, and the dynamical re- sponses to the deformation of piles, including configuration, bending moment and shear force, are graphically illuminated. In calculation, two types of initial displacements and dynamical loads are applied, and the effects of parameters on the dynamical responses of piles are analyzed in detail.

BOUNDARY ELEMENT METHOD FOR SOLVING DYNAMICAL RESPONSE OF VISCOELASTIC THIN PLATE(I)

In this paper, a boundary element method for solving dynamical response of viscoelastic thin plate is given. In Laplace domain, we propose two methods to approximate the fundamental solution and develop the corresponding boundary element method. Then using the improved Bellman's numerical inversion of the Laplace transform, the solution of the original problem is obtained. The numerical results show that this method has higher accuracy and faster convergence.

On the problem of the dynamical reactions of a rolling wheelset to real track irregularities

We investigate numerically the dynamical reactions of a moving wheelset model to real measured track irregularities.The background is to examine whether the dynamics are suitable as the input to the inverse problem:determine the true track geometry from measured wheelset dynamical reactions.It is known that the method works well for the vertical position of the rails but the computed lateral position is often flawed.We find that the lateral motion of the wheelset often may differ from the track geometry.The cases are investigated closely but the reasons remain unknown.While the wheelset dynamics reflect the larger(>4-6 mm)aperiodic track disturbances and single large disturbances quite well,this does not seem to be the case for general smaller or periodic track irregularities or sections behind single large disturbances.The resulting dynamics of a wheelset to lateral track irregularities are in general not sufficiently accurate to be used as the basis for a description of the track irregularities.

Quasi-static and dynamical bending of a cantilever poroelastic beam

Based on the theory of porous media, the quasi-static and dynamical bending of a cantilever poroelastic beam subjected to a step load at its free end is investigated, and the influences of its permeability on bending deformation is examined. The initial boundary value problems for dynamical and quasi-static responses are solved with the Laplace transform technique, and the deflections, the bending moments of the solid skeleton and the equivalent couples of the pore fluid pressure are shown in figures. It is shown that the dynamical and quasi-static behavior of the saturated poroelastic beam depends closely on the permeability conditions at the beam ends. Under the different permeability conditions, the deflections of the beam may oscillate or not. The Mandel-Cryer effect also exists in liquid-saturated poroelastic beams.

The dynamical and thermodynamical analysis of the oceanic response to storm

In this paper, the discussion is made on the problem of the oceanic response caused by air-sea interaction under storm. First, the perturbation differential equations for the problem are given, and the interaction functions are supposed to be the solving conditions. Next, the nonlinear diffusion equations of the problem are solved by using the method of the given variable transforms and the specific variable power series. Finally, the response disturbances to the circular intense storm is calculated so as to discribe quantitatively the evolution processes of the oceanic response.

Impact resistance performance and optimization of the sand-EPE composite cushion in rock sheds

Rock sheds are widely used to prevent rockfall disasters along roads in mountainous areas.To improve the capacity of rock sheds for resisting rockfall impact,a sand and expandable polyethylene(EPE)composite cushion was proposed.A series of model experiments of rockfall impact on rock sheds were conducted,and the buried depth of the EPE foam board in the sand layer was considered.The impact load and dynamic response of the rock shed were investigated.The results show that the maximum impact load and dynamic response of the rock shed roof are all significantly less than those of the sand cushion.Moreover,as the distance between the EPE foam board and rock shed roof decreases,the maximum rockfall impact force and impact pressure gradually decrease,and the maximum displacement,acceleration and strain of the rock shed first decrease and then change little.In addition,the vibration acceleration and vertical displacement of the rock shed roof decrease from the centre to the edge and decrease faster along the longitudinal direction than that along the transverse direction.In conclusion,the buffering effect of the sand-EPE composite cushion is better than that of the pure sand cushion,and the EPE foam board at a depth of 1/3 the thickness of the sand layer is appropriate.

Dynamic response of honeycomb-FGS shells subjected to the dynamic loading using non-polynomial higher-order IGA

The main goal of this study is to use higher-order isogeometric analysis(IGA)to study the dynamic response of sandwich shells with an auxetic honeycomb core and two different functionally graded materials(FGM)skin layers(namely honeycomb-FGS shells)subjected to dynamic loading.Touratier's non-polynomial higher-order shear deformation theory(HSDT)is used due to its simplicity and performance.The governing equation is derived from Hamilton's principle.After verifying the present approach,the effect of input parameters on the dynamic response of honeycomb-FGS shells is carried out in detail.

