In 1990, a pilot project was started at the Alfred Gessow Rotorcraft Center (University of Maryland) to build a smart rotor with embedded piezoelectric strips. Soon, it attracted the attention of Dr. Gary Anderson of the Army Research Office (ARO). He encouraged us to put together outlines for a major initiative in the smart structures area, which subsequently resulted in the award of a multi-year (1992–1997) University Research Initiative (URI). This provided us an opportunity to develop an effective team of interdisciplinary faculty from Aerospace, Mechanical, Electrical, and Material Engineering. As a result, there was an enormous growth of smart structures research activities on our campus. Following the success of this URI, we were awarded another multi-year (1996–2001) Multi University Research Initiative (MURI) in smart structures by ARO. For this major program, we collaborated with Penn State and Cornell University. This further nurtured the ongoing smart structures activities at Maryland. We deeply acknowledge the support and friendship of many faculty colleagues at Maryland: Appa Anjannappa, Bala Balachandran, James Baeder, Amr Baz, Roberto Celi, Ramesh Chandra, Abhijit Dasgupta, Allison Flatau, James Hubbard, P. S. Krishnaprasad, Gordon Leishman, V. T. Nagaraj, Darryll Pines, Don Robbins, Jim Sirkis, Fred Tasker, Norman Wereley, and Manfred Wuttig.

While the research frontier in smart structures was expanding at the Alfred Gessow Rotorcraft Center, we also initiated classroom teaching at the graduate level in the smart structures area.

Certain classes of metallic alloys have a special ability to “memorize” their shape at a low temperature and recover large deformations imparted at a low temperature on thermal activation. These alloys are called shape memory alloys (SMAs). The recovery of strains imparted to the material at a lower temperature, as a result of heating, is called the shape memory effect (SME). The SME was first discovered by Chang and Read in 1951 in the Au-Cd (gold-cadmium) alloy system. However, the effect became more well known after the discovery of nickel-titanium alloys.

Buehler and Wiley [1, 2] discovered a nickel-titanium alloy in 1961 called NiTiNOL (i.e., Nickel Titanium alloy developed at the Naval Ordinance Lab) that exhibited a much greater SME than previous materials. This material was a binary alloy of nickel and titanium in a ratio of 55% to 45%, respectively. A 100% recovery of strain up to a maximum of about 8% pre-strain was achieved in this alloy. Another interesting feature noticed was a more than 200% increase in Young's modulus in the high-temperature phase compared to the low-temperature phase. Subsequently, it was determined that the percentage of nickel and titanium influences the material properties of Nitinol and can be varied to control the transformation temperatures in the material [3]. Also, the addition of a third or fourth element (most commonly copper) to NiTi can be used to selectively control some properties of SMA wires.

The previous chapter discussed the modeling of beam-like structures with induced-strain actuation. Many practical structures can be simplified and analyzed as beams, but such an assumption is not accurate in a large number of other structures, such as fuselage panels in aircraft, low aspect-ratio wings, and large control surfaces. It is possible to treat such structures as plates and perform a simple two-dimensional analysis to estimate their behavior. Some of the theories discussed in the previous chapter can be extended to two-dimensional plate-like structures. This chapter describes the modeling of isotropic and composite plate structures with induced-strain actuation. It will combine both the actuators and substrate into one integrated structure to model its behavior. The discussion focuses on induced-strain actuation by means of piezoceramic sheets, but the general techniques may be equally applicable to other forms of induced-strain actuation.

Plate analysis, including induced-strain actuation, is based on the classical laminated plate theory (CLPT), sometimes referred to as classical laminated theory (CLT). It is an equivalent single layer (ESL) plate theory in which the effects of transverse shear strains are neglected. It is valid for thin plates that have thicknesses of one to two orders of magnitude smaller than their planar dimensions (length and width). In the CLPT formulation, a plane-stress state assumption is used.

