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eISSN 25871110 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response Edip Öztürk1 ORCID 1Gaziantep University Aeronautics and Aerospace Aeronautics and Aerospace Engineering 27310 Gaziantep Türkiye Abstract Quadcopters are widely used rotorcraft members of the UAV family Since they have four motors and four propellers they are exposed to dynamic loads and vibratory motion This study presents vibration analysis of a wellknown F450 quadcopter frame Modal analysis was performed to identify the natural frequencies and mode shapes followed by harmonic response analysis to observe the dynamic behaviour under a periodic force Harmonic response analysis frequency range covered all critical frequencies obtained by modal analysis Two additional axes in addition to hovering direction were considered in order to simulate the propeller imbalance case Numerical solution of analysis was performed by finite element method Critical frequencies were examined in terms of motor angular velocities and compared with real life motor rpm values Harmonic response analysis for Yaxis displacements revealed significant peaks near 222 Hz and 410 Hz corresponding to motor speeds of approximately 1200024000 RPM For an unbalanced propeller simulated along the Xaxis significant response peaks were observed near 277 Hz and 620 Hz corresponding to motor speeds of approximately 15000360000 RPM Similarly for the Zaxis peaks were observed near 200 Hz and 420 Hz also corresponding to motor speeds of approximately 15000360000 RPM These results indicate potential risks of structural resonance during quadcopter operation particularly under high throttle or unbalanced loading conditions Keywords modal analysis quadcopter vibration analysis harmonic response structural vibration 1 Introduction Unmanned aerial vehicles especially quadcopters are susceptible to structural vibrations that can compro mise flight stability and sensor performance Analysing the dynamic behaviour of the frame components is crit ical in enhancing durability and performance Faraz Ahmad et al investigate the vibration characteristics of a quadcopter propeller They design the 3D model of the propeller in Creo 20 and analyse it using Ansys They compare the vibration behaviour of different ma terials G10 aluminium and CFRP and determine the first 6 natural frequencies and mode shapes by modal analysis As a result they find that CFRP material ex hibits higher frequency values and is more suitable for heavy loadings1 Bhandari et al deal with modelling and vibration analysis of the quadcopter body frame by changing boundary conditions Thus the failure fre quency range can be controlled Simulation results help researchers to design quadcopter frames for heavydu ty applications2 Chen et al study the structural vibration problems of multirotor drones in order to solve the structural dam age problem of large multirotor manned drones From this study researchers find that the main vibrations of a large multirotor manned drone arm are lowfrequen cy vibrations below 200Hz and the vibrations mainly produce torsional and bending modes3 Kuantama et al performed vibration analysis using the finite ele ment method In this analysis it was investigated that the existence of rotational speeds in each propeller flow field will significantly affect the thrust efficiency which may cause flight instability or body frame vibration4 Lostaunau et al perform an analysis of the measured vibration of a quadcopter during hovering under vary ing propeller speeds and track compliance To collect data four accelerometers are mounted on the drones arm The collected data are analysed using time do main plots and spectrograms obtained from the Gabor transform5 Kalay and Özkul6 investigated the role of vibrations in Unmanned Aerial Vehicles UAVs ef ficiency measurement techniques and their effects on Corresponding author Email edipozturkgantepedutr Authors 2025 This work is distributed under httpscreativecommonsorglicensesby40 History dates Received 27042025 Revision Request 17052025 Last Revision Received 26052025 Accepted 08062025 Cite this article as Öztürk E 2025 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response European Mechanical Science 92 189195 httpsdoi org1026701ems1685031 Research Article EUROPEAN MECHANICAL SCIENCE performance using theoretical and experimental meth ods such as frequency analysis mode analysis and fi nite element analysis they understood the vibration dynamics of UAVs and achieved higher performance longer operational life and increased precision Lalem et al7 investigated AI and vibration signal process ing for anomaly detection in quadcopter systems they demonstrated the effectiveness of the combination of AI and the Internet of Things IoT to improve fault detection and problem diagnosis in UAVs by obtaining 9778 accuracy with Random Forest and Support Vec tor Machine SVM classifiers by extracting features from accelerometer data Salem et al8 investigated