Forced Vibration & Resonance Workstation Frame
Provides rigid calibrated mounting, regulated excitation, and alignment for frequency response function (frf), phase angle 90° at resonance & transmissibility.
Mechanical Engineering / Forced Vibration & Resonance
FREE TO EXPLORELABORATORY 30 · MECHANICAL ENGINEERING
Harmonic Base-Excited Forced Vibration, Dynamic Magnification Factor (Q), and Resonance
Excite a single-degree-of-freedom mechanical resonator with an eccentric motor shaker, evaluating steady-state displacement amplitudes, phase lag angles, and resonance peak magnification. Explore interactive mechanical simulation, stress-strain telemetry, and continuum mechanics.
SOLID MECHANICS · FLUID MECHANICS · THERMODYNAMICS · DYNAMICS & VIBRATIONS · MACHINE DESIGN · MECHATRONICS & HVAC
Your virtual mechanical engineering laboratory.
RESONANT STEADY-STATE AMPLITUDE X_0—
CALIBRATED STRAIN & DYNAMOMETER TELEMETRY
Ready to sample with Excitation Force F_0 = 15.0 N.
Adjust Excitation Force F_0, then execute mechanical acquisition.
Mechanical measurements are captured using precision transducers and 64-bit IEEE 754 floating-point logging. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support comprehensive stress, thermal, and dynamical evaluation.
Mechanical engineering continuum and boundary limits
All structural components assume isotropic linear elastic behavior within small-strain deformation limits. Fluid flow fields comply with Navier-Stokes continuum conservation under negligible thermal dissipation.
Laboratory apparatus & testing equipment.
Digital Load Cell & S-Beam Force Transducer (Class 0.5)
Measures applied axial, transverse, or shear mechanical forces with ±0.05% baseline accuracy.
Linear Variable Differential Transformer (LVDT) & Dial Indicator
Quantifies minute mechanical displacements, elastic deflections, and strain elongations with 0.001 mm resolution.
High-Speed Multi-Channel Digital Telemetry Data Logger
Samples strain gauge bridge signals, load cell voltages, temperature probes, and pressure transducers at 1 kHz.
Calibrated Reference Standard & Shunt Calibration Box
Supplies verified physical calibration benchmarks to establish standardized excitation force f_0 setpoints.
Four-Terminal Shielded Lead Wiring & Grounded Sensor Cabling
Eliminates thermal EMF drift, lead wire resistance errors, and ambient mechanical vibration noise.
FOLLOW THE METHOD
A reason behind every step.
Excite a single-degree-of-freedom mechanical resonator with an eccentric motor shaker, evaluating steady-state displacement amplitudes, phase lag angles, and resonance peak magnification. Standardized parameter settings: 5.0, 10.0, 15.0, 20.0, 25.0, 30.0 N.
- Visual Inspection & Apparatus Zero Tare: Inspect all mechanical fixtures, load train alignments, safety cages, and hydraulic/electrical connections. Execute zero tare on digital indicators and balance the measurement bridge.
- Initial Calibration & Datum Alignment: Apply a minor pre-load to eliminate mechanical backlash and seating slack. Calibrate the excitation force f_0 against the primary standard datum.
- Systematic Parameter Variation & Settling: Increment the excitation force f_0 systematically across the designated experimental range (5.0 to 30.0 N), permitting mechanical and thermal equilibrium at each step.
- Multi-Sensor Telemetry Acquisition: Record the primary dependent variable (Resonant Steady-State Amplitude X_0) alongside auxiliary channel telemetry. Verify linear proportionality and signal stability before advancing.
- Forward & Reverse Hysteresis Verification: Execute both ascending loading and descending unloading sequences to detect any friction lag, mechanical backlash, or permanent plastic deformation in the test assembly.
- Controlled De-Energization & Data Archival: Release all mechanical loads smoothly to zero, de-energize primary drives, secure moving linkages, and export all digital telemetry observations to the persistent laboratory notebook.
YOUR NOTEBOOK · 0 OBSERVATIONS
Turn measurements into mechanical engineering insight.
Points are your recorded observations. The solid regression line validates Forced Vibration & Resonance mathematical scaling.
LINEAR REGRESSION FIT · y = mx + b
X_0 = 0.4500 · F_0
| # | Harmonic Excitation Force Amplitude F_0 (N) | Resonant Steady-State Amplitude X_0 (mm) | Harmonic excitation force F_0 (N) | Resonant amplitude X_0 (mm) |
|---|
No readings yet. Execute a mechanical trial and record it.
CHECK YOUR UNDERSTANDING
Explain what the mechanical engineering metrics mean.
Question 1: In the experimental study of Forced Vibration & Resonance, the primary dependent variable measured is:
The experimental protocol directly measures Resonant Steady-State Amplitude X_0 as a function of the manipulated Excitation Force F_0.
Question 2: The governing mathematical constitutive equation for Forced Vibration & Resonance is modeled as:
Linear regression across calibrated observations confirms the governing equation X_0 = 0.4500 · F_0 with R² > 0.999.
Question 3: The target benchmark parameter derived from regression analysis is:
The experimental slope and intercept directly yield Resonant Mechanical Admittance Q/k with a theoretical reference value of 0.45 mm/N.
Question 4: Which transducer principle provides high-accuracy measurement of minute structural deflections and strain?
LVDT inductive transducers and bonded piezoresistive foil strain gauges provide sub-micron resolution for precision structural deflection and strain measurement.
THEORY AND CONTINUUM CONTEXT
Mechanical Engineering background & physical principles.
Excite a single-degree-of-freedom mechanical resonator with an eccentric motor shaker, evaluating steady-state displacement amplitudes, phase lag angles, and resonance peak magnification.
X_0 = 0.4500 · F_0
Mechanical engineering principles build upon continuum mechanics, thermodynamics, fluid dynamics, and rigid-body kinetics.