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Papers by hamed babazadeh

... Learn more... ProQuest. Active Flow Control of a Precessing Jet. by Babazadeh, Hamed, M.Sc., ... more ... Learn more... ProQuest. Active Flow Control of a Precessing Jet. by Babazadeh, Hamed, M.Sc., UNIVERSITY OF ALBERTA , 2011, 181 pages; MR70929. Abstract: ... Advisor: School: UNIVERSITY OF ALBERTA. Source: MAI 49/04, p. , Aug 2011. Source Type: M.Sc. ...

International Journal of Modern Physics B, 2009

This paper implements He's max–min method to solve accurately strong nonlinear oscillators. M... more This paper implements He's max–min method to solve accurately strong nonlinear oscillators. Maximal and minimal solution thresholds of a nonlinear problem can be easily found, and an approximate solution of the nonlinear equation can be easily deduced using He Chengtian's interpolation, which has a millennia history. Some typical examples are employed to illustrate its validity, effectiveness, and flexibility.

2016 North American Power Symposium (NAPS), 2016

Although wind energy provides a viable solution to address ongoing challenges of the economy and ... more Although wind energy provides a viable solution to address ongoing challenges of the economy and the environment in electric power grids, the variable generation of this technology results in major technical challenges for system operators. This issue is becoming more severe as the penetration of wind generation is increasing. As a result, wind generation is commonly subject to specific regulations which limit generation fluctuations. Three methods of reducing wind generation fluctuation are investigated in this paper from an economic perspective, including (a) dumping the wind generation, (b) using battery energy storage (BES) to capture excess wind generation, and (c) a hybrid method combining this two approaches. The economic viability of the hybrid method is investigated via a developed linear programming model with the objective of profit maximization, which in extreme cases will converge to one of the other methods. Numerical simulations exhibit the merits of the proposed model.

2012 IEEE Power and Energy Society General Meeting, 2012

This paper introduces a new control strategy for battery energy storage systems used in wind gene... more This paper introduces a new control strategy for battery energy storage systems used in wind generation. It is specifically targeted to large wind installations, specifically offshore wind applications. This control strategy maximizes the life of the battery and increases the efficiency of the energy storage system while still balancing the power fluctuations of a large wind turbine system. The depth of discharge and remaining battery life are the key parameters considered in this approach. The proposed control scheme is applied to the battery package such that each battery cell is controlled individually. Individual cell depth of discharge is controlled and cell life is calculated periodically so that all cells within the package reach the end of life at the same. Total storage capacity and individual battery cell size are calculated based on the characteristics of the wind turbine. To verify the presented method, a case is studied in PSCAD and corresponding results are provided.

Journal of the Taiwan Institute of Chemical Engineers, 2010

2013 IEEE Green Technologies Conference (GreenTech), 2013

In this paper, we introduce a new method for finding the proper size of energy storage system (ES... more In this paper, we introduce a new method for finding the proper size of energy storage system (ESS). This design is dedicated to reduce the size of ESS considering the uncertainty of wind speed. It considers the statistical behavior and also the state of charge (SOC) of ESS. The impact of wind uncertainty on power production and its impact on the SOC of ESS are studied. The optimization is done by using the defined uncertainty limits and some other criteria. The probability density function and cumulative density function are calculated in this method. The presented method provides a significant reduction in the size of ESS in terms of power and energy capacity which consequently reduces a considerable capital cost of ESSs for applications in wind turbine generators. The main goal of this design is to reduce the unnecessarily large capacity of ESS which causes the high cost of ESS.. All the calculations and plotting are done using MATLAB.

Journal of Corporate Accounting & Finance, 1992

FAS 109, “Accounting for Income Taxes,” is the result of a significant effort by the Financial Ac... more FAS 109, “Accounting for Income Taxes,” is the result of a significant effort by the Financial Accounting Standards Board to address the concerns of preparers and users of financial statements. The new standard recognizes the likelihood of recognition of deferred taxes and in particular of the benefit of deferred tax assets. More guidance is provided for the recognition of deferred tax assets in the form of negative and positive evidence. Examples are presented that illustrate the application of the new standard to various typical problems of accounting for income taxes.