the vibration analysis using multilayer perceptron ar tificial neural networks MLPANN to detect rotor imbalance in quadrotor UAVs trained the MLPANN model by extracting time frequency and timefre quency domain features from accelerometer data and detected rotor imbalance with a high accuracy of up to 991In this study Geronel et al9 investigated the vibration analysis of a load connected to a quadrotor type UAV with a shape memory alloy SMA spring by analysing the natural frequencies and damping prop erties of the load they evaluated the vibration isolation and adaptive damping potential of SMA springs When the literature is examined it is easily seen that there are not many studies on quadcopter vibration analysis In this study the solid model of the wellknown F450 cod ed Figure 1 quadcopter frame is prepared and ABS material is assigned to the prepared model Figure 1 F450 quadcopter frame The frame has a cross length of 450 mm and an arm length of 210 mm ABS material has a density of 1050 kg per cubic meter volume an elastic modulus of 24 GPa and a shear modulus of 08 GPa Boundary condi tions are determined for the model and vibration and harmonic response analysis are performed As a result of these analyses the critical natural frequencies and harmonic responses for the frame are determined At the end of the study the mode shapes related to natural frequencies and the critical frequencies obtained as a result of the harmonic response are interpreted In ad dition to these the connection between the harmonic response critical frequencies and the motor speed rela tions is also mentioned 2 Materials and Methods 21 Modal Analysis Modal analysis examines the dynamic properties of a structure or system in the frequency domain Its main purpose is to determine the natural vibration frequen cies of the structure and the mode shapes correspond ing to these frequencies This analysis is critical for un derstanding how a system or a structure will respond to external forces or vibratory motions If one of the natural frequencies of a structure matches the frequency of the applied external force resonance oc curs This can lead to excessive vibrations and structural damage Modal analysis identifies these potential reso nant frequencies allowing design changes to be made 1 Modal analysis solves the mathematical free vibration equation Equation 1 and solving the eigenvalue prob lem Equation 2 gives natural frequencies and mode shapes corresponding to natural frequencies10 2 ANSYS uses the finite element method in order to dis cretize geometry into smaller elements This discreti zation enables a numerical solution of the structural dynamic equations11 Modal analysis in ANSYS begins with preparing the geometry of the quadcopter frame Since the quadcop ter frame is symmetric a single arm of the frame is suf ficient enough to perform modal analysis Singlearm geometry is isolated and in the modal analysis section boundary conditions are applied Fixed support is as signed in Figure 2 in order to model connection single arm to middle body plates Figure 2 Fixed support locations The main purpose of modal analysis is to obtain the nat ural frequencies of single arm Therefore external force European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 190 httpsdoiorg1026701ems1685031 is not applied A total of 38135 elements and 68200 nodes are generated at the end of the meshing operation Fig ure 3 Skewness is selected as a mesh quality indicator Average value of skewness is obtained as 042 and this value is sufficient enough to perform modal analysis Figure 3 Mesh view First six natural frequencies in Table 1 and mode shapes corresponding to natural frequencies are obtained Table 1 Modal analysis results Mode Frequency Hz 1 47018 2 13506 3 23777 4 27009 5 54744 6 76169 In this mode the structure essentially makes an up warddownward bending movement Figure 4 This mode represents the first frequency at which vertical vibrations from engines or external factors during flight can cause resonance Entering this frequency range es pecially during takeoff or landing can lead to vibration growth Figure 4 First mode shape In the second mode the structure exhibits bending be haviour in the horizontal plane Figure 5 This mode represents the natural frequency that can occur in side slip manoeuvres It is important to understand the lat eral vibrations of the body Figure 5 Second mode shape In this mode the structure exhibits transverse torsion al motion Figure 6 Torsional modes can often be triggered by propeller imbalance or engine vibrations Therefore engine speeds close to the frequency of the third mode should be avoided Figure 6 Third mode shape This mode acts as a combination of the previous bend ing modes with a combined bending tendency in differ ent planes Figure 7 When engines operate at high speeds these modes can also be excited creating simul taneous vibrations in various axes of the structure In the fifth mode there is more pronounced torsion and asymmetric bending Figure 