We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was ...We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.展开更多
A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at roo...A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.展开更多
基金supported by the European Union’s Horizon 2020 Research and Innovation Programme under the Marie Sklodowska-Curie Grant Agreement(823731CONMECH)supported by National Natural Science Foundation of China(11671101),supported by National Natural Science Foundation of China(11961074)+2 种基金Guangxi Natural Science Foundation(2021GXNSFAA075022)Project of Guangxi Education Department(2020KY16017)Yulin normal university of scientific research fund for high-level talents(G2019ZK39,G2021ZK06)。
文摘We consider a differential variational-hemivariational inequality with constraints,in the framework of reflexive Banach spaces.The existence of a unique mild solution of the inequality,together with its stability,was proved in[1].Here,we complete these results with existence,uniqueness and convergence results for an associated penalty-type method.To this end,we construct a sequence of perturbed differential variational-hemivariational inequalities governed by perturbed sets of constraints and penalty coefficients.We prove the unique solvability of each perturbed inequality as well as the convergence of its solution to the solution of the original inequality.Then,we consider a mathematical model which describes the equilibrium of a viscoelastic rod in unilateral contact.The weak formulation of the model is in a form of a differential variational-hemivariational inequality in which the unknowns are the displacement field and the history of the deformation.We apply our abstract penalty method in the study of this inequality and provide the corresponding mechanical interpretations.
基金supported by the Fundamental Research Funds of China for the Central Universities(GK201001008)
文摘A method to identify complex Young＇s modulus of viscoelastic materials using forced longitudinal vibration of slender rods is proposed. The method differs from the beam one. Experimental tests were carried out at room temperature with different lengths in 108 mm, 100 mm, 90 ram, 83.5 mm, 80 ram, 74.5 mm, 70 mm for the polycarbonate bars, and the curves of ratios A2/A1 between two ends of a viscoelastic bar versus frequencies are obtained, furthermore, the corresponding 3 dB bandwidth and the storage and loss modulus can be calculated. Sufficient number of obtained complex Young＇s modulus at different frequency allows us to calculate other ones using the least square method. If the step of the tested frequency is 5 Hz, the maximum error of results can be less than 6%. By comparison with the measurement methods which the previous literature mentioned, this new method simplifies the calculation, and the physical meaning appears apparently and clearly.
