Abstract: In our consideration, we studied vibrations analysis and dynamic responses of a Hybrid Rayleigh-Van der Pol- Duffing oscillator. This system presented by one -degree- of - freedom containing the fifth order of nonlinear terms and an external force. The proportional derivative controller (PD) was used to control the vibration of the main system. The average method used to obtain the approximate solution of the vibrating system. The stability of the system is investigated at the primary resonance case (Ω = ω). Numerically, we used Runge-Kutta of the fourth order to scrutinize the time histories of the system before and after using PD. For response curves, we investigated the performance of some chosen parameters of studied system. Finally, there is a good agreement between the approximate solution which obtained from the average method and the numerical one.

Resumo Este estudo foi realizado para determinar uma substituição adequada de farinha de peixe com aminoácidos (AA) e níveis otimizados de proteína em dietas práticas para Oreochromis niloticus com peso corporal inicial médio de 12,52 ± 0,63 g. Seis dietas experimentais e controle (total de 7 dietas) divididas em dois grupos, e uma dieta controle (D1) contendo 32% de proteína. O primeiro grupo continha três dietas que incluíam diferentes níveis de proteína na dieta, viz. 20 (D2), 25 (D3) e 30% (D4) com AAs ao substituir a farinha de peixe por fontes de proteína vegetal. No segundo grupo, as dietas continham 20 (D5), 25 (D6) e 30% (D7) sem AAs. O melhor desempenho de crescimento foi alcançado em peixes alimentados com dieta D1. O consumo total de ração foi aumentado com o aumento do nível de proteína na dieta com AAs. A taxa de crescimento específico mostrou um padrão semelhante com uma diferença significativa entre o controle, D4 e D7 em comparação com outros grupos. A taxa de conversão alimentar diminuiu quando os níveis de proteína nas dietas aumentaram. A taxa de eficiência protéica apresentou desempenho semelhante, com discreto aumento entre a dieta controle e as dietas com AAs. Entretanto, diferenças insignificantes (P> 0,05) foram observadas entre dietas com e sem AAs. Uma avaliação econômica indicou que a inclusão de farinha de peixe baixa em dietas de tilápia reduziu o preço / kg de dietas em relação ao controle.

Abstract This study was conducted to determine an appropriate replacement of fishmeal with amino acids (AAs) and optimized protein levels in practical diets for Oreochromis niloticus with mean initial body weight 12.52±0.63g. Six experimental and a control diet (total 7 diets) divided into two groups, and a control diet (D1) containing 32% protein. The first group contained three diets that included different dietary protein levels, viz. 20 (D2), 25 (D3), and 30% (D4) with AAs when replacing fishmeal by plant protein sources. In the second group, the diets were contained 20 (D5), 25 (D6), and 30% (D7) without AAs. The best growth performance was achieved in fish fed with diet D1. Total feed intake was increased with an increase in dietary protein level with AAs. The specific growth rate showed a similar pattern with a significant difference between control, D4 and D7 compared to other groups. The feed conversion ratio decreased when protein levels in the diets increased. The protein efficiency ratio showed a similar performance, with a slight increase between the control diet and diets with AAs. However, insignificant differences (P>0.05) were observed between diets with and without AAs. An economic evaluation indicated that inclusion of low fishmeal in tilapia diets reduced the price/kg of diets compared to control.