8 In this mode a more complex vibration pattern is ob served in the upper part of the structure and in the pro peller mounting area Figure 9 Edip Öztürk 191 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031 Figure 7 Fourth mode shape Figure 8 Fifth mode shape Figure 9 Sixth mode shape 22 Harmonic Response Analysis Harmonic response analysis is a type of analysis used to determine the steadystate dynamic response caused by sinusoidally varying loads applied to a structure or system This analysis is critical for understanding the structures forced vibration behaviour at specific fre quencies determining resonant frequencies and am plitudes and assessing structural integrity Harmonic response analysis for a forced vibration system is mod elled as in Equation 312 3 Force is modelled as a constant amplitude sine wave Equation 4 4 System response under constant amplitude harmonic force is given in Equation 5 5 The response amplitude is calculated using the expres sion in Equation 6 6 Since the frequencies to which the system responds are important rather than the magnitude of the response given by the system in the harmonic response analysis a force of 1 N magnitude is applied as in Figure 10 In harmonic response analysis the 1 N load is a stan dardization tool to determine the frequencydependent behaviour of the system against a unit load This allows the results obtained to be easily scaled to other load ing cases and provides a clearer understanding of the dynamic properties of the system such as resonance damping and amplitude The force applied in this di rection will be used to obtain the vibration behaviours that the quadcopter will be exposed to during takeoff and landing Figure 10 Force applied in the Y axis The frequency range to be scanned in the harmon ic response analysis should be selected to include the frequencies obtained as a result of the modal analysis Therefore the frequency range is assigned as between 20 Hz and 800 Hz In order to determine the vibration response of the propeller due to the inhomogeneous mass distribution caused by production and the unex pected forces that will occur in the propeller imbalance situation harmonic response analysis is performed again by applying force in the Z direction shown in Figure 11 In a similar way harmonic response analysis is per European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 192 httpsdoiorg1026701ems1685031 formed again by applying force in the Z direction shown in Figure 12 Figure 11 Force applied in the Z axis Figure 12 Force applied in the X axis 3 Results and Discussions The modal analysis revealed the first six natural fre quencies of the isolated F450 arm made of ABS materi al These modes include bending torsional and coupled vibration shapes with the first mode appearing at ap proximately 47 Hz and the sixth mode at 761 Hz The distribution and symmetry of mode shapes are consis tent with cantileverlike boundary conditions and sug gest that excitation in certain frequency bands can lead to dynamic amplification The harmonic response anal ysis focused on Yaxis displacements which are critical for vertical stability in flight Figure 13 Significant response peaks were observed at frequencies near 222 Hz and 410 Hz These correspond to motor speeds of approximately 1200024000 RPM If the quadcopter operates in this regime resonance phenomena could amplify structural vibrations potentially affecting flight control systems or inducing fatigue An unbalanced propeller scenario was simulated along the Xaxis to investigate lateral vibrational effects Sig nificant response peaks were observed at frequencies near 277 Hz and 620 Hz Figure 14 These correspond to motor speeds of approximately 15000360000 RPM This result indicates that lateral vibrations may still influence the camera payload or sensor accuracy during highspeed manoeuvres In a similar way an unbalanced propeller scenario was simulated along the Zaxis to investigate vibrational ef fects Significant response peaks were observed at fre quencies near 200 Hz and 420 Hz Figure 15 These correspond to motor speeds of approximately 15000 Figure 13 Harmonic response for Y direction Edip Öztürk 193 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031 360000 RPM It is observed that the y data results and the z data results are very close except for the phase angle The phase angle at the peaks of the yaxis is 0 degrees while the phase angle on the zaxis is 180 degrees The phase angle is the angle between the applied force and the de formation 4 Conclusions This study conducted a detailed modal and harmonic response analysis of a single ABS arm of the F450 quad copter frame using ANSYS Modal results revealed key frequencies susceptible to resonance while harmon ic analysis showed significant amplitude peaks in the Ydirection within common motor speed ranges These results indicate potential risks of structural resonance Figure 14 Harmonic response for X direction Figure 15 Harmonic response for Z direction