International Journal of Modern Physics B, 2009

The main objective of this paper is to apply the parameter expansion technique (a modified Lindst... more The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt–Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the s...

Frontiers of Mechanical Engineering, 2011

ABSTRACT Nonlinear functions are crucial points and terms in engineering problems. Actual and phy... more ABSTRACT Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step. Keywordsmin-max method–nonlinear oscillation–duffing equation–mathematical pendulum–He’s energy balance method

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels, 2008

ABSTRACT

Progress In Electromagnetics Research M, 2008

This paper presents a new approach for solving accurate approximate analytical solution for stron... more This paper presents a new approach for solving accurate approximate analytical solution for strong nonlinear oscillators. The new algorithm offers a promising approach by Hamiltonian for the nonlinear oscillator. We find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.

Experiments in Fluids, 2015

ABSTRACT A precessing jet nozzle with water as the working fluid is investigated under passive an... more ABSTRACT A precessing jet nozzle with water as the working fluid is investigated under passive and active flow control. The actuation effectiveness of 12 microjets around the nozzle inlet for active control of the precessing jet is the focus of this work. Passive control is also applied by modifying the geometry of the precessing jet either by adding a center body near the chamber exit or varying the chamber length. The flow behavior under control is studied using pressure measurement at the chamber exit plane to monitor jet precession. The pressure data are analyzed using a phase plane representation to determine the motion of the jets high-velocity region in the chamber exit plane. The standard deviation of the phase of the triggered pressure data is used for stability analysis. This analysis results in a phase diagram in terms of Reynolds number and actuation frequency. Active control can be utilized over a range of actuation frequencies (and corresponding Strouhal numbers) to control precession direction and stability which can be further enhanced with passive control mechanisms. However, the flow follows the actuation with the lowest variation when the active actuation matches with the natural Strouhal number \((0.002

2011 North American Power Symposium, 2011

ABSTRACT The permanent magnet synchronous generator (PMSG) based variable speed wind turbine is c... more ABSTRACT The permanent magnet synchronous generator (PMSG) based variable speed wind turbine is connected to the power grid via a full-scale converter. The full-scale converter presented in this paper consists of an active rectifier, an inverter and DC-DC converter for Energy Storage System (ESS). The rectifier controller uses the rotor flux oriented control (FOC) system and achieves Maximum Power Point Tracking (MPPT) which is necessary for the wind turbine to obtain maximum power conversion. The grid side controller uses a voltage oriented control system to regulate the active and reactive power dispatched to the power grid. The employed voltage source inverter (VSI) regulates the output power at desired reference value (in our case 1 pu) while keeping the output voltage in a sinusoidal waveform. The output electrical power from the PMSG is fluctuating, which is unacceptable from the standpoint of power system operation. An energy storage system (ESS) can help accommodate the difference between fluctuating wind power and that dispatched to the grid. The ESS absorbs the extra energy from the DC-link (via charging) and releases the stored energy to the DC-link when required (via discharging). The presented ESS for this paper is a Hybrid Energy Storage System (HESS) consisting of high power density supercapacitors and high energy density batteries. The HESS controller is designed to smooth and regulate the output power while help increase the battery's life. In the control system of DC-DC controller some logic gates are employed to appropriately disconnect the battery from DC-link. The system is modeled and simulated in PSCAD software.

PES T&D 2012, 2012

ABSTRACT In this paper, we introduce a new hybrid energy storage system (HESS) design for wind po... more ABSTRACT In this paper, we introduce a new hybrid energy storage system (HESS) design for wind power generation application and corresponding calculation of the proper size of the battery and supercapacitor. The design has an objective to increase the battery life time. The boundary levels of the state of charge of the battery and that of the supercapacitor are used in the control strategy. In the controller, some logic gates are also used to control the operating time durations of the battery. The sizing method is based on the average fluctuation of wind profiles of a specific wind station which consequently provides some fluctuations in the generated wind power. The calculated battery size is dependent on the size of the supercapacitor, state of charge of the supercapacitor and battery wear. To verify the presented method, two different cases are studied in PSCAD and corresponding results are provided.