Dynamic response of mountain tunnel,bridge,and embankment along the Sichuan-Tibet transportation corridor to active fault based on model tests

The Sichuan-Tibet transportation corridor is prone to numerous active faults and frequent strong earthquakes.While extensive studies have individually explored the effect of active faults and strong earthquakes on different engineering structures,their combined effect remains unclear.This research employed multiple physical model tests to investigate the dynamic response of various engineering structures,including tunnels,bridges,and embankments,under the simultaneous influence of cumulative earthquakes and stick-slip misalignment of an active fault.The prototype selected for this study was the Kanding No.2 tunnel,which crosses the Yunongxi fault zone within the Sichuan-Tibet transportation corridor.The results demonstrated that the tunnel,bridge,and embankment exhibited amplification in response to the input seismic wave,with the amplification effect gradually decreasing as the input peak ground acceleration(PGA)increased.The PGAs of different engineering structures were weakened by the fault rupture zone.Nevertheless,the misalignment of the active fault may decrease the overall stiffness of the engineering structure,leading to more severe damage,with a small contribution from seismic vibration.Additionally,the seismic vibration effect might be enlarged with the height of the engineering structure,and the tunnel is supposed to have a smaller PGA and lower dynamic earth pressure compared to bridges and embankments in strong earthquake zones crossing active faults.The findings contribute valuable insights for evaluating the dynamic response of various engineering structures crossing an active fault and provide an experimental reference for secure engineering design in the challenging conditions of the Sichuan-Tibet transportation corridor.

Dynamic response of a thermal transistor to time-varying signals

Thermal transistor,the thermal analog of an electronic transistor,is one of the most important thermal devices for microscopic-scale heat manipulating.It is a three-terminal device,and the heat current flowing through two terminals can be largely controlled by the temperature of the third one.Dynamic response plays an important role in the application of electric devices and also thermal devices,which represents the devices’ability to treat fast varying inputs.In this paper,we systematically study two typical dynamic responses of a thermal transistor,i.e.,the response to a step-function input(a switching process)and the response to a square-wave input.The role of the length L of the control segment is carefully studied.It is revealed that when L is increased,the performance of the thermal transistor worsens badly.Both the relaxation time for the former process and the cutoff frequency for the latter one follow the power-law dependence on L quite well,which agrees with our analytical expectation.However,the detailed power exponents deviate from the expected values noticeably.This implies the violation of the conventional assumptions that we adopt.

Micro defects formation and dynamic response analysis of steel plate of quasi-cracking area subjected to explosive load

As the protective component,steel plate had attracted extensive attention because of frequently threats of explosive loads.In this paper,the evolution of microstructure and the mechanism of damage in the quasi-cracking area of steel plate subjected to explosive load were discussed and the relationships between micro defects and dynamic mechanical response were revealed.After the explosion experiment,five observation points were selected equidistant from the quasi-cracking area of the section of the steel plate along the thickness direction,and the characteristics of micro defects at the observation points were analyzed by optical microscope(OM),scanning electron microscope(SEM) and electron backscattered diffraction(EBSD).The observation result shows that many slip bands(SBs) appeared,and the grain orientation changed obviously in the steel plate,the two were the main damage types of micro defects.In addition,cracks,peeling pits,grooves and other lager micro defects were appeared in the lower area of the plate.The stress parameters of the observation points were obtained through an effective numerical model.The mechanism of damage generation and crack propagation in the quasicracking area were clarified by comparing the specific impulse of each observation point with the corresponding micro defects.The result shows that the generation and expansion of micro defects are related to the stress area(i.e.the upper compression area,the neutral plane area,and the lower tension area).The micro defects gather and expand at the grain boundary,and will become macroscopic damage under the continuous action of tensile stress.Besides,the micro defects at the midpoint of the section of the steel plate in the direction away from the explosion center(i.e.the horizontal direction) were also studied.It was found that the specific impulse at these positions were much smaller than that in the thickness direction,the micro defects were only SBs and a few micro cracks,and the those decreased with the increase of the distance from the explosion center.

