1- Kiang CH, Endo M, Ajayan PM, Dresselhaus G, Dresslhaus MS. Size effects in carbon nanotubes. Phys Rev Lett. 1998;81(9):1869-1872. [
Link] [
DOI:10.1103/PhysRevLett.81.1869]
Abbaszadeh Bidokhti A, Sadough Vanini A, Eslami MR. Active control of piezo-fgm beams [Internet]. Dijon, France: MATERIAUX. 13-17 November; 2006 [cited 2018 July 06]. Available from: https://bit.ly/311zrhG [
Link]
Kargarnovin MH, Najafzadeh MM, Viliani NS. Vibration control of functionally graded material plate patched with piezoelectric actuators and sensors under a constant electric charge. Smart Mater Struct. 2007;16(4):1252-1259. [
Link] [
DOI:10.1088/0964-1726/16/4/037]
Li SR, Su HD, Cheng CJ. Free vibration of functionally graded material beams with surface-bonded piezoelectric layers in thermal environment. Appl Math Mech. 2009;30(8):969-982. [
Link] [
DOI:10.1007/s10483-009-0803-7]
Simsek M, Kocatürk T. Free and forced vibration of functionally graded beam subjected to a concentrated moving harmonic load. Compos Struct. 2009;90(4):465-473. [
Link] [
DOI:10.1016/j.compstruct.2009.04.024]
Simsek M. Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load. Compos Struct. 2010;92(10):2532-2546. [
Link] [
DOI:10.1016/j.compstruct.2010.02.008]
Khalili SMR, Jafari AA, Eftekhari SA. A mixed Ritz-DQ method for forced vibration of functionally graded beams carrying moving loads. Compos Struct. 2010;92(10):2497-2511. [
Link] [
DOI:10.1016/j.compstruct.2010.02.012]
Jafari AA, Fathabadi M. Forced vibration of FGM Timoshenko beam with piezoelectric layers carrying moving load. Aerospace Mech J. 2013;9(2):69-77. [Persian] [
Link]
Shahraeeni M, Shakeri R, Hasheminejad SM. An analytical solution for free and forced vibration of a piezoelectric laminated plate coupled with an acoustic enclosure. Comput Math Appl. 2015;69(11):1329-1341. [
Link] [
DOI:10.1016/j.camwa.2015.03.022]
Hou H, He G. Static and dynamic analysis of two-layer Timoshenko composite beams by weak-form quadrature element method. Appl Math Model. 2018;55:466-483. [
Link] [
DOI:10.1016/j.apm.2017.11.007]
Hosseini SAH, Rahmani O. Bending and vibration analysis of curved FG nanobeams via nonlocal Timoshenko model. Smart Construct Res. 2018;2(2):1-17. [
Link] [
DOI:10.18063/scr.v2i2.401]
Kadoli R, Akhtar K, Ganesan N. Static analysis of functionally graded beams using higher order shear deformation theory. Appl Math Model. 2008;32(12):2509-2525. [
Link] [
DOI:10.1016/j.apm.2007.09.015]
Sina SA, Navazi HM, Haddadpour H. An analytical method for free vibration analysis of functionally graded beams. Mater Des. 2009;30(3):741-747. [
Link] [
DOI:10.1016/j.matdes.2008.05.015]
Leissa AW, Qatu MS. Vibrations of continuous systems. New York: MacGraw Hill; 2011. [
Link]
Tiersten HF. Linear Piezoelectric Plate Vibration. New York:Plenum press; 1969. [
Link] [
DOI:10.1007/978-1-4899-6453-3]
Qatu MS. Vibration of laminated shells and plates. 1ST Edition. New York: Academic Press; 2004. [
Link] [
DOI:10.1016/B978-008044271-6/50006-5]
Majkut L. Free and forced vibrations of Timoshenko beams described by single difference equation. J Theor Appl Mech. 2009;47(1):193-210. [
Link]
Aydogdu M. Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method. Int J Mech Sci. 2005;47(11):1740-1755. [
Link] [
DOI:10.1016/j.ijmecsci.2005.06.010]
Gdoutos EE, Marioli-Riga ZP, editors. Recent advances in composite materials. In Honor of SA Paipetis. Dordrecht: Springer Science & Business Media; 2013. [
Link]