2012 IEEE Power Electronics and Machines in Wind Applications, 2012

This paper proposes a trustworthy and practical approach to predict wind speed, which could be us... more This paper proposes a trustworthy and practical approach to predict wind speed, which could be used as input to predict wind power generation. In the prediction model, we applied the variable speed wind as input of this model. Then the Gaussian noise is added to the input due to existing of noise in measuring of wind speed. Kalman filtering is used as the prediction method in this study. The parameters of shaping filter are calculated using power spectral analysis and Gauss-Markov theory. Results under different time horizon of prediction are compared with actual data and the comparison shows that the results obtained using Kalman filter is reliable. The proposed method works well for an hour ahead prediction and for short-time prediction works even better. The application of Kalman filter on wind speed prediction is implemented in MATLAB software and results are provided in this paper.

2013 North American Power Symposium (NAPS), 2013

ABSTRACT In remote district without power supply from bulk electric grid, wind energy can be util... more ABSTRACT In remote district without power supply from bulk electric grid, wind energy can be utilized to generate a large quantity of power when power plants are installed in an islanded micro-grid. Due to fluctuations in wind speed and resulting variable wind power, a small-scale diesel generator assists the wind power generator in providing a stable, sustained and efficient power generation. In addition, a Battery Energy Storage System (BESS) is capable of regulating its active power output in coordination with other generators to balance dynamic power demand and supply. Since the cost and efficiency is always the first issue for the control and operation of micro-grid in remote areas, energy management becomes the primary criterion in central control unit of micro-grids. The energy management of the wind power generator in micro-grid aims to optimize the system in terms of generation, cost, and load. Due to high uncertainty and volatility of wind speed, the Dynamic Programming Method (DPM) is employed in order to reduce the impact of wind speed uncertainty and fluctuation. For this purpose, a combined short term and long term optimization is studied in this paper. Meanwhile, a micro-grid system is modeled and simulated using MATLAB software.

International Journal of Nonlinear Sciences and Numerical Simulation, 2009

In this paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a strong method to... more In this paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a strong method to solve accurately higher-order approximate analytical solutions of coupled two-degree-of-freedom (CTDOF), which is described with a system of two coupled strong non-linear differential equations. MHHPM is modified version of He's HPM by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution into the second-order linear differential equation. For the first approximation we achieve a high accuracy of solutions with a maximal relative error less than 3.14 % for small and large values of oscillation amplitude, while for the second iteration the fabulous relative error is 0.064 %. It is predicted that MHHPM can be found widely applicable in engineering which needs extremely accurate solutions.

Progress In Electromagnetics Research M, 2008

This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservativ... more This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservative, non-natural, single-degreeof-freedom system with odd nonlinearity. By extending the Variational approach proposed by He, we established approximate analytical formulas for the period and periodic solution. To illustrate the applicability and accuracy of the method, two examples are presented: (i) the motion of a rigid rod rocking back and forth on the circular surface without slipping, and (ii) Cubic-Quintic Duffing Oscillators. Comparison of the result which is obtained by this method with the obtained result by the Exact solution reveals that the He's Variational approach is very effective and convenient and can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other sciences.

... Learn more... ProQuest. Active Flow Control of a Precessing Jet. by Babazadeh, Hamed, M.Sc., ... more ... Learn more... ProQuest. Active Flow Control of a Precessing Jet. by Babazadeh, Hamed, M.Sc., UNIVERSITY OF ALBERTA , 2011, 181 pages; MR70929. Abstract: ... Advisor: School: UNIVERSITY OF ALBERTA. Source: MAI 49/04, p. , Aug 2011. Source Type: M.Sc. ...

International Journal of Modern Physics B, 2009

This paper implements He's max–min method to solve accurately strong nonlinear oscillators. M... more This paper implements He's max–min method to solve accurately strong nonlinear oscillators. Maximal and minimal solution thresholds of a nonlinear problem can be easily found, and an approximate solution of the nonlinear equation can be easily deduced using He Chengtian's interpolation, which has a millennia history. Some typical examples are employed to illustrate its validity, effectiveness, and flexibility.

