Roman Starosta - Academia.edu (original) (raw)

Papers by Roman Starosta

Research paper thumbnail of Nonlinear vibrations of rotating system near resonance

Vibrations in Physical Systems, 2014

Research paper thumbnail of The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

Applied Sciences, 2022

This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three... more This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system...

Research paper thumbnail of Periodic Vibrations of Nano/Micro Plates

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Oscillator with a Springs-in-Series

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Nonlinear vibrations of rotating system near resonance

Vibrations in Physical Systems, 2014

Research paper thumbnail of Asymptotic Multiple Scale Method in Time Domain

Research paper thumbnail of The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

Applied Sciences, 2022

This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three... more This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system...

Research paper thumbnail of Spring Pendulum Revisited

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Periodic Vibrations of Nano/Micro Plates

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Kinematically Excited Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Oscillator with a Springs-in-Series

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Asymptotic Multiple Scale Method in Time Domain

Research paper thumbnail of Spring Pendulum Revisited

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Resonance in the Cart-Pendulum System—An Asymptotic Approach

Applied Sciences, 2021

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-p... more The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instabi...

Research paper thumbnail of Kinematically Excited Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Nonlinear vibration of a lumped system with springs-in-series

Meccanica, 2020

The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear spr... more The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping are included into considerations. The mathematical model contains both differential and algebraic equations, so it belongs to the class of dynamical systems governed by the differential–algebraic system of equations (DAEs). An approximate analytical approach is used to solve the initial value problem for the DAEs. We adopt the multiple scales method (MSM) that allows one to obtain the sufficiently correct approximate solutions both far from the resonance and at the resonance conditions. The steady and non-steady resonant vibrations are analyzed by employing the modulation equations of the amplitudes and phases which are yielded by the MSM procedure.

Research paper thumbnail of Resonance in the Cart-Pendulum System—An Asymptotic Approach

Applied Sciences, 2021

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-p... more The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instabi...

Research paper thumbnail of Optimization of the Geometry of Aeroelastic Energy Harvester

Springer Proceedings in Mathematics & Statistics, 2022

Research paper thumbnail of Nonlinear vibrations of rotating system near resonance

Vibrations in Physical Systems, 2014

Research paper thumbnail of The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

Applied Sciences, 2022

This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three... more This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system...

Research paper thumbnail of Periodic Vibrations of Nano/Micro Plates

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Oscillator with a Springs-in-Series

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Nonlinear vibrations of rotating system near resonance

Vibrations in Physical Systems, 2014

Research paper thumbnail of Asymptotic Multiple Scale Method in Time Domain

Research paper thumbnail of The Stability Analysis of a Vibrating Auto-Parametric Dynamical System Near Resonance

Applied Sciences, 2022

This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three... more This paper examines a new vibrating dynamical motion of a novel auto-parametric system with three degrees of freedom. It consists of a damped Duffing oscillator as a primary system attached to a damped spring pendulum as a secondary system. Lagrange’s equations are utilized to acquire the equations of motion according to the number of the system’s generalized coordinates. The perturbation technique of multiple scales is applied to provide the solutions to these equations up to a higher order of approximations, with the aim of obtaining more accurate novel results. The categorizations of resonance cases are presented, in which the case of primary external resonance is examined to demonstrate the conditions of solvability of the steady-state solutions and the equations of modulation. The time histories of the achieved solutions, the resonance curves in terms of the modified amplitudes and phases, and the regions of stability are outlined for various parameters of the considered system...

Research paper thumbnail of Spring Pendulum Revisited

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Periodic Vibrations of Nano/Micro Plates

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Kinematically Excited Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Oscillator with a Springs-in-Series

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Asymptotic Multiple Scale Method in Time Domain

Research paper thumbnail of Spring Pendulum Revisited

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Resonance in the Cart-Pendulum System—An Asymptotic Approach

Applied Sciences, 2021

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-p... more The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instabi...

Research paper thumbnail of Kinematically Excited Spring Pendulum

Asymptotic Multiple Scale Method in Time Domain, 2022

Research paper thumbnail of Nonlinear vibration of a lumped system with springs-in-series

Meccanica, 2020

The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear spr... more The paper deals with the dynamics of a lumped mass mechanical system containing two nonlinear springs connected in series. The external harmonic excitation, linear and nonlinear damping are included into considerations. The mathematical model contains both differential and algebraic equations, so it belongs to the class of dynamical systems governed by the differential–algebraic system of equations (DAEs). An approximate analytical approach is used to solve the initial value problem for the DAEs. We adopt the multiple scales method (MSM) that allows one to obtain the sufficiently correct approximate solutions both far from the resonance and at the resonance conditions. The steady and non-steady resonant vibrations are analyzed by employing the modulation equations of the amplitudes and phases which are yielded by the MSM procedure.

Research paper thumbnail of Resonance in the Cart-Pendulum System—An Asymptotic Approach

Applied Sciences, 2021

The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-p... more The major objective of this research is to study the planar dynamical motion of 2DOF of an auto-parametric pendulum attached with a damped system. Using Lagrange’s equations in terms of generalized coordinates, the fundamental equations of motion (EOM) are derived. The method of multiple scales (MMS) is applied to obtain the approximate solutions of these equations up to the second order of approximation. Resonance cases are classified, in which the primary external and internal resonance are investigated simultaneously to establish both the solvability conditions and the modulation equations. In the context of the stability conditions of these solutions, the equilibrium points are obtained and graphically displayed to derive the probable steady-state solutions near the resonances. The temporal histories of the attained results, the amplitude, and the phases of the dynamical system are depicted in graphs to describe the motion of the system at any instance. The stability and instabi...

Research paper thumbnail of Optimization of the Geometry of Aeroelastic Energy Harvester

Springer Proceedings in Mathematics & Statistics, 2022