European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 194 httpsdoiorg1026701ems1685031 during operation especially under high throttle or un balanced loading Future studies may explore fullframe analysis in corporate motor and propeller coupling effects and validate results with experimental modal testing Optimizing the frame geometry or integrating vibra tionabsorbing materials could further improve perfor mance and durability Research ethics Not applicable Author contributions The author solely conducted all stages of this research Competing interests The author states no conflict of interest Research funding None declared Data availability Not applicable Peerreview Externally peerreviewed Orcid Edip Öztürk ORCID httpsorcidorg0000000218161553 References 1 Ahmad F et al 2019 Modeling and mechanical vibration chara cteristics analysis of a quadcopter propeller using FEA IOP Confe rence Series Materials Science and Engineering IOP Publishing 2 Bhandari A et al 2019 Design and vibration characteristics analy sis of quadcopter body frame International Journal of Applied Engi neering Research 149 6670 3 Chen K et al 2023 An investigation on the structural vibrations of multirotor passenger drones International Journal of Micro Air Vehicles 15 17568293231199097 4 Kuantama E Craciun D Tarca R 2016 Quadcopter body fra me model and analysis Annals of the University of Oradea 7174 5 Lostaunau O et al 2024 Analysis of quadcopter body frame vib ration during hovering flight with variable rotor speeds In 2024 8th International Symposium on Instrumentation Systems Circuits and Transducers INSCIT IEEE 6 Kalay E Özkul İ 2024 İnsansız hava araçlarında titreşimlerin rolü verimlilik ölçüm teknikleri ve performans etkileri Turkey Un manned Aerial Vehicle Journal Türkiye İnsansız Hava Araçları Der gisi 62 7 Lalem M S E I Ouadah M Touhami O 2024 Anomaly detec tion in quadcopter systems using AI and vibration signal processing 8 Abdullah Salem B T S et al 2025 Vibration analysis using mul tilayer perceptron neural networks for rotor imbalance detection in quadrotor UAV Drones 92 102 9 Geronel R S Bueno D Botez R M 2022 Vibration analysis of a payload connected to quadrotortype UAV by SMA spring In AIAA SciTech 2022 Forum 10 Rao S S Yap F F 1995 Mechanical vibrations Vol 4 Addi sonWesley 11 Bhavikatti S 2005 Finite element analysis New Age International 12 Rao S S 2019 Vibration of continuous systems John Wiley Sons Edip Öztürk 195 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031
Texto de pré-visualização
eISSN 25871110 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response Edip Öztürk1 ORCID 1Gaziantep University Aeronautics and Aerospace Aeronautics and Aerospace Engineering 27310 Gaziantep Türkiye Abstract Quadcopters are widely used rotorcraft members of the UAV family Since they have four motors and four propellers they are exposed to dynamic loads and vibratory motion This study presents vibration analysis of a wellknown F450 quadcopter frame Modal analysis was performed to identify the natural frequencies and mode shapes followed by harmonic response analysis to observe the dynamic behaviour under a periodic force Harmonic response analysis frequency range covered all critical frequencies obtained by modal analysis Two additional axes in addition to hovering direction were considered in order to simulate the propeller imbalance case Numerical solution of analysis was performed by finite element method Critical frequencies were examined in terms of motor angular velocities and compared with real life motor rpm values Harmonic response analysis for Yaxis displacements revealed significant peaks near 222 Hz and 410 Hz corresponding to motor speeds of approximately 1200024000 RPM For an unbalanced propeller simulated along the Xaxis significant response peaks were observed near 277 Hz and 620 Hz corresponding to motor speeds of approximately 15000360000 RPM Similarly for the Zaxis peaks were observed near 200 Hz and 420 Hz also corresponding to motor speeds of approximately 15000360000 RPM These results indicate potential risks of structural resonance during quadcopter operation particularly under high throttle or unbalanced loading conditions Keywords modal analysis quadcopter vibration analysis harmonic response structural vibration 1 Introduction Unmanned aerial vehicles especially quadcopters are susceptible to structural vibrations that can compro mise flight stability and sensor performance Analysing the dynamic behaviour of the frame components is crit ical in enhancing durability and performance Faraz Ahmad et al investigate the vibration characteristics of a quadcopter propeller They design the 3D model of the propeller in Creo 20 and analyse it using Ansys They compare the vibration behaviour of different ma terials G10 aluminium and CFRP and determine the first 6 natural frequencies and mode shapes by modal analysis As a result they find that CFRP material ex hibits higher frequency values and is more suitable for heavy loadings1 Bhandari et al deal