caa a22 4500 445811463 CHVBK 20180317145213.0 cr unu---uuuuu 170323e20110901xx s 000 0 eng 10.1007/s00419-010-0488-6 doi (NATIONALLICENCE)springer-10.1007/s00419-010-0488-6 Frequency equations for the in-plane vibration of orthotropic circular annular plate [Elektronische Daten] [M. Karamooz Ravari, M. Forouzan] Orthotropic circular annular plates have a lot of applications in engineering such as space structures and rotary machines. In this paper, frequency equations for the in-plane vibration of the orthotropic circular annular plate for general boundary conditions were derived. To obtain the frequency equation, first the equation of motion for the circular annular plate in the cylindrical coordinate is derived by using the stress-strain- displacement expressions. Helmholtz decomposition is used to uncouple the equations of motion. The wave equation is obtained by assumption a harmonic solution for the uncoupled equations. Using the separation of the variables leads to the general wave equation solution and the in-plane displacements in the r and θ directions. Finally, boundary conditions are exerted and the natural frequency is derived for general boundary conditions. The obtained results are validated by comparing with the previously reported and those from finite element analysis. Springer-Verlag, 2010 In-plane nationallicence Vibration nationallicence Orthotropic material nationallicence Frequency equation nationallicence General boundary condition nationallicence R : Outer radius nationallicence R 0 : Inner radius nationallicence ξ : Dimensionless coordinates r/R nationallicence η : Radius ratio R 0/R nationallicence ρ : Density nationallicence E r , E θ : Youngs moduli related to the r and θ directions, respectively nationallicence ν r , ν θ : Poisson ratios related to r and θ directions, respectively nationallicence G : Modulus of elasticity in shear nationallicence b : Stiffness ratio E θ /E r nationallicence g : Dimensionless shear modulus defined in text nationallicence t : Time nationallicence σ r , σ θ : Normal stress in r and θ direction respectively nationallicence τ r θ : shear stress nationallicence ε r , ε θ : Normal strain in r and θ direction respectively nationallicence γ r θ : Shear strain nationallicence u , v : Displacements in r and θ directions, respectively nationallicence $${\varphi, {\bf H}}$$ : Scalar and vector potentials nationallicence Ω : Non-dimensional natural frequencies defined in text nationallicence $${\nabla}$$ : Gradient operator nationallicence Karamooz Ravari M. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut Forouzan M. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut Archive of Applied Mechanics Springer-Verlag 81/9(2011-09-01), 1307-1322 0939-1533 81:9<1307 2011 81 419 https://doi.org/10.1007/s00419-010-0488-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00419-010-0488-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Karamooz Ravari M. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut NATIONALLICENCE 700 1- Forouzan M. Department of Mechanical Engineering, Isfahan University of Technology, 84156-83111, Isfahan, Iran aut NATIONALLICENCE 773 0- Archive of Applied Mechanics Springer-Verlag 81/9(2011-09-01), 1307-1322 0939-1533 81:9<1307 2011 81 419 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer