The general problem of thermoelastic waves in anisotropic periodically laminated composites

Hawwa, Muhammad A.; Nayfeh, Adnan H.

doi:10.1016/0961-9526(95)00087-4

Cited by 22 publications

(13 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The material used in this study is orthotropic and are considered from Hawwa and Nayfeh (1995). Numerical examples demonstrate dispersion curves and characteristic curves in the lamina and laminate (Figures 1, 2, 3 and 4).…”

Section: Resultsmentioning

confidence: 99%

“…Nayfeh and Chementi (1991) developed a transfer matrix technique to obtain the dispersion relation curves of elastic wave propagating in multilayered anisotropic media, i.e., composite laminate. However, Nayfeh's formulations in elasticity Chementi 1989, 1991;Jones 1975Jones , 1999Liu et al 1990) and in thermoelasticity (Hawwa and Nayfeh 1995) were limited to a given plane of incidence from a line load parallel to the y-axis such that the problem reduces to a generalized plane deformation where all the three displacement components are functions of x and z. Verma (2012) studied thermoelastic waves in anisotropic laminated composite plates. Yuan (2005, 2006) studied damage identification in a composite plate using prestack reverse-time and propagation of lamb wave in composite laminates experimentally.…”

Section: Introductionmentioning

confidence: 99%

“…Achenbach (1973), Banerjee and Pao (1974), and Dhaliwal and Sherief (1980) generalized these theories further to anisotropic heat conducting elastic materials. Hawwa and Nayfeh (1995) studied the general problem of thermoelastic waves in anisotropic periodically laminated composites. Studies of Hawwa and Nayfeh (1996), Thangjitham and Choi (1991), and Tao and Prevost (1984) contain more detailed discussions on this phenomenon.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

Verma

2014

Int J Mech Mater Eng

View full text Add to dashboard Cite

Background: Coupling term in coupled thermoelasticity generally is small for all materials and can be neglected. Neglecting the coupling term simplifies the analysis without noticeable effect on the frequency spectrum. In generalized theory of thermoelasticity, effect of increasing the relaxation time is to lower the speeds of the thermal modes. Since the effect of anisotropy of the material is quite pronounced on waves propagating in different directions along the plate. Thus, it is significant to consider the anisotropy of the material in order to accurately model the propagation characteristics. Methods: A theoretical framework is developed for displacements and temperature expression of plane harmonic waves in generalized theory of thermoelasticity using three dimensional thermoelasticity with a thermal relaxation time. Subsequently, the Lamb waves in a single lamina where a compact closed-form dispersion relation is derived by separating thermoelastic symmetric and anti-symmetrical modes using trigonometric functions through the lamina thickness. Results: Propagation of guided thermoelastic waves in a homogeneous, orthotropic, thermally conducting plate is investigated within the framework of the generalized theory of thermoelasticity. The results show that both elastic and thermal modes are attenuated, the thermal modes exhibit much larger attenuation than the elastic modes. The attenuation of the former is quite small. Results obtained are extended to a general laminate with an arbitrary layup. On employing boundary conditions on both mid-plane and top surfaces is developed to decouple the wave modes for symmetric and anti-symmetrical modes for laminates. Conclusions: Propagation of guided thermoelastic waves in a homogeneous, orthotropic, thermally conducting plate is investigated employing generalized theory of thermoelasticity which includes a thermal relaxation time in the heat conduction equation in order to model the finite speed of the thermal wave. Both elastic and thermal modes are attenuated; the thermal modes exhibit much larger attenuation than the elastic modes. The effect of increasing the relaxation time is to lower the speeds of the thermal modes. The effect of anisotropy of the material is quite pronounced on waves propagating in different directions. Thus, it is important to consider the anisotropy of the material in order to accurately model the propagation characteristics.

show abstract

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

Verma

2014

Int J Mech Mater Eng

View full text Add to dashboard Cite

show abstract

“…to solve it as an analytic function by considering representative orthotropic (fictitious) material given in [12] with the following properties: second .…”

Section: Numerical Results and Discussionmentioning

confidence: 99%

“…A thermoelastic problem is studied in [24], considering equations for anisotropic heat conducting solids with thermal relaxation time. Hawwa and Nayfeh [12] studied the general problem of thermoelastic waves in anisotropic periodically laminated composites. In [26,27], wave propagation in plates of general anisotropic media for generalized thermoelasticity is studied.…”

Section: Introductionmentioning

confidence: 99%

On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

Verma¹,

Hasebe

2004

Journal of Applied Mathematics

View full text Add to dashboard Cite

Analysis for the propagation of plane harmonic thermoelastic waves in an infinite homogeneous orthotropic plate of finite thickness in the generalized theory of thermoelasticity with two thermal relaxation times is studied. The frequency equations corresponding to the extensional (symmetric) and flexural (antisymmetric) thermoelastic modes of vibration are obtained and discussed. Special cases of the frequency equations are also discussed. Numerical solution of the frequency equations for orthotropic plate is carried out, and the dispersion curves for the first six modes are presented for a representative orthotropic plate. The three motions, namely, longitudinal, transverse, and thermal, of the medium are found dispersive and coupled with each other due to the thermal and anisotropic effects. The phase velocity of the waves gets modified due to the thermal and anisotropic effects and is also influenced by the thermal relaxation time. Relevant results of previous investigations are deduced as special cases.

show abstract

Wave propagation in transversely isotropic plates in generalized thermoelasticity

Verma¹,

Hasebe²

2002

Archive of Applied Mechanics (Ingenieur Archiv)

View full text Add to dashboard Cite

In this paper, the boundary value problem in generalized thermoelasticity concerning the propagation of plane harmonic waves in a thin, flat, infinite homogeneous, transversely isotropic plate of finite width is solved. The frequency equations corresponding to the symmetric and antisymmetric modes of vibration of the plate are obtained. The limiting and special cases of the frequency equations have also been discussed. Finally, a numerical solution of the frequency equations for a NaF crystal is carried out, and the dispersion curves for the lowest six modes of the symmetric and antisymmetric vibrations are represented graphically at different values of thermal relaxation time.

show abstract

The general problem of thermoelastic waves in anisotropic periodically laminated composites

Cited by 22 publications

References 22 publications

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

Thermoelastic symmetric and antisymmetric wave modes with trigonometric functions in laminated plates

On the flexural and extensional thermoelastic waves in orthotropic plates with two thermal relaxation times

Wave propagation in transversely isotropic plates in generalized thermoelasticity

Contact Info

Product

Resources

About