with modelling and vibration analysis of the quadcopter body frame by changing boundary conditions Thus the failure fre quency range can be controlled Simulation results help researchers to design quadcopter frames for heavydu ty applications2 Chen et al study the structural vibration problems of multirotor drones in order to solve the structural dam age problem of large multirotor manned drones From this study researchers find that the main vibrations of a large multirotor manned drone arm are lowfrequen cy vibrations below 200Hz and the vibrations mainly produce torsional and bending modes3 Kuantama et al performed vibration analysis using the finite ele ment method In this analysis it was investigated that the existence of rotational speeds in each propeller flow field will significantly affect the thrust efficiency which may cause flight instability or body frame vibration4 Lostaunau et al perform an analysis of the measured vibration of a quadcopter during hovering under vary ing propeller speeds and track compliance To collect data four accelerometers are mounted on the drones arm The collected data are analysed using time do main plots and spectrograms obtained from the Gabor transform5 Kalay and Özkul6 investigated the role of vibrations in Unmanned Aerial Vehicles UAVs ef ficiency measurement techniques and their effects on Corresponding author Email edipozturkgantepedutr Authors 2025 This work is distributed under httpscreativecommonsorglicensesby40 History dates Received 27042025 Revision Request 17052025 Last Revision Received 26052025 Accepted 08062025 Cite this article as Öztürk E 2025 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response European Mechanical Science 92 189195 httpsdoi org1026701ems1685031 Research Article EUROPEAN MECHANICAL SCIENCE performance using theoretical and experimental meth ods such as frequency analysis mode analysis and fi nite element analysis they understood the vibration dynamics of UAVs and achieved higher performance longer operational life and increased precision Lalem et al7 investigated AI and vibration signal process ing for anomaly detection in quadcopter systems they demonstrated the effectiveness of the combination of AI and the Internet of Things IoT to improve fault detection and problem diagnosis in UAVs by obtaining 9778 accuracy with Random Forest and Support Vec tor Machine SVM classifiers by extracting features from accelerometer data Salem et al8 investigated the vibration analysis using multilayer perceptron ar tificial neural networks MLPANN to detect rotor imbalance in quadrotor UAVs trained the MLPANN model by extracting time frequency and timefre quency domain features from accelerometer data and detected rotor imbalance with a high accuracy of up to 991In this study Geronel et al9 investigated the vibration analysis of a load connected to a quadrotor type UAV with a shape memory alloy SMA spring by analysing the natural frequencies and damping prop erties of the load they evaluated the vibration isolation and adaptive damping potential of SMA springs When the literature is examined it is easily seen that there are not many studies on quadcopter vibration analysis In this study the solid model of the wellknown F450 cod ed Figure 1 quadcopter frame is prepared and ABS material is assigned to the prepared model Figure 1 F450 quadcopter frame The frame has a cross length of 450 mm and an arm length of 210 mm ABS material has a density of 1050 kg per cubic meter volume an elastic modulus of 24 GPa and a shear modulus of 08 GPa Boundary condi tions are determined for the model and vibration and harmonic response analysis are performed As a result of these analyses the critical natural frequencies and harmonic responses for the frame are determined At the end of the study the mode shapes related to natural frequencies and the critical frequencies obtained as a result of the harmonic response are interpreted In ad dition to these the connection between the harmonic response critical frequencies and the motor speed rela tions is also mentioned 2 Materials and Methods 21 Modal Analysis Modal analysis examines the dynamic properties of a structure or system in the frequency domain Its main purpose is to determine the natural vibration frequen cies of the structure and the mode shapes correspond ing to these frequencies This analysis is critical for un derstanding how a system or a structure will respond to external forces or vibratory motions If one of the natural frequencies of a structure matches the frequency of the applied external force resonance oc curs This can lead to excessive vibrations and structural damage Modal analysis identifies these potential reso nant frequencies allowing design changes to be made 1 Modal analysis solves the mathematical free vibration equation Equation 1 and solving the eigenvalue prob lem Equation 2 gives natural frequencies and mode shapes corresponding to natural frequencies10 2 ANSYS uses the finite element method in order to dis cretize geometry