Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

Pinnola, Francesco Paolo; Barretta, Raffaele; Sciarra, Francesco Marotti de; Pirrotta, Antonina

doi:10.3390/math10030477

Cited by 13 publications

(5 citation statements)

References 46 publications

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“…The most basic models include the Maxwell model ( Figure 7 a) and the Kelvin model ( Figure 7 b), and then a series of more accurate constitutive models such as the viscoelastic fractional derivative model (VFD) ( Figure 7 c), and the integral constitutive relationship has been formed [ 47 , 48 , 49 , 50 , 51 ].…”

Section: Finite Element Simulation Analysis Of Htpb Propellantsmentioning

confidence: 99%

Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

Cao

et al. 2022

Polymers

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As a typical viscoelastic material, solid propellants have a large difference in mechanical properties under static and dynamic loading. This variability is manifested in the difference in values of the relaxation modulus and dynamic modulus, which serve as the entry point for studying the dynamic and static mechanical properties of propellants. The relaxation modulus and dynamic modulus have a clear integral relationship in theory, but their consistency in engineering practice has never been verified. In this paper, by introducing the “catch-up factor λ” and “waiting factor γ”, a method for the inter-conversion of the dynamic storage modulus and relaxation modulus of HTPB propellant is established, and the consistency between them is verified. The results show that the time region of the calculated conversion values of the relaxation modulus obtained by this method covers 10−8–104 s, spanning twelve orders of magnitude. Compared to that of the relaxation modulus (10−4–104 s, spanning eight orders of magnitude), an expansion of four orders of magnitude is achieved. This enhances the expression ability of the relaxation modulus on the mechanical properties of the propellant. Furthermore, when the conversion method is applied to the dynamic–static modulus conversion of the other two HTPB propellants, the results show that the correlation coefficient between the calculated and measured conversion values is R2 > 0.933. This proves the applicability of this method to the dynamic–static modulus conversion of other types of HTPB propellants. It was also found that λ and γ have the same universal optimal value for different HTPB propellants. As a bridge for static and dynamic modulus conversion, this method greatly expands the expression ability of the relaxation modulus and dynamic storage modulus on the mechanical properties of the HTPB propellant, which is of great significance in the research into the mechanical properties of the propellant.

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Section: Finite Element Simulation Analysis Of Htpb Propellantsmentioning

confidence: 99%

Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

Cao

et al. 2022

Polymers

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“…Hosseini-Hashemi et al [23] delved into the vibration frequency of an FGV cylindrical plate based on the Zener model and discussed the factors affecting the dynamic characteristics of the model. Based on Timoshenko beam theory, Pinnola et al [24] derived the differential equations of motion of fractional derivative viscoelastic microbeams and analyzed the effects of nonlocal parameters and viscoelasticity on the vibration response of the system. Fu et al [25] studied the vibration characteristics of a viscoelastic axially functionally graded material pipe, wherein the fluid is considered to undergo a pulsating internal flow, and analyzed the influence of material characteristics on the nonlinear dynamic characteristics of the system.…”

Section: Introductionmentioning

confidence: 99%

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Ma,

Wang

2024

Mathematics

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In this study, the Kevin–Voigt viscoelastic constitutive relationship is used to investigate the vibration characteristics and stability of a functionally graded viscoelastic(FGV) fluid-conveying pipe with initial geometric defects under thermal–magnetic coupling fields. First, the nonlinear dimensionless differential equations of motion are derived by applying Timoshenko beam theory. Second, by solving the equilibrium position of the system, the nonlinear term in the differential equations of motion is approximated as the sum of the longitudinal displacement at the current time and longitudinal displacement relative to the position, and the equations are linearized. Third, these equations are discretized using the Galerkin method and are numerically solved under simply supported conditions. Finally, the effects of dimensionless temperature field parameters, dimensionless magnetic field parameters, thermal–magnetic coupling, initial geometric defect types, and the power-law exponent on the complex frequency of the pipe are examined. Results show that increasing the magnetic field intensity enhances the critical velocity of first-order mode instability, whereas a heightened temperature variation reduces the critical velocity of first-order diverge instability. Under thermal–magnetic fields, when the magnetic field intensity and temperature difference are simultaneously increased, their effects on the complex frequency can partially offset each other. Increasing the initial geometric defect amplitude increases the imaginary parts of the complex frequencies; however, for different types of initial geometric defect tubes, it exhibits the most distinct influence only on a certain order.

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“…This effectively introduces a notion of nonlocal interaction and hence an internal length scale in the analysis. This effectively invalidates the local hypothesis of the CCM [50], and emphasises the need to develop a nonlocal viscoelastic modelling framework that will incorporate size dependent length scale parameter.…”

Section: Introductionmentioning

confidence: 99%

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Galadima

Oterkus

Öterkuş

et al. 2023

Engineering with Computers

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This paper proposes a framework for implementing viscoelastic constitutive model from the classical continuum mechanics (CCM) theory within non-ordinary state-based peridynamics (NOSBPD). The motivation stems from the inadequacy of CCM to model very complex material behaviours such as initiation and propagation of cracks and nonlocal behaviour due to size effects. The proposed formulation leverages on the constitutive correspondence between NOSBPD and CCM to incorporate a CCM viscoelastic constitutive model based on hereditary integral into NOSBPD. The combination of hereditary constitutive model and NOSBPD effectively makes this formulation a nonlocal time–space viscoelastic framework where temporal nonlocality is incorporated by a hereditary viscoelastic model which stipulates that the behaviour of a material at any point in time depends on both the present action and the complete history of previous actions on the material, and spatial nonlocality on the other hand is incorporated via the nonlocal mechanism provided by the NOSBPD. For model validation, three benchmark problems were solved using the proposed framework. Results obtained were compared to results from analytical solution and solutions from referenced literature. In addition, parametric study was conducted to determine the influence of nonlocality on numerical prediction. Conclusions drawn from the validation studies presented are that the proposed framework is able to predict viscoelastic responses that agree well with local macro models as well as nonlocal micromodels/nanomodels as reported in the literature.

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Analytical Solutions of Viscoelastic Nonlocal Timoshenko Beams

Cited by 13 publications

References 46 publications

Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

Numerical Conversion Method for the Dynamic Storage Modulus and Relaxation Modulus of Hydroxy-Terminated Polybutadiene (HTPB) Propellants

Vibration Characteristics of a Functionally Graded Viscoelastic Fluid-Conveying Pipe with Initial Geometric Defects under Thermal–Magnetic Coupling Fields

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

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