Dynamic Response of A Group of Cylindrical Storage Tanks with Baffles Considering the Effect of Soil Foundation

The sloshing in a group of rigid cylindrical tanks with baffles and on soil foundation under horizontal excitation is studied analytically.The solutions for the velocity potential are derived out by the liquid subdomain method.Equivalent models with mass-spring oscillators are established to replace continuous fluid.Combined with the least square technique,Chebyshev polynomials are employed to fit horizontal,rocking and horizontal-rocking coupling impedances of soil,respectively.A lumped parameter model for impedance is presented to describe the effects of soil on tank structures.A mechanical model for the soil-foundation-tank-liquid-baffle system with small amount of calculation and high accuracy is proposed using the substructure technique.The analytical solutions are in comparison with data from reported literature and numerical codes to validate the effectiveness and correctness of the model.Detailed dynamic properties and seismic responses of the soil-tank system are given for the baffle number,size and location as well as soil parameter.

Microscopic defects formation and dynamic mechanical response analysis of Q345 steel plate subjected to explosive load

As the basic protective element, steel plate had attracted world-wide attention because of frequent threats of explosive loads. This paper reports the relationships between microscopic defects of Q345 steel plate under the explosive load and its macroscopic dynamics simulation. Firstly, the defect characteristics of the steel plate were investigated by stereoscopic microscope(SM) and scanning electron microscope(SEM). At the macroscopic level, the defect was the formation of cave which was concentrated in the range of 0-3.0 cm from the explosion center, while at the microscopic level, the cavity and void formation were the typical damage characteristics. It also explains that the difference in defect morphology at different positions was the combining results of high temperature and high pressure. Secondly, the variation rules of mechanical properties of steel plate under explosive load were studied. The Arbitrary Lagrange-Euler(ALE) algorithm and multi-material fluid-structure coupling method were used to simulate the explosion process of steel plate. The accuracy of the method was verified by comparing the deformation of the simulation results with the experimental results, the pressure and stress at different positions on the surface of the steel plate were obtained. The simulation results indicated that the critical pressure causing the plate defects may be approximately 2.01 GPa. On this basis, it was found that the variation rules of surface pressure and microscopic defect area of the Q345 steel plate were strikingly similar, and the corresponding mathematical relationship between them was established. Compared with Monomolecular growth fitting models(MGFM) and Logistic fitting models(LFM), the relationship can be better expressed by cubic polynomial fitting model(CPFM). This paper illustrated that the explosive defect characteristics of metal plate at the microscopic level can be explored by analyzing its macroscopic dynamic mechanical response.

A novel algorithm for evaluating cement azimuthal density based on perturbation theory in horizontal well

Cement density monitoring plays a vital role in evaluating the quality of cementing projects,which is of great significance to the development of oil and gas.However,the presence of inhomogeneous cement distribution and casing eccentricity in horizontal wells often complicates the accurate evaluation of cement azimuthal density.In this regard,this paper proposes an algorithm to calculate the cement azimuthal density in horizontal wells using a multi-detector gamma-ray detection system.The spatial dynamic response functions are simulated to obtain the influence of cement density on gamma-ray counts by the perturbation theory,and the contribution of cement density in six sectors to the gamma-ray recorded by different detectors is obtained by integrating the spatial dynamic response functions.Combined with the relationship between gamma-ray counts and cement density,a multi-parameter calculation equation system is established,and the regularized Newton iteration method is employed to invert casing eccentricity and cement azimuthal density.This approach ensures the stability of the inversion process while simultaneously achieving an accuracy of 0.05 g/cm^(3) for the cement azimuthal density.This accuracy level is ten times higher compared to density accuracy calculated using calibration equations.Overall,this algorithm enhances the accuracy of cement azimuthal density evaluation,provides valuable technical support for the monitoring of cement azimuthal density in the oil and gas industry.

Loads and Dynamic Response Characteristic on FPSO Under Internal Solitary Waves

According to the established prediction model of internal solitary wave loads on FPSO in the previous work,the lumped mass model and the movement equations of finite displacement in time domain,the dynamic response model of interaction between internal solitary waves and FPSO with mooring lines were established.Through calculations and analysis,time histories of dynamic loads of FPSO exerted by internal solitary waves,FPSO’s motion and dynamic tension of mooring line were obtained.The effects of the horizontal pretension of mooring line,the amplitude of internal solitary wave and layer fluid depth on dynamic response behavior of FPSO were mastered.It was shown that the internal solitary waves had significant influence on FPSO,such as the large magnitude horizontal drift and a sudden tension increment.With internal solitary wave of −170 m amplitude in the ocean with upper and lower layer fluid depth ratio being 60:550,the dynamic loads reached 991.132 kN(horizontal force),18067.3 kN(vertical force)and−5042.92 kN·m(pitching moment).Maximum of FPSO’s horizontal drift was 117.56 m.Tension increment of upstream mooring line approached 401.48 kN and that of backflow mooring line was−140 kN.Moreover,the loads remained nearly constant with different pretension but increased obviously with the changing amplitude and layer fluid depth ratio.Tension increments of mooring lines also changed little with the pretension but increased rapidly when amplitude and layer fluid depth ratio increased.However,FPSO’s motion increased quickly with not only the horizontal pretension but also the amplitude of internal solitary wave and layer fluid depth ratio.