into smaller elements This discreti zation enables a numerical solution of the structural dynamic equations11 Modal analysis in ANSYS begins with preparing the geometry of the quadcopter frame Since the quadcop ter frame is symmetric a single arm of the frame is suf ficient enough to perform modal analysis Singlearm geometry is isolated and in the modal analysis section boundary conditions are applied Fixed support is as signed in Figure 2 in order to model connection single arm to middle body plates Figure 2 Fixed support locations The main purpose of modal analysis is to obtain the nat ural frequencies of single arm Therefore external force European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 190 httpsdoiorg1026701ems1685031 is not applied A total of 38135 elements and 68200 nodes are generated at the end of the meshing operation Fig ure 3 Skewness is selected as a mesh quality indicator Average value of skewness is obtained as 042 and this value is sufficient enough to perform modal analysis Figure 3 Mesh view First six natural frequencies in Table 1 and mode shapes corresponding to natural frequencies are obtained Table 1 Modal analysis results Mode Frequency Hz 1 47018 2 13506 3 23777 4 27009 5 54744 6 76169 In this mode the structure essentially makes an up warddownward bending movement Figure 4 This mode represents the first frequency at which vertical vibrations from engines or external factors during flight can cause resonance Entering this frequency range es pecially during takeoff or landing can lead to vibration growth Figure 4 First mode shape In the second mode the structure exhibits bending be haviour in the horizontal plane Figure 5 This mode represents the natural frequency that can occur in side slip manoeuvres It is important to understand the lat eral vibrations of the body Figure 5 Second mode shape In this mode the structure exhibits transverse torsion al motion Figure 6 Torsional modes can often be triggered by propeller imbalance or engine vibrations Therefore engine speeds close to the frequency of the third mode should be avoided Figure 6 Third mode shape This mode acts as a combination of the previous bend ing modes with a combined bending tendency in differ ent planes Figure 7 When engines operate at high speeds these modes can also be excited creating simul taneous vibrations in various axes of the structure In the fifth mode there is more pronounced torsion and asymmetric bending Figure 8 In this mode a more complex vibration pattern is ob served in the upper part of the structure and in the pro peller mounting area Figure 9 Edip Öztürk 191 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031 Figure 7 Fourth mode shape Figure 8 Fifth mode shape Figure 9 Sixth mode shape 22 Harmonic Response Analysis Harmonic response analysis is a type of analysis used to determine the steadystate dynamic response caused by sinusoidally varying loads applied to a structure or system This analysis is critical for understanding the structures forced vibration behaviour at specific fre quencies determining resonant frequencies and am plitudes and assessing structural integrity Harmonic response analysis for a forced vibration system is mod elled as in Equation 312 3 Force is modelled as a constant amplitude sine wave Equation 4 4 System response under constant amplitude harmonic force is given in Equation 5 5 The response amplitude is calculated using the expres sion in Equation 6 6 Since the frequencies to which the system responds are important rather than the magnitude of the response given by the system in the harmonic response analysis a force of 1 N magnitude is applied as in Figure 10 In harmonic response analysis the 1 N load is a stan dardization tool to determine the frequencydependent behaviour of the system against a unit load This allows the results obtained to be easily scaled to other load ing cases and provides a clearer understanding of the dynamic properties of the system such as resonance damping and amplitude The force applied in this di rection will be used to obtain the vibration behaviours that the quadcopter will be exposed to during takeoff and landing Figure 10 Force applied in the Y axis The frequency range to be scanned in the harmon ic response analysis should be selected to include the frequencies obtained as a result of the modal analysis Therefore the frequency range is assigned as between 20 Hz and 800 Hz In order to determine the vibration response of the propeller due to the inhomogeneous mass distribution caused by production and the unex pected forces that will occur in the propeller imbalance situation harmonic response analysis is performed again by applying force in the Z direction shown in Figure 11 In a similar way harmonic response analysis is per European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 192 httpsdoiorg1026701ems1685031 formed again by applying force in the Z direction shown in Figure 12 Figure 11 Force applied in the Z axis Figure 12 Force applied in the X