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Nonlocal stress gradient formulation for damping vibration analysis of viscoelastic microbeam in thermal environment

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Applied Mathematics and Mechanics(English Edition) 2023年第5期44卷 773-786页

作者： Hai QING Huidiao SONG State Key Laboratory of Mechanics and Control for Aerospace Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China

An integral nonlocal stress gradient viscoelastic model is proposed on the basis of the integral nonlocal stress gradient model and the standard viscoelastic model,and is utilized to investigate the free damping vibration analysis of the viscoelastic BernoulliEuler microbeams in thermal ***'s principle is used to derive the differential governing equations and corresponding boundary *** integral relations between the strain and the nonlocal stress are converted into a differential form with constitutive *** size-dependent axial thermal stress due to the variation of the environmental temperature is derived *** Laplace transformation is utilized to obtain the explicit expression for the bending deflection and *** the boundary conditions and constitutive constraints,one can get a nonlinear equation with complex coefficients,from which the complex characteristic frequency can be determined.A two-step numerical method is proposed to solve the elastic vibration frequency and the damping *** effects of length scale parameters,viscous coefficient,thermal stress,vibration order on the vibration frequencies,and critical viscous coefficient are investigated numerically for the viscoelastic Bernoulli-Euler microbeams under different boundary conditions.

关键词： damping vibration size effect integral nonlocal stress gradient model standard viscoelastic model Laplace transformation

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Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation

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Applied Mathematics and Mechanics(English Edition) 2023年第1期44卷 89-108页

作者： Pei ZHANG P.SCHIAVONE Hai QING State Key Laboratory of Mechanics and Control of Mechanical Structures Nanjing University of Aeronautics and AstronauticsNanjing 210016China Department of Mechanical Engineering University of AlbertaEdmontonAlberta T6G 1H9Canada

A nonlocal study of the vibration responses of functionally graded(FG)beams supported by a viscoelastic Winkler-Pasternak foundation is *** damping responses of both the Winkler and Pasternak layers of the foundation are considered in the formulation,which were not considered in most literature on this subject,and the bending deformation of the beams and the elastic and damping responses of the foundation as nonlocal by uniting the equivalently differential formulation of well-posed strain-driven(ε-D)and stress-driven(σ-D)two-phase local/nonlocal integral models with constitutive constraints are comprehensively considered,which can address both the stiffness softening and toughing effects due to scale *** generalized differential quadrature method(GDQM)is used to solve the complex eigenvalue *** verifying the solution procedure,a series of benchmark results for the vibration frequency of different bounded FG beams supported by the foundation are ***,the effects of the nonlocality of the foundation on the undamped/damping vibration frequency of the beams are examined.

关键词： two-phase nonlocal elasticity damping vibration functionally graded(FG)beam nonlocal viscoelastic Winkler-Pasternak foundation generalized differential quadrature method(GDQM)

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