P 1 ¼
1
4
F _
u 3 L
ð Þ
½
à þ F
Ã
_
u 3 L
ð Þ
½
f
g ,
P 2 ¼
1
4
IV
Ã
þ IV
Ã
f
g ,
ð3:149Þ
where an asterisk represents complex conjugate. The efficiency is given by P 2 /P 1 .
Figure 3.20 shows P 1 , P 2 , and P 2 /P 1 versus the driving frequency of the applied
force when Z is real and represents a resistor load. P 1 and P 2 assume maxima at
resonance frequencies as expected. As the ratio between two functions of the driving
frequency, the behavior of the efficiency is somewhat involved, not necessarily
assuming maxima at resonance frequencies.
Fig. 3.19 Displacement
fields at the first three
resonances. Z ¼ 1.
Q ¼ 100. (a) Real parts. (b)
Imaginary parts
66
3 Extension of Rods
1
4
F _
u 3 L
ð Þ
½
à þ F
Ã
_
u 3 L
ð Þ
½
f
g ,
P 2 ¼
1
4
IV
Ã
þ IV
Ã
f
g ,
ð3:149Þ
where an asterisk represents complex conjugate. The efficiency is given by P 2 /P 1 .
Figure 3.20 shows P 1 , P 2 , and P 2 /P 1 versus the driving frequency of the applied
force when Z is real and represents a resistor load. P 1 and P 2 assume maxima at
resonance frequencies as expected. As the ratio between two functions of the driving
frequency, the behavior of the efficiency is somewhat involved, not necessarily
assuming maxima at resonance frequencies.
Fig. 3.19 Displacement
fields at the first three
resonances. Z ¼ 1.
Q ¼ 100. (a) Real parts. (b)
Imaginary parts
66
3 Extension of Rods