Classical Laminated Plate Theory (CLPT) Formulation without Actuation

A composite laminate consists of a number of laminae or plies, each with different elastic properties.

Vascular endothelial cells are cultured on the inside of a 10-cm long hollow tube that has aninternal diameter of 3 mm. Culture medium flows through the tube at Q= 1 ml/s. The cells produce a cytokine, EDGF, at a rate nEDGF (production rate per cell area) that depends on the local wall shear stressaccording to nEDGF = kτwall, wherek is an unknown constant with units of ng/dyne per s. The flow in the tubeis not fully developed, such that the shear stress is known to vary with axial position according toτwall = τ0(1 –βx), where β= 0.02 cm−1, τ0= 19 dyne/cm2, and x is the distance from the tubeentrance. Under steady conditions a sample of medium is taken from the outlet of the tube, and theconcentration of EDGF is measured to be 35 ng/ml in this sample. What isk?

Flow occurs through a layer of epithelial cells that line the airways of the lung due to avariety of factors, including a pressure difference across the epithelial layer(ΔP = P0) and, in the case of transientcompression, to a change in the separation between the two cell membranes, w2, as a function of time. We consider these cases sequentially below. Note that the depthof the intercellular space into the paper is L, and the transition in cellseparation from w1 to w2 occurs over alength δ much smaller than H1 andH2. (See the figure overleaf.)

Consider a membrane of thickness 10 μm that has a number of tiny cylindrical pores (of radius 10 nm) passing through it. The density of pores in the membrane is such that the porosity (fractions of water-filled space) of the membrane is 0.1%.

1. (a) Find the hydraulic conductivity (Lp, flow rate per unit area per unit pressure drop) of this membrane.

2. (b) Consider a 4 mM solution of a large protein on one side of this membrane and physiologic saline on the other, with the same pressure on both sides of the membrane. Assume that the protein is sufficiently large that it cannot pass through the membrane and that van ’t Hoff’s law holds for this solute. Calculate the initial flow rate of saline through a membrane of area 5 cm2 at a temperature of 300 K.

The graph shown in the figure overleaf is adapted from a 1927 paper [16] in which Landis proved the existence of Starling’s phenomenon by occluding capillaries. The ordinate is the volume of fluid leaking out of (or re-entering) the capillary per unit capillary wall area, j. Although it is not precisely true, for the purposes of this question you may assume that the reflection coefficient of this capillary wall to plasma proteins is unity.

1. (a) Assuming that p – Π for the interstitium is –5 cm H2O, estimate the plasma osmotic pressure (Π) from the figure. Note that the plasma proteins are the main species influencing the osmotic pressure difference across the capillary wall.

2. (b) Estimate the filtration coefficient Lp for this capillary.

3. (c) Consider a capillary 0.05 cm long of diameter 8 µm, for which the arteriolar and venular luminal pressures are 25 and 5 cm H2O, respectively. Assume that Lp and Π are constant and that the pressure drop varies linearly along the capillary. What is the net rate of fluid loss (gain) from the capillary?

Fluid often passes through pores in cell membranes or cell layers. The dimensions are small and the velocities low, so viscous forces dominate (low Reynolds number). Use dimensional analysis, or an approximate method of analysis based on the viscous flow equations, to determine the scaling law that expresses the dependence of the pressure drop across a pore (ΔP) on the flow rate through it (Q). The other parameters that are given include the pore radius, R, and the viscosity of the fluid, μ. The membrane itself should be considered infinitesimally thin so that its thickness does not influence the pressure drop.

Using a stroboscope, it has been observed that freely falling water drops vibrate. The characteristic time for this vibration does not depend on the viscosity of the water (except for very, very small drops). Determine what parameters you expect this vibration time to depend on, and find a relationship between the vibration time and these parameters. Estimate the characteristic vibration time for a water droplet of diameter 2 mm at a temperature of 25° C. (Hint: this time-scale is the same for a droplet inside of a rocket in space as it is for a droplet falling on the Earth.)