2016 North American Power Symposium (NAPS), 2016

Although wind energy provides a viable solution to address ongoing challenges of the economy and ... more Although wind energy provides a viable solution to address ongoing challenges of the economy and the environment in electric power grids, the variable generation of this technology results in major technical challenges for system operators. This issue is becoming more severe as the penetration of wind generation is increasing. As a result, wind generation is commonly subject to specific regulations which limit generation fluctuations. Three methods of reducing wind generation fluctuation are investigated in this paper from an economic perspective, including (a) dumping the wind generation, (b) using battery energy storage (BES) to capture excess wind generation, and (c) a hybrid method combining this two approaches. The economic viability of the hybrid method is investigated via a developed linear programming model with the objective of profit maximization, which in extreme cases will converge to one of the other methods. Numerical simulations exhibit the merits of the proposed model.

2012 IEEE Power and Energy Society General Meeting, 2012

This paper introduces a new control strategy for battery energy storage systems used in wind gene... more This paper introduces a new control strategy for battery energy storage systems used in wind generation. It is specifically targeted to large wind installations, specifically offshore wind applications. This control strategy maximizes the life of the battery and increases the efficiency of the energy storage system while still balancing the power fluctuations of a large wind turbine system. The depth of discharge and remaining battery life are the key parameters considered in this approach. The proposed control scheme is applied to the battery package such that each battery cell is controlled individually. Individual cell depth of discharge is controlled and cell life is calculated periodically so that all cells within the package reach the end of life at the same. Total storage capacity and individual battery cell size are calculated based on the characteristics of the wind turbine. To verify the presented method, a case is studied in PSCAD and corresponding results are provided.

Journal of the Taiwan Institute of Chemical Engineers, 2010

2013 IEEE Green Technologies Conference (GreenTech), 2013

In this paper, we introduce a new method for finding the proper size of energy storage system (ES... more In this paper, we introduce a new method for finding the proper size of energy storage system (ESS). This design is dedicated to reduce the size of ESS considering the uncertainty of wind speed. It considers the statistical behavior and also the state of charge (SOC) of ESS. The impact of wind uncertainty on power production and its impact on the SOC of ESS are studied. The optimization is done by using the defined uncertainty limits and some other criteria. The probability density function and cumulative density function are calculated in this method. The presented method provides a significant reduction in the size of ESS in terms of power and energy capacity which consequently reduces a considerable capital cost of ESSs for applications in wind turbine generators. The main goal of this design is to reduce the unnecessarily large capacity of ESS which causes the high cost of ESS.. All the calculations and plotting are done using MATLAB.

Journal of Corporate Accounting & Finance, 1992

FAS 109, “Accounting for Income Taxes,” is the result of a significant effort by the Financial Ac... more FAS 109, “Accounting for Income Taxes,” is the result of a significant effort by the Financial Accounting Standards Board to address the concerns of preparers and users of financial statements. The new standard recognizes the likelihood of recognition of deferred taxes and in particular of the benefit of deferred tax assets. More guidance is provided for the recognition of deferred tax assets in the form of negative and positive evidence. Examples are presented that illustrate the application of the new standard to various typical problems of accounting for income taxes.

International Journal of Modern Physics B, 2009

The main objective of this paper is to apply the parameter expansion technique (a modified Lindst... more The main objective of this paper is to apply the parameter expansion technique (a modified Lindstedt–Poincaré method) to calculate the first, second, and third-order approximations of motion of a nonlinear oscillator arising in rigid rod rocking back. The dynamics and frequency of motion of this nonlinear mechanical system are analyzed. A meticulous attention is carried out to the study of the introduced nonlinearity effects on the amplitudes of the oscillatory states and on the bifurcation structures. We examine the synchronization and the frequency of systems using both the strong and special method. Numerical simulations and computer's answers confirm and complement the results obtained by the analytical approach. The approach proposes a choice to overcome the difficulty of computing the periodic behavior of the oscillation problems in engineering. The solutions of this method are compared with the exact ones in order to validate the approach, and assess the accuracy of the s...

