Application Cases

Experiment Name: Application of High-Voltage Amplifier in Inverse Electromechanical Research on Bone

Research Direction: Biomedical Engineering

Test Objective:
Collagen and hydroxyapatite in bone are unevenly distributed along its thickness. When a DC voltage is applied to a bone specimen, conduction currents within the specimen cause its internal temperature to rise. The resulting inconsistent thermal deformation of different components leads to bending of the specimen. The deformation response of bone under an electric field directly reflects its polarization characteristics within the field. The conclusions drawn above not only deepen the understanding of the electromechanical properties of bone but also hold reference significance for the treatment and rehabilitation of orthopedic conditions. The ultimate goal of exploring the (inverse) electromechanical properties of bone is to explain the mechanism by which these properties influence bone remodeling, thereby providing technical and theoretical support for the design of medical devices used in clinical treatment of bone diseases or for the development of  alternative materials .

Testing Equipment: ATA-2081 High-Voltage Amplifier, Signal Generator, etc.

Experimental Procedure:

Figure: Schematic Diagram of the Experimental Test System

A schematic diagram of the experimental test system is shown above. The lower end of the bone specimen is clamped, leaving the other end free, forming a vertically placed cantilever beam with a span of 65 mm. The signal generator is connected to the high-voltage amplifier (ATA-2081), forming a voltage source capable of outputting various waveform signals with a peak-to-peak voltage range of -400 to 400 V and a frequency range of 0 to 60 MHz. The output terminals of the high-voltage amplifier are connected to the lead wires attached to the two side surfaces of the bone cantilever beam specimen. By setting the waveform, frequency of the output signal from the signal amplifier, and the amplification factor of the high-voltage amplifier, a series of swept-frequency voltages within a given frequency range can be applied to the bone cantilever beam specimen, as can a single fixed-frequency, fixed-amplitude voltage. Preliminary experiments revealed that after applying an alternating voltage to the bone specimen, the specimen vibrates under the influence of the alternating electric field generated within it. A single-point laser vibrometer system is used to measure the vibration displacement of the bone specimen under voltage excitation. This vibrometer has high precision, with a displacement resolution reaching 0.1 pm. To  eliminate the influence of the external environment on the test, the bone specimen, fixture, and the laser scanning probe of the vibrometer are placed on an optical anti-vibration table. The specimen and fixture are placed on a height-adjustable stage fixed to the optical table. By adjusting the height stage, the laser emitted by the laser scanning probe is directed onto the blank area  at the upper part of the specimen, allowing measurement of the vibration displacement over time at that point on the target surface. Specifically, it measures the projection component of the vibration displacement vector along the direction of the incident laser beam on the object's surface. The vibrometer control unit receives the signal from the laser scanning probe, transmits it to a computer, records the vibration displacement of the bone specimen, and uses Fast Fourier Transform (FFT) to calculate and obtain the corresponding frequency spectrum in real-time.

Figure: Experimental Test System (a) Physical image of the experimental test system; (b) Specimen and lead wire fixing device

In this experiment, electrodes are coated on the two side surfaces (x-z plane) of the bone specimen. When voltage is applied, the bone specimen is polarized along its thickness direction (y-direction). It was experimentally observed that under an alternating voltage, the bone cantilever beam specimen vibrates both along its thickness direction (y-direction) and its width direction (x-direction). During actual testing, the laser beam is first aligned perpendicular to the side surface (x-z plane) of the bone specimen. This allows measurement of the vibration perpendicular to the measured surface, i.e., along the thickness direction (y-direction). Then, the specimen is rotated 90 degrees, and when the laser beam irradiates the y-z plane, the measured vibration is along the width direction (x-direction). During the test, the height of the laser incidence point on the specimen surface remains constant, with the measurement point  2 mm from the free end of the specimen.

