模态分析实验：刚性锤端宽频带低幅值激发特性成因问询

Great question—this boils down to the physics of impulse signals and mechanical impedance matching between the hammer and the test structure. Let’s break it into key, easy-to-grasp points:

• Impulse frequency content depends entirely on rise time
  A hammer strike delivers an impulse to the structure. From basic Fourier transform principles: the shorter an impulse's rise time, the wider its frequency bandwidth. A rigid tip (like steel) barely deforms on impact, so the contact time is extremely short, creating a sharp, fast-spiking impulse. This sharp impulse carries energy across a broad range of frequencies. In contrast, a soft tip (rubber, foam) deforms significantly, lengthening contact time and producing a slower, rounded impulse—this limits energy to only lower frequencies.

• Fixed energy gets spread thinner across wider bands
  When you apply "equal energy" hammer strikes, the total energy input to the system stays constant. For a rigid tip, that fixed energy has to be distributed across a much broader frequency spectrum. Think of it like pouring the same amount of water into a wide bucket vs. a narrow one: the wide bucket (broad frequency band) will have a lower "level" (amplitude) at any single point. A soft tip concentrates all that energy into a narrow low-frequency range, so those frequencies get a much higher amplitude boost.

• Impedance mismatch reduces per-frequency energy transfer
  Rigid hammers have far higher mechanical impedance (stiffness + mass) compared to most test structures. This mismatch makes the hammer bounce off quickly—while it excites many frequencies, the energy transferred to any individual frequency band is relatively low. Soft tips have lower impedance that matches better with the structure’s impedance at low frequencies; this longer contact time lets more energy transfer specifically to those low-frequency modes, resulting in higher amplitude responses.

If you want to see this in action, record the force signal from the hammer’s built-in load cell for both tip types. You’ll spot the rigid tip’s force pulse as narrow and sharp, while the soft tip’s is wider and peaks higher in the low-frequency range.

内容的提问来源于stack exchange，提问作者H. Vabri