Frontiers of Mechanical Engineering, 2011

ABSTRACT Nonlinear functions are crucial points and terms in engineering problems. Actual and phy... more ABSTRACT Nonlinear functions are crucial points and terms in engineering problems. Actual and physical problems can be solved by solving and processing such functions. Thus, most scientists and engineers focus on solving these equations. This paper presents a novel method called the max-min method for presenting an accurate approximate analytical solution to strong nonlinear oscillators. It can solve many linear or nonlinear differential equations without the tangible restriction of sensitivity to the degree of the nonlinear term. It is also quite convenient due to the reduction in the size of calculations. The algorithm suggests a promising approach and is systematically illustrated step by step. Keywordsmin-max method–nonlinear oscillation–duffing equation–mathematical pendulum–He’s energy balance method

ASME 2008 6th International Conference on Nanochannels, Microchannels, and Minichannels, 2008

ABSTRACT

Progress In Electromagnetics Research M, 2008

This paper presents a new approach for solving accurate approximate analytical solution for stron... more This paper presents a new approach for solving accurate approximate analytical solution for strong nonlinear oscillators. The new algorithm offers a promising approach by Hamiltonian for the nonlinear oscillator. We find that these attained solutions are not only with high degree of accuracy, but also uniformly valid in the whole solution domain.

Experiments in Fluids, 2015

ABSTRACT A precessing jet nozzle with water as the working fluid is investigated under passive an... more ABSTRACT A precessing jet nozzle with water as the working fluid is investigated under passive and active flow control. The actuation effectiveness of 12 microjets around the nozzle inlet for active control of the precessing jet is the focus of this work. Passive control is also applied by modifying the geometry of the precessing jet either by adding a center body near the chamber exit or varying the chamber length. The flow behavior under control is studied using pressure measurement at the chamber exit plane to monitor jet precession. The pressure data are analyzed using a phase plane representation to determine the motion of the jets high-velocity region in the chamber exit plane. The standard deviation of the phase of the triggered pressure data is used for stability analysis. This analysis results in a phase diagram in terms of Reynolds number and actuation frequency. Active control can be utilized over a range of actuation frequencies (and corresponding Strouhal numbers) to control precession direction and stability which can be further enhanced with passive control mechanisms. However, the flow follows the actuation with the lowest variation when the active actuation matches with the natural Strouhal number \((0.002

2011 North American Power Symposium, 2011

ABSTRACT The permanent magnet synchronous generator (PMSG) based variable speed wind turbine is c... more ABSTRACT The permanent magnet synchronous generator (PMSG) based variable speed wind turbine is connected to the power grid via a full-scale converter. The full-scale converter presented in this paper consists of an active rectifier, an inverter and DC-DC converter for Energy Storage System (ESS). The rectifier controller uses the rotor flux oriented control (FOC) system and achieves Maximum Power Point Tracking (MPPT) which is necessary for the wind turbine to obtain maximum power conversion. The grid side controller uses a voltage oriented control system to regulate the active and reactive power dispatched to the power grid. The employed voltage source inverter (VSI) regulates the output power at desired reference value (in our case 1 pu) while keeping the output voltage in a sinusoidal waveform. The output electrical power from the PMSG is fluctuating, which is unacceptable from the standpoint of power system operation. An energy storage system (ESS) can help accommodate the difference between fluctuating wind power and that dispatched to the grid. The ESS absorbs the extra energy from the DC-link (via charging) and releases the stored energy to the DC-link when required (via discharging). The presented ESS for this paper is a Hybrid Energy Storage System (HESS) consisting of high power density supercapacitors and high energy density batteries. The HESS controller is designed to smooth and regulate the output power while help increase the battery's life. In the control system of DC-DC controller some logic gates are employed to appropriately disconnect the battery from DC-link. The system is modeled and simulated in PSCAD software.