Since the amplitude of the specimen is related to its natural frequency, it is necessary to know the natural frequency of the cantilever beam specimen during free vibration. When bone is considered a homogeneous, linearly elastic material, it can be calculated using the standard formula. When the specimen vibrates along the thickness direction, the moment of inertia I = bh³/12, and the calculated first and second-order natural frequencies are 44.03 Hz and 275.94 Hz, respectively. When the specimen vibrates along the width direction, the moment of inertia I = hb³/12, and the natural frequency is 1655 Hz. Using an impact method, an impulsive force was applied to the bone cantilever beam specimen to excite its free vibration along the thickness direction. The measured first and second-order natural frequencies were 49.22 Hz and 279.69 Hz, respectively, consistent with the theoretical calculations. All specimen dimensions, along with the measured natural frequency along the width direction, are listed together in the chart below.

Figure: Specimen Dimensions and Natural Frequencies Along the Thickness Direction (y-direction)

The specific tests were conducted according to the following steps: Adjust the signal generator and voltage amplifier to apply an AC voltage of fixed frequency and amplitude to the specimen. Record the frequency spectra of the specimen's vibration along the thickness (y) direction and width (x) direction under this voltage excitation. For measuring vibration along the thickness direction, the excitation voltage  frequency range was 0-500 Hz, with a step size of 10 Hz. For measuring vibration along the width direction, the excitation voltage frequency range was set to 0-5000 Hz, with a step size of 50 Hz. Near the natural frequency, the step size was appropriately reduced  to observe the variation of amplitude with frequency as precisely as possible.

Experimental Results:

Figure 4(a) shows the vibration frequency spectrum along the thickness direction for Specimen 2 when the excitation voltage frequency is 50 Hz. The spectrum contains both the 50 Hz component, its multiples (e.g., 100 Hz), and the specimen's natural frequency of 41 Hz. The observed frequency multiplication phenomenon here is a characteristic feature of typical nonlinear vibration . When the excitation voltage frequency approaches the first or second-order natural frequency of the beam, the amplitude reaches an extreme value, also known as superharmonic resonance . Figure 4(b) presents a composite frequency spectrum of the vibration along the thickness direction for Specimen 5 under multiple excitation frequencies. It can be seen that in the spectra for excitation frequencies of 35 Hz, 67.5 Hz, and 157.5 Hz, there are corresponding frequency multiplication components.

Figure 4(c) shows the vibration frequency spectrum along the width direction for Specimen 2 when the excitation voltage frequency is 1050 Hz. At 1050 Hz, the amplitude is approximately 270 nm, but no frequency multiplication, as seen in (a) and (b), is observed. Figure 4(d) presents the frequency spectra for Specimen 5 under multiple different frequency voltage excitations. The vibration spectra along the width direction contain only the component with the same frequency as the excitation voltage, with no frequency multiplication components, and can be considered линейное колебание   linear vibration .

Figure 4: Vibration Frequency Spectra of Specimen 2 and Specimen 5 Under Voltage Excitation at Arbitrary Frequencies

(a) Vibration along thickness direction for Specimen 2, excitation frequency 50 Hz; (b) Vibration along thickness direction for Specimen 5; (c) Vibration along width direction for Specimen 2, excitation frequency 1050 Hz; (d) Vibration along width direction for Specimen 5

To understand the influence of the excitation voltage amplitude on the vibration amplitude, we tested the effect of varying the voltage amplitude on the amplitude of the cantilever beam specimen while keeping the excitation voltage frequency constant. Figures 5(a) and 5(b) below show the relationship between amplitude and voltage amplitude for Specimen 3 vibrating along the thickness direction at a voltage frequency of 50 Hz and along the width direction at a voltage frequency of 1260 Hz, respectively. By adjusting the amplification factor to change the excitation voltage amplitude, it can be observed that when the excitation voltage frequency is constant, the amplitude of the bone specimen increases with increasing voltage. Fitting with a linear function, based on the obtained correlation coefficient R², it