Resonance Mitigation through Frequency-Constrained Topology Optimization: An Alternative Structural Design Strategy

Abstract

A sub frame is an intermediate structure between vehicle chassis and various functional subsystems. Unlike conventional approach of designing a structure free from external vibration excitations, topology optimisation using Solid Isotropic Material with Penalisation (SIMP) model is used to redistribute the material on the sub frame through constraining mass and eigen frequencies within desired limit to achieve resonance free structure. A comparative study is carried out to evaluate the distribution of material on the sub frame of road transporter vehicle (RTV) to develop a high stiff sub frame with minimum weight considering dynamic properties. The sub frame is subjected to steady state forced vibrations and subsequently its functional performance is studied and improvised through frequency-constrained topology optimization (Dynamic Topology Optimisation). Manufacturing aspects of sub frame is considered while performing topology optimisation in Finite Element Analysis tool.

Introduction

The main objective is to improve the strength-to-weight ratio of the subframe while minimizing vibration-induced failure under steady-state forced vibrations. The subframe acts as the structural base connecting key subsystems and is exposed to harmonic excitation from rotating equipment, which can lead to resonance and fatigue damage, especially at critical payload-supporting regions.

To address this, the study applies density-based topology optimisation (SIMP) with mass constraints and eigenfrequency constraints to redistribute material in the subframe. This helps shift natural frequencies away from excitation frequencies of onboard machinery (around 30 Hz), thereby reducing resonance risk. The formulation includes compliance minimization, stiffness-mass relationships, and eigenvalue-based frequency constraints.

The system is modeled using finite element analysis (ANSYS), where subsystems are represented as point masses and the subframe is discretized using hexahedral elements. Static analysis is performed under load, followed by modal and frequency response analysis to identify natural frequencies and vibration behavior. Optimization targets a mass retention of about 20–23% of the original subframe mass while maintaining structural integrity.

The literature review shows that topology optimization (especially SIMP and ESO methods) is widely used for structural optimization and vibration control, but limited research exists on steady-state forced vibration mitigation using frequency-constrained topology optimization, which this study addresses.

Conclusion

A comparative study was conducted to investigate the design limitations of mechanical structures subjected to vibration loads. An alternative approach is proposed to achieve a resonance-free structure by redistributing material while considering mass and dynamic characteristics as constraints in topology optimization. In this study, the SIMP method with frequency constraints was employed to develop a sub-frame with a high strength-to-weight ratio and free from critical modes and resonant frequencies. once the optimal material distribution was obtained, a manufactural design considering practical fabrication constraints was developed and validated through linear static stress analysis. The initial rectangular sub-frame, with a mass of 47,262 kg, exhibited a maximum stress of 5.52 MPa under 1g static loading with all subsystems mounted on it. In contrast, the dynamically optimized sub-frame, under identical boundary conditions, showed a maximum stress of 102.34 MPa against a material yield strength of 690 MPa, with a significantly reduced mass of 5,792 kg. This corresponds to an 87.74% reduction in sub-frame mass with only a moderate increase in stress. Modal and harmonic analyses were performed to evaluate the real-time dynamic effects induced by on board rotating machinery. Although the final stress levels, mass, and shape of the optimized sub-frame may vary depending on the initial dimensions and mass retention criteria, the proposed methodology demonstrates a novel design procedure beyond conventional topology optimization practices.

References

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Copyright

Copyright © 2026 Abhishek Ranjan Singh, Vinaykumar Rokade. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.