The cantilever is affixed to the free end of a square cross-section piezoelectric (PZT) block, which...

The cantilever is affixed to the free end of a square cross-section piezoelectric (PZT) block, which is fixed at the other end. Draw the schematic of the lumped-parameter model of the cantilever-PZT system, obtain the mathematical model of this mechanical system, and derive the lumped mass and stiffness of the PZT knowing that la = 0.01 m (length of PZT block), a = 0.005 m (side length of PZT cross-section), EPZT = 55 GPa (Young’s modulus), ?PZT = 7500 kg/m3 (mass density). The piezoelectric material losses are represented by an equivalent viscous damping coefficient cPZT = 60 N-s/m.

Expert Solution

samet mamat answered 2 years ago

A cantilever of circular solid cross section is fixed at one end and carries a concentrated...

A cantilever of circular solid cross section is fixed at one end and carries a concentrated load P at the free end. The diameter at the free end is 200mm and increases uniformly to 400 mm at the fixed end over a length of 2m. At what distance from the free will the bending stresses in the cantilever be maximum? Also calculate the value of the maximum bending stress if the concentrated load P=300 KN (a) 1.23 m, 12.32 MPa...

Determine the limiting values of the width a of a waveguide of square cross section which...

Determine the limiting values of the width a of a waveguide of square cross section which will transmit a wave of length lambda in the TE10 mode but not in the TE11 or TM11 modes.

The block of glass (n = 1.5) shown in cross section in Figure 1 is surrounded...

The block of glass (n = 1.5) shown in cross section in Figure 1 is surrounded by air. A ray of light enters the block at its left-hand face with incident angle θ1 and reemerges into the air from the right-hand face directed parallel to the block's base. Determine the angle θ1.

An aluminum rod with a square cross section is 1.2 m long and 5.0 mm on...

An aluminum rod with a square cross section is 1.2 m long and 5.0 mm on edge. (a) What is the resistance between its ends? (b) What must be the diameter of a cylindrical copper rod of length 1.2 m if its resistance is to be the same as that of the aluminum rod? The resistivity of aluminum is 2.75 × 10-8 Ω·m and the resistivity of copper is 1.69 × 10-8 Ω·m.

A polymer rod is tested to determine its viscoelastic response. The rod’s cross-section is square with...

A polymer rod is tested to determine its viscoelastic response. The rod’s cross-section is square with the side of 5mm. The rod’s length before loading is 500mm. A tensile force of 500N is applied to the rod and the rod’s length under load was measured as a function of time. Instantly after applying the load, the rod is stretched to 508mm. After 24 and 48 hour under load, the rod’s length was measured as 550mm and 570mm, respectively. The load...

A direct shear test is conducted on a large specimen of dry sand (square cross section...

A direct shear test is conducted on a large specimen of dry sand (square cross section with following dimensions: 7.5 cm x 7.5 cm x 3.0 cm [height], Mass = 271.0 g) with a normal stress of 500 kPa. Failure occurred when the horizontal force was 1.96 kN. For the same sand, tests were also conducted to determine the specific gravity and the maximum and minimum void ratios. These tests yielded the following results: Gs= 2.65, emax=0.80, emin = 0.45....

A glass with a square cross section when viewed directly from above is filled with water....

A glass with a square cross section when viewed directly from above is filled with water. The glass is 8.0 cm wide on each side and is 17.6 cm high. (a) Find the net horizontal force exerted by the water on each side. (b) Find the net horizontal force exerted by the water on all four walls of the glass. (c) Find the net force exerted by the water on the bottom of the glass.

A precast square concrete pile 305x305 mm in cross section is driven into ground using a...

A precast square concrete pile 305x305 mm in cross section is driven into ground using a steam hammer. If HE = 40 kN-m, E = 0.85, WR = 35 kN, weight of pile cap = 3.0 kN, L = 25 m, n = 0.4, Ep = 21 x 106 kN/m2 , number of blows for the last 25.4 mm pile penetration is 7 blows, unit weight of concrete = 24 kN/m3 . Compute the allowable pile capacity using: (a) Modified...

Air flows through a heating duct with a square cross-section with 5-inch sides at a speed...

Air flows through a heating duct with a square cross-section with 5-inch sides at a speed of 5.3 ft/s. Just before reaching an outlet in the floor of a room, the duct widens to assume a square cross-section with sides equal to 13 inches. Compute the speed of the air flowing into the room (in ft/s), assuming that we can treat the air as an incompressible fluid. Answer should be in Ft/s

10 cm of copper with square cross section of 1x1 cm exposed to 200 KN tension...

10 cm of copper with square cross section of 1x1 cm exposed to 200 KN tension force caused 15% permanent reduction in cross section area , if the fracture got on this point, calculate the following: 1 – the ductility 2 – stress 3 – true stress 4- fracture stress

Question