An analytical technique to obtain higher-order approximate periods for the nonlinear oscillator

In this paper, an analytical technique has been proposed to obtain higher-order approximate periods for the nonlinear oscillator with the square of the angular frequency depends quadratically on the velocity which is based on the harmonic balance method (HBM). Analytical investigation of the appeared set of nonlinear algebraic equations is usually cumbersome, which is addressed by the proposed technique in a novel way. In this paper, this limitation is eradicated and provides desired results without much numerical complexity. Besides, a new suitable truncation formula has been introduced in which the approximate periods measures much better results than existing periods. The proposed technique is applied to the benchmark nonlinear oscillatory problem with the square of the angular frequency depends quadratically on the velocity to illustrate its novelty, reliability and wider applicability. Remarkableyimprotant that using the proposed technique a third-order approximate period gives an excellent agreement as compared with the exact ones. ********************************************************** Penulisan ini berkenan simulasi pengaruh pelbagai nilai indeks modulasi ( ) dalam strategi PWM berasaskan aplikasi dalam menghasilkan bentuk gelombang yang bertingkat. Bentuk gelombang ini diuji untuk aplikasi dalam topologi MMCs. Penilaian dan hasil dari artikle ini termasuk variasi komponen asas (50 Hz) dalam voltan keluar. Ia juga meneliti jumlah penyelarasan harmonik voltan keluar (THDv) dan arus keluaran (THDi) apabila indeks modulasi ditukar dalam rantau modulasi linear, 0 <