Modelling of an Optimal Membrane with Patches

1. Banichuk N. V., "Introduction to optimization of structures, New York: Springer (1990). 2. Berdy D. F., "Srisungsitthisunti P., Jung B., Xianfan X., Rhoads J. F., "Low-frequency meandering piezoelectric vibration energy harvester, IEEE transactions on ultrasonics", ferroelectrics, and frequency control, 59 (2012) 846-858. 3. Dong L., Grissom M., Fisher F. T., "Resonant frequency of mass-loaded membranes for vibration energy", Energy, 3, (2015) 344-359. 4. Cuccu F., Porru G., "Emamizadeh B., "Design of a Composite Membrane with Patches", Appl. Math. Optim, 62 (2010) 169-184. 5. Chanillo S., Grieser D., Imai M., Kurata K., Ohnishi I., "Symmetry breaking and other phenomena in the optimization of eigenvalues for composite membranes", Commun, Math. Phys, 214 (2000) 315-337. 6. Cox S. J., McLaughlin J. R., "Extremal eigenvalue problems for composite membranes", I. Appl. Math. Optim, 22 (1990) 153-167. 7. Henrot A., "Extremum problems for eigenvalues of elliptic operators", Basel: Birkhäuser-Verlag (2006). 8. Mohammadi S. A., Voss H., "A minimization problem for an elliptic eigenvalue problem with nonlinear dependence on the eigenparameter", Nonlinear Anal. RWA. 31 (2016) 119-131. 9. Mohammadi S. A., "Extremal energies of Laplacian operator: Different configurations for steady vortices", J. Math. Anal. Appl. 448 (2017) 140-155. 10. Mohammadi S. A., Bahrami F., "A nonlinear eigenvalue problem arising in a nanostructured quantum dot, Commun. Nonlinear", Sci. Numer Simulat, 19, (2014) 3053-3062. 11. Zivari-Rezapour M., "Maximax rearrangement optimization related to a homogeneous Dirichlet problem", Arab. J. Math, 2, (2013) 427-433. 12. Zivari-Rezapour M., Emamaizadeh B., "Optimization of the principal eigenvalue of the pseudo p-Laplacian operator with Robin boundary conditions", International Journal of Mathematics, 23 (2012) 25-127. 13. Kao C.Y., Su S., "An efficient rearrangement algorithm for shape optimization on eigenvalue problems", J. Sci. Comput, 54 (2013) 492–512. 14. Burton G. R., "Variational problems on classes of rearrangements and multiple configurations for steady vortices", Ann. Inst. H. Poincaré. Anal. NonLinéaire, 6 (1989) 295-319. 15. Osher J., Santosa F., "Level set methods for optimization problems involving geometry and constraints i. Frequencies of a two-density inhomogeneous drum", J. Comput, Phys, 7 (2001) 1272–288.