Vibration and deflection analysis of thin cracked and submerged orthotropic plate under thermal environment using strain gradient theory

  • Shashank Soni
  • N. K. Jain
  • P. V. JoshiEmail author
Original Paper


Based on a non-classical plate theory, a nonlinear analytical model is proposed to analyze transverse vibration of thin partially cracked and submerged orthotropic plate in the presence of thermal environment. The governing equation for the cracked plate is derived using the Kirchhoff’s thin plate theory in conjunction with the strain gradient theory of elasticity. The effect of centrally located surface crack is deduced using appropriate crack compliance coefficients based on the simplified line spring model, whereas the effect of thermal environment is introduced using moments and in-plane forces. The influence of fluidic medium is incorporated in the governing equation in the form of fluid forces associated with its inertial effects. The equation has been solved by transforming the lateral deflection in terms of modal functions. The shift in primary resonance due to crack, length scale parameter and temperature has also been derived with central deflection. To demonstrate the accuracy of the present model, a few comparison studies are carried out with the published literature. The variation in fundamental frequency of the cracked plate is studied considering various parameters such as crack length, plate thickness, level of submergence, temperature and length scale parameter. It has been concluded that the frequency is affected by crack length, temperature and level of submergence. A comparison has also been made for the results obtained from the classical plate theory and Strain gradient theory. Furthermore, the variation in frequency response and peak amplitude of the cracked plate is studied using method of multiple scales to show the phenomenon of bending hardening or softening as affected by level of submergence, temperature, crack length and length scale parameter .


Vibration Crack Temperature Fluid–structure interaction Virtual added mass 



This research work is not funded by any organization.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Mechanical Engineering DepartmentNational Institute of TechnologyRaipurIndia
  2. 2.Department of Basic Sciences and EngineeringIndian Institute of Information TechnologyNagpurIndia

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