Mechanical Vibrations Calculators
Free and forced vibration, isolation, critical speed, dynamic absorbers, FFT analysis, multi-DOF systems
Mechanical Vibrations covers free and forced vibration, isolation, critical speed, dynamic absorbers, fft analysis, multi-dof systems.
This engineering course provides rigorous analysis tools for vibrations problems encountered in professional practice. Students work through both theoretical derivations and applied numerical examples to build the quantitative skills needed in industry.
The tools and techniques developed in Vibrations are applied daily by practicing engineers and form essential prerequisites for advanced coursework and professional engineering practice.
Key Concepts
- •Core theory and principles of vibrations
- •Applied problem-solving using industry-standard methods
- •Quantitative analysis with real engineering units and magnitudes
- •Connections to other engineering disciplines
Prerequisites
Calculus
Most engineering analysis courses require differential and integral calculus.
Introductory Physics
Familiarity with basic mechanics and energy concepts provides context for engineering-level analysis.
Vibrations Calculators
Free Vibration SDOF Calculator
Natural frequency, damping ratio, and free response of a single-DOF spring-mass-damper system with decay envelope plot
Forced Vibration SDOF Calculator
Steady-state amplitude ratio, phase angle, and frequency response for harmonically forced SDOF systems
Vibration Isolation Calculator
Transmissibility, isolation efficiency, and required mount stiffness for vibration isolation systems
Critical Speed Calculator
First critical speed of a rotating shaft with disk masses using Dunkerley's and Rayleigh's methods
Dynamic Vibration Absorber Calculator
Design a tuned mass damper: optimal absorber tuning, anti-resonance frequency, and primary system response
2-DOF Natural Frequencies Calculator
Natural frequencies, mode shapes, and frequency response for a 2-degree-of-freedom spring-mass system
FFT Analyzer Calculator
FFT magnitude spectrum, dominant frequencies, and THD from generated or custom time-domain signals
Whirling Shaft Critical Speed Calculator
Critical whirling speed of a shaft with mounted disks using Rayleigh's energy method, with deflection shape plot
Vibration Measurement Calculator
Convert between acceleration, velocity, and displacement; peak/RMS conversions; ISO 10816 severity classification
Seismic Instrument Calculator
Instrument response ratio, phase error, and operating range recommendations for seismometers and accelerometers