Analysis of the Nonlinear Structural-Acoustic Resonant Frequencies of a Rectangular Tube with a Flexible End Using Harmonic Balance and Homotopy Perturbation Methods

Table 1

(a) Harmonic term convergence for various amplitudes (1st resonant frequency). (b) Harmonic term convergence for various amplitudes (2nd resonant frequency).

(a)  

	Homotopy perturbation	No. of harmonic terms = 1	2	3
𝐴/𝑡=0.2	𝜔/𝜔𝑠=0.64348	0.64348	0.64347	0.64347
0.6	0.66140	0.66140	0.66094	0.66091
1	0.67759	0.67759	0.67641	0.67619
1.4	0.68721	0.68721	0.68580	0.68530

(b)  

	Homotopy perturbation	No. of harmonic terms = 1	2	3
𝐴/𝑡=0.2	𝜔/𝜔𝑠=1.07786	1.07786	1.07784	1.07784
0.6	1.19539	1.19539	1.1936	1.19356
1	1.40661	1.40661	1.4005	1.40024
1.4	1.66715	1.66715	1.65219	1.6600