Propagation and attenuation of guided waves in stressed viscoelastic waveguides

Li, Chunlei; Han, Qiang; Wang, Zhan; Liu, Yijie

doi:10.1177/1081286519861823

Cited by 10 publications

(3 citation statements)

References 32 publications

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“…Consequently, in addition to their actuation and sensing properties, which are crucial in many industrial applications that involve sensors, these materials have acquired tremendous interest due to their damping capability and are widely used as elastic filters, noise reduction controllers, acoustic filters, vibration shields, and so on. Several very recent papers are related to the acoustoelasticity [23] and thermoelasticity [24–27] properties of these materials, their mathematical models via fractional derivatives, and various industrial applications. Some of these applications point to far-reaching possibilities even in the field of biomechanics engaging production and testing of dental filling composites [28], optimizing pharmacokinetics [29], studying the blood flow through arteries [30], and exploring the kinetics of ligaments and muscle-tendon units [31].…”

Section: Introductionmentioning

confidence: 99%

Stochastic Zener model with complex order fractional derivatives

Atanacković

Pilipović

Seleši

2022

Mathematics and Mechanics of Solids

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We analyze the dissipation inequality for the constitutive equation of a complex order fractional Zener model and obtain appropriate thermodynamical restrictions for the wave-type model equation in terms of its Laplace transform. These constraints obtained on the model parameters are less restrictive than the ones known in the previous literature. The main results of this paper are related to explicitly solving this equation in spaces of tempered distributions, proving the existence and uniqueness of the solution and discussing its regularity properties. The second set of results is related to the analysis of including random perturbations such as white noise in the model resulting in stochastic wave propagation models. We analyze various stochastic body forces, random initial excitations, and random initial velocities as input data followed by deriving the stochastic solution and calculating its most important statistical characteristics. All these results significantly extend our previous results related to a real order fractional Zener model. MSC[2020]: 26A33, 35L05, 35R11, 35R60, 60G10, 60G15, 74D05, 74J05, 82D30

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Section: Introductionmentioning

confidence: 99%

Stochastic Zener model with complex order fractional derivatives

Atanacković

Pilipović

Seleši

2022

Mathematics and Mechanics of Solids

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“…The research on the multimode characteristics and dispersion relationship of guided waves has been a hot topic. Predoi [1] and Li et al [2] investigated the longitudinal guided wave in hollow cylinders by the finite element method. It must be noted that the longitudinal guided wave is suitable to detect of the circumferential defect for that its displacement vibration direction is mainly on axial direction.…”

Section: Introductionmentioning

confidence: 99%

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates

Wang

et al. 2020

Z Angew Math Mech

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An improved Legendre polynomial series approach (AILPSA) is presented to investigate the circumferential thermoelastic Lamb wave in a fractional order orthotropic cylindrical plate. In the AILPSA, the analytical integration is developed based on the orthogonality and recursive properties of the Legendre polynomial to simplify the integral computation involved in the solving progress. As a consequence, the computational efficiency is improved significantly. Results are compared with those from the previous article to confirm the validity of the introduced method. Using the AILPSA, guided wave characteristics in various fractional order orthotropic cylindrical plates are investigated by solving the eigenvalues and eigenvectors of the system of algebraic equations. The influences of fractional order and radius‐thickness ratio on dispersion curve and displacement, temperature amplitudes are illustrated. The results show that the fractional order almost has no effect on the phase velocities of quasi‐elastic wave modes, but has notable effect on their attenuations. A smaller fractional order means a smaller temperature amplitude for the quasi‐elastic wave mode, but means a larger temperature amplitude for the thermal wave mode. A smaller radius thickness ratio indicates a smaller attenuation and a larger temperature amplitude.

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“…Nowadays, there is a strong trend toward using functionally graded materials [4, 5]. They are mainly used to achieve a high strength-to-weight ratio.…”

Section: Introductionmentioning

confidence: 99%

Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints

Sindi

Othman

Almitani

2020

Mathematics and Mechanics of Solids

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Adhesively bonded joints have widely been used in a number of engineering applications, owing to their improved mechanical performance as compared with other mechanical joining techniques, such as rivets or bolts. In this study, a theoretical solution of double-lap joints is established, with functionally graded adhesive and isotopic adherends, under harmonic loads. Assuming a parabolic distribution of the adhesive shear modulus along the overlap length, the analytical harmonic solution is expressed in terms of the solution of the nonlinear Heun differential equation. Furthermore, a two-dimensional finite-element model was developed to validate the analytical solution. We show that using softer adhesive at the edges of the bond line leads to less stress concentration. We also conclude that the adhesive’s shear modulus gradient along the bond line should be greater as the ratio of the adhesive’s shear stiffness to the adherends’ shear stiffness increases. An equation has also been established to determine the optimal shear modulus gradient in terms of the stiffness ratio.

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Propagation and attenuation of guided waves in stressed viscoelastic waveguides

Cited by 10 publications

References 32 publications

Stochastic Zener model with complex order fractional derivatives

Stochastic Zener model with complex order fractional derivatives

Circumferential thermoelastic Lamb wave in fractional order cylindrical plates

Theoretical solution for the axial vibration of functionally graded double-lap adhesive joints

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