The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are...The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the effects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial dif- ferential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge-Kutta method. Moreover, the effects of different truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.展开更多
For neural network potentials(NNPs)to gain widespread use,researchers must be able to trust model outputs.However,the blackbox nature of neural networks and their inherent stochasticity are often deterrents,especially...For neural network potentials(NNPs)to gain widespread use,researchers must be able to trust model outputs.However,the blackbox nature of neural networks and their inherent stochasticity are often deterrents,especially for foundationmodels trained over broad swaths of chemical space.Uncertainty information provided at the time of prediction can help reduce aversion to NNPs.In this work,we detail two uncertainty quantification(UQ)methods.Readout ensembling,by finetuning the readout layers of an ensemble of foundation models,provides information about model uncertainty,while quantile regression,by replacing point predictions with distributional predictions,provides information about uncertainty within the underlying training data.We demonstrate our approach with the MACE-MP-0 model,applying UQ to the foundation model and a series of finetuned models.The uncertainties produced by the readout ensemble and quantile methods are demonstrated to be distinct measures by which the quality of the NNP output can be judged.展开更多
This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived u...This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.展开更多
基金supported by the State Key Program of National Natural Science Foundation of China (10932006 and 11232009)Innovation Program of Shanghai Municipal Education Commission (12YZ028)
文摘The present paper investigates the dynamic response of finite Timoshenko beams resting on a sixparameter foundation subjected to a moving load. It is for the first time that the Galerkin method and its convergence are studied for the response of a Timoshenko beam supported by a nonlinear foundation. The nonlinear Pasternak foundation is assumed to be cubic. Therefore, the effects of the shear deformable beams and the shear deformation of foundations are considered at the same time. The Galerkin method is utilized for discretizing the nonlinear partial dif- ferential governing equations of the forced vibration. The dynamic responses of Timoshenko beams are determined via the fourth-order Runge-Kutta method. Moreover, the effects of different truncation terms on the dynamic responses of a Timoshenko beam resting on a complex foundation are discussed. The numerical investigations shows that the dynamic response of Timoshenko beams supported by elastic foundations needs super high-order modes. Furthermore, the system parameters are compared to determine the dependence of the convergences of the Galerkin method.
基金supported by the"Transferring exascale computational chemistry to cloud computing environment and emerging hardware technologies(TEC4)"project,which is funded by the U.S.Department of Energy,Office of Science,Office of Basic Energy Sciences,the Division of Chemical Sciences,Geosciences,and Biosciences(under FWP 82037)supported by the U.S.Department of Energy(DOE),Office of Science,Office of Basic Energy Sciences,Division of Chemical Sciences,Geosciences&Biosciences(under FWP 47319)Pacific Northwest National Laboratory(PNNL)is a multiprogram national laboratory operated for the U.S.Department of Energy(DOE)by Battelle Memorial Institute under Contract No.DE-AC05-76RL0-1830.
文摘For neural network potentials(NNPs)to gain widespread use,researchers must be able to trust model outputs.However,the blackbox nature of neural networks and their inherent stochasticity are often deterrents,especially for foundationmodels trained over broad swaths of chemical space.Uncertainty information provided at the time of prediction can help reduce aversion to NNPs.In this work,we detail two uncertainty quantification(UQ)methods.Readout ensembling,by finetuning the readout layers of an ensemble of foundation models,provides information about model uncertainty,while quantile regression,by replacing point predictions with distributional predictions,provides information about uncertainty within the underlying training data.We demonstrate our approach with the MACE-MP-0 model,applying UQ to the foundation model and a series of finetuned models.The uncertainties produced by the readout ensemble and quantile methods are demonstrated to be distinct measures by which the quality of the NNP output can be judged.
文摘This paper deals with the free vibration analysis of circular alumina （Al2O3） nanobeams in the presence of surface and thermal effects resting on a Pasternak foun- dation. The system of motion equations is derived using Hamilton＇s principle under the assumptions of the classical Timoshenko beam theory. The effects of the transverse shear deformation and rotary inertia are also considered within the framework of the mentioned theory. The separation of variables approach is employed to discretize the governing equa- tions which are then solved by an analytical method to obtain the natural frequencies of the alumina nanobeams. The results show that the surface effects lead to an increase in the natural frequency of nanobeams as compared with the classical Timoshenko beam model. In addition, for nanobeams with large diameters, the surface effects may increase the natural frequencies by increasing the thermal effects. Moreover, with regard to the Pasternak elastic foundation, the natural frequencies are increased slightly. The results of the present model are compared with the literature, showing that the present model can capture correctly the surface effects in thermal vibration of nanobeams.