PES T&D 2012, 2012

ABSTRACT In this paper, we introduce a new hybrid energy storage system (HESS) design for wind po... more ABSTRACT In this paper, we introduce a new hybrid energy storage system (HESS) design for wind power generation application and corresponding calculation of the proper size of the battery and supercapacitor. The design has an objective to increase the battery life time. The boundary levels of the state of charge of the battery and that of the supercapacitor are used in the control strategy. In the controller, some logic gates are also used to control the operating time durations of the battery. The sizing method is based on the average fluctuation of wind profiles of a specific wind station which consequently provides some fluctuations in the generated wind power. The calculated battery size is dependent on the size of the supercapacitor, state of charge of the supercapacitor and battery wear. To verify the presented method, two different cases are studied in PSCAD and corresponding results are provided.

2012 IEEE Power Electronics and Machines in Wind Applications, 2012

This paper proposes a trustworthy and practical approach to predict wind speed, which could be us... more This paper proposes a trustworthy and practical approach to predict wind speed, which could be used as input to predict wind power generation. In the prediction model, we applied the variable speed wind as input of this model. Then the Gaussian noise is added to the input due to existing of noise in measuring of wind speed. Kalman filtering is used as the prediction method in this study. The parameters of shaping filter are calculated using power spectral analysis and Gauss-Markov theory. Results under different time horizon of prediction are compared with actual data and the comparison shows that the results obtained using Kalman filter is reliable. The proposed method works well for an hour ahead prediction and for short-time prediction works even better. The application of Kalman filter on wind speed prediction is implemented in MATLAB software and results are provided in this paper.

2013 North American Power Symposium (NAPS), 2013

ABSTRACT In remote district without power supply from bulk electric grid, wind energy can be util... more ABSTRACT In remote district without power supply from bulk electric grid, wind energy can be utilized to generate a large quantity of power when power plants are installed in an islanded micro-grid. Due to fluctuations in wind speed and resulting variable wind power, a small-scale diesel generator assists the wind power generator in providing a stable, sustained and efficient power generation. In addition, a Battery Energy Storage System (BESS) is capable of regulating its active power output in coordination with other generators to balance dynamic power demand and supply. Since the cost and efficiency is always the first issue for the control and operation of micro-grid in remote areas, energy management becomes the primary criterion in central control unit of micro-grids. The energy management of the wind power generator in micro-grid aims to optimize the system in terms of generation, cost, and load. Due to high uncertainty and volatility of wind speed, the Dynamic Programming Method (DPM) is employed in order to reduce the impact of wind speed uncertainty and fluctuation. For this purpose, a combined short term and long term optimization is studied in this paper. Meanwhile, a micro-grid system is modeled and simulated using MATLAB software.

International Journal of Nonlinear Sciences and Numerical Simulation, 2009

In this paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a strong method to... more In this paper we apply a Modified He's Homotopy Perturbation Method (MHHPM) as a strong method to solve accurately higher-order approximate analytical solutions of coupled two-degree-of-freedom (CTDOF), which is described with a system of two coupled strong non-linear differential equations. MHHPM is modified version of He's HPM by truncating the infinite series corresponding to the first-order approximate solution before introducing this solution into the second-order linear differential equation. For the first approximation we achieve a high accuracy of solutions with a maximal relative error less than 3.14 % for small and large values of oscillation amplitude, while for the second iteration the fabulous relative error is 0.064 %. It is predicted that MHHPM can be found widely applicable in engineering which needs extremely accurate solutions.

Progress In Electromagnetics Research M, 2008

This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservativ... more This paper deals with Approximate Analytical Solutions to nonlinear oscillations of a conservative, non-natural, single-degreeof-freedom system with odd nonlinearity. By extending the Variational approach proposed by He, we established approximate analytical formulas for the period and periodic solution. To illustrate the applicability and accuracy of the method, two examples are presented: (i) the motion of a rigid rod rocking back and forth on the circular surface without slipping, and (ii) Cubic-Quintic Duffing Oscillators. Comparison of the result which is obtained by this method with the obtained result by the Exact solution reveals that the He's Variational approach is very effective and convenient and can be easily extended to other nonlinear systems and can therefore be found widely applicable in engineering and other sciences.