axis 3 Results and Discussions The modal analysis revealed the first six natural fre quencies of the isolated F450 arm made of ABS materi al These modes include bending torsional and coupled vibration shapes with the first mode appearing at ap proximately 47 Hz and the sixth mode at 761 Hz The distribution and symmetry of mode shapes are consis tent with cantileverlike boundary conditions and sug gest that excitation in certain frequency bands can lead to dynamic amplification The harmonic response anal ysis focused on Yaxis displacements which are critical for vertical stability in flight Figure 13 Significant response peaks were observed at frequencies near 222 Hz and 410 Hz These correspond to motor speeds of approximately 1200024000 RPM If the quadcopter operates in this regime resonance phenomena could amplify structural vibrations potentially affecting flight control systems or inducing fatigue An unbalanced propeller scenario was simulated along the Xaxis to investigate lateral vibrational effects Sig nificant response peaks were observed at frequencies near 277 Hz and 620 Hz Figure 14 These correspond to motor speeds of approximately 15000360000 RPM This result indicates that lateral vibrations may still influence the camera payload or sensor accuracy during highspeed manoeuvres In a similar way an unbalanced propeller scenario was simulated along the Zaxis to investigate vibrational ef fects Significant response peaks were observed at fre quencies near 200 Hz and 420 Hz Figure 15 These correspond to motor speeds of approximately 15000 Figure 13 Harmonic response for Y direction Edip Öztürk 193 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031 360000 RPM It is observed that the y data results and the z data results are very close except for the phase angle The phase angle at the peaks of the yaxis is 0 degrees while the phase angle on the zaxis is 180 degrees The phase angle is the angle between the applied force and the de formation 4 Conclusions This study conducted a detailed modal and harmonic response analysis of a single ABS arm of the F450 quad copter frame using ANSYS Modal results revealed key frequencies susceptible to resonance while harmon ic analysis showed significant amplitude peaks in the Ydirection within common motor speed ranges These results indicate potential risks of structural resonance Figure 14 Harmonic response for X direction Figure 15 Harmonic response for Z direction European Mechanical Science 2025 92 Unravelling quadcopter frame dynamics A study on vibration analysis and harmonic response 194 httpsdoiorg1026701ems1685031 during operation especially under high throttle or un balanced loading Future studies may explore fullframe analysis in corporate motor and propeller coupling effects and validate results with experimental modal testing Optimizing the frame geometry or integrating vibra tionabsorbing materials could further improve perfor mance and durability Research ethics Not applicable Author contributions The author solely conducted all stages of this research Competing interests The author states no conflict of interest Research funding None declared Data availability Not applicable Peerreview Externally peerreviewed Orcid Edip Öztürk ORCID httpsorcidorg0000000218161553 References 1 Ahmad F et al 2019 Modeling and mechanical vibration chara cteristics analysis of a quadcopter propeller using FEA IOP Confe rence Series Materials Science and Engineering IOP Publishing 2 Bhandari A et al 2019 Design and vibration characteristics analy sis of quadcopter body frame International Journal of Applied Engi neering Research 149 6670 3 Chen K et al 2023 An investigation on the structural vibrations of multirotor passenger drones International Journal of Micro Air Vehicles 15 17568293231199097 4 Kuantama E Craciun D Tarca R 2016 Quadcopter body fra me model and analysis Annals of the University of Oradea 7174 5 Lostaunau O et al 2024 Analysis of quadcopter body frame vib ration during hovering flight with variable rotor speeds In 2024 8th International Symposium on Instrumentation Systems Circuits and Transducers INSCIT IEEE 6 Kalay E Özkul İ 2024 İnsansız hava araçlarında titreşimlerin rolü verimlilik ölçüm teknikleri ve performans etkileri Turkey Un manned Aerial Vehicle Journal Türkiye İnsansız Hava Araçları Der gisi 62 7 Lalem M S E I Ouadah M Touhami O 2024 Anomaly detec tion in quadcopter systems using AI and vibration signal processing 8 Abdullah Salem B T S et al 2025 Vibration analysis using mul tilayer perceptron neural networks for rotor imbalance detection in quadrotor UAV Drones 92 102 9 Geronel R S Bueno D Botez R M 2022 Vibration analysis of a payload connected to quadrotortype UAV by SMA spring In AIAA SciTech 2022 Forum 10 Rao S S Yap F F 1995 Mechanical vibrations Vol 4 Addi sonWesley 11 Bhavikatti S 2005 Finite element analysis New Age International 12 Rao S S 2019 Vibration of continuous systems John Wiley Sons Edip Öztürk 195 European Mechanical Science 2025 92 httpsdoiorg1026701ems1685031