Dynamic Response of Foundations during Startup of High-Frequency Tunnel Equipment

The specialized equipment utilized in long-line tunnel engineering is evolving towards large-scale,multifunctional,and complex orientations.The vibration caused by the high-frequency units during regular operation is supported by the foundation of the units,and the magnitude of vibration and the operating frequency fluctuate in different engineering contexts,leading to variations in the dynamic response of the foundation.The high-frequency units yield significantly diverse outcomes under different startup conditions and times,resulting in failure to meet operational requirements,influencing the normal function of the tunnel,and causing harm to the foundation structure,personnel,and property in severe cases.This article formulates a finite element numerical computation model for solid elements using three-dimensional elastic body theory and integrates field measurements to substantiate and ascertain the crucial parameter configurations of the finite element model.By proposing a comprehensive startup timing function for high-frequency dynamic machines under different startup conditions,simulating the frequency andmagnitude variations during the startup process,and suggesting functions for changes in frequency and magnitude,a simulated startup schedule function for high-frequency machines is created through coupling.Taking into account the selection of the transient dynamic analysis step length,the dynamic response results for the lower dynamic foundation during its fundamental frequency crossing process are obtained.The validation checks if the structural magnitude surpasses the safety threshold during the critical phase of unit startup traversing the structural resonance region.The design recommendations for high-frequency units’dynamic foundations are provided,taking into account the startup process of the machine and ensuring the safe operation of the tunnel.

Dynamic response of buildings under debris flow impact

This study employs the smoothed particle hydrodynamics–finite element method(SPH–FEM) coupling numerical method to investigate the impact of debris flow on reinforced concrete(RC)-frame buildings. The methodology considers the variables of debris flow depth and velocity and introduces the intensity index IDV(IDV = DV) to evaluate three different levels of debris flow impact intensity. The primary focus of this study is to investigate the dynamic response and failure mechanism of RC-frame buildings under debris flow impact, including structural failure patterns, impact force and column displacement. The results show that under a highintensity impact, a gradual collapse process of the RCframe building can be observed, and the damage mode of the frame column reflects shear failure or plastic hinge failure mechanism. First, the longitudinal infill walls are damaged owing to their low out-of-plane flexural capacity;the critical failure intensity index IDV value is approximately 7.5 m2/s. The structure cannot withstand debris flows with an intensity index IDV greater than 16 m2/s, and it is recommended that the peak impact force should not exceed 2100 k N. The impact damage ability of debris flow on buildings mostly originates from the impact force of the frontal debris flow, with the impact force of the debris flow body being approximately 42% lower than that of the debris flow head. Finally, a five-level classification system for evaluating the damage status of buildings is proposed based on the numerical simulation and investigation results of the disaster site.

Dynamic thermo-mechanical responses of road-soft ground system under vehicle load and daily temperature variation

A complete road-soft ground model is established in this paper to study the dynamic responses caused by vehicle loads and/or daily temperature variation.A dynamic thermo-elastic model is applied to capturing the behavior of the rigid pavement,the base course,and the subgrade,while the soft ground is characterized using a dynamic thermo-poroelastic model.Solutions to the road-soft ground system are derived in the Laplace-Hankel transform domain.The time domain solutions are obtained using an integration approach.The temperature,thermal stress,pore water pressure,and displacement responses caused by the vehicle load and the daily temperature variation are presented.Results show that obvious temperature change mainly exists within 0.3 m of the road when subjected to the daily temperature variation,whereas the stress responses can still be found in deeper places because of the thermal swelling/shrinkage deformation within the upper road structures.Moreover,it is important to consider the coupling effects of the vehicle load and the daily temperature variation when calculating the dynamic responses inside the road-soft ground system.