Numerical modeling of thermopiezoelectricity steady state forced vibrations problem using adaptive Finite Element Method

Stelmashchuk, Vitaliy; Shynkarenko, H. А.

doi:10.1201/b20057-117

Cited by 1 publication

(4 citation statements)

References 2 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now substituting the estimates (21) and (22) into energy equation (14) and applying the Gronwall's lemma [7] we finally come to the following statements.…”

Section: -4mentioning

confidence: 99%

“…10 s for gases to 14 10 s for metals. Therefore, in our numerical experiment, we will take the "relaxation time"…”

Section: Finite Element Semi-discretizationmentioning

confidence: 99%

“…More details about physical and mechanical properties of piezoelectric and pyroelectric materials you can find in [5,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Setting 0 0 t in equation (4) eliminates heat flux q from the set of independent variables and we come to the equations of the classic thermopiezoelectricity problem [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Numerical solution of Lord-Shulman thermopiezoelectricity dynamical problem

Stelmashchuk

Shynkarenko

2018

AIP Conference Proceedings

View full text Add to dashboard Cite

Abstract. Using Lord-Shulman hypothesis we formulate the initial boundary value problem and its corresponding variational problem of a generalized linear thermopiezoelectricity in terms of the displacement, electrical potential, temperature increment and heat flux, which describes the dynamic behavior of the coupled mechanic, electric and heat waves in pyroelectric materials. We construct the corresponding energy balance equation and determine input data regularity for the variational problem, which guarantees the existence, uniqueness and stability of its solution in the problem energy norm. Based on these results, we propose a numerical scheme for solving this problem, which includes spatial finite element semi-discretization and one-step recurrent time integration procedures and generalizes the similar one for classic thermopiezoelectricity problem. We give the sufficient conditions on the values of the scheme parameters which guarantee properties of conservatism and unconditional stability of the scheme. The rest of the article is devoted to the analysis of performed numerical experiments with 1D model problem and their results are then compared with the ones obtained by the other researchers.

show abstract

“…Now substituting the estimates (21) and (22) into energy equation (14) and applying the Gronwall's lemma [7] we finally come to the following statements.…”

Section: -4mentioning

confidence: 99%

“…10 s for gases to 14 10 s for metals. Therefore, in our numerical experiment, we will take the "relaxation time"…”

Section: Finite Element Semi-discretizationmentioning

confidence: 99%

“…More details about physical and mechanical properties of piezoelectric and pyroelectric materials you can find in [5,12,13,14].…”

Section: Introductionmentioning

confidence: 99%

“…Setting 0 0 t in equation (4) eliminates heat flux q from the set of independent variables and we come to the equations of the classic thermopiezoelectricity problem [12,13,14].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations