Review Vibrations of straight and curved composite beams: A review Mehdi Hajianmaleki, Mohamad S. Qatu ⇑ Mechanical Engineering Department, Mississippi State University, Starkville, MS 39762, United States article info Article history: Available online 11 January 2013 Keywords: Beams Curved Vibration Review abstract Laminated composite straight and curved beams are frequently used in various engineering applications. This work attempts to review most of the research done in recent years (1989–2012) on the vibration analysis of composite beams. This review is conducted with emphasis given to the theory being applied (thin, thick, layerwise), methods for solving equations (finite element analysis, differential transform and others) experimental methods, smart beams (piezoelectric or shape memory), complicating effects in both material and structure (viscoelastic, rotating, tip mass and others) and other areas that have been considered in research. A simple classic and shear deformation model would be explained that can be used for beams with any laminate. Ó 2013 Elsevier Ltd. All rights reserved. Contents 1. Introduction ......................................................................................................... 219 2. Beam theories ........................................................................................................ 219 2.1. Stiffness parameters ............................................................................................. 219 2.2. Effect of shear deformation ....................................................................................... 219 2.2.1. Classical beam theory..................................................................................... 220 2.2.2. Shear deformation theories ................................................................................ 220 2.2.3. First order shear deformation theories ....................................................................... 221 2.2.4. Higher order shear deformation theories ..................................................................... 221 2.3. Layerwise theories............................................................................................... 222 2.4. Other theories .................................................................................................. 222 3. Methods for solving equations of motion .................................................................................. 223 3.1. Differential transform method ..................................................................................... 223 3.2. Dynamic stiffness matrix method .................................................................................. 223 3.3. State space approach (transfer matrix method) ....................................................................... 223 3.4. Finite element methods .......................................................................................... 223 4. Experimental investigation ............................................................................................. 224 5. Smart beams ......................................................................................................... 224 5.1. Piezoelectric beams .............................................................................................. 224 5.2. Beams with shape memory alloys .................................................................................. 225 6. Complicating effects ................................................................................................... 225 6.1. Dynamic loading and excitation .................................................................................... 225 6.2. Rotating beams ................................................................................................. 226 6.2.1. Shafts .................................................................................................. 226 6.2.2. Blades ................................................................................................. 226 6.3. Damaged beams ................................................................................................ 226 6.3.1. Damage effect on natural frequencies ........................................................................ 227 6.3.2. Vibration monitoring ..................................................................................... 227 6.4. Added mass effect ............................................................................................... 227 6.5. Damped and viscoelastic beams .................................................................................... 227 6.6. Beams on elastic support ......................................................................................... 228 0263-8223/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.compstruct.2013.01.001 ⇑ Corresponding author. Address: School of Engineering and Technology, Central Michigan University, United States. Tel.: +1 989 774 3063. E-mail address: qatu1ms@cmich.edu (M.S. Qatu). Composite Structures 100 (2013) 218–232 Contents lists available at SciVerse ScienceDirect Composite Structures journal homepage: www.elsevier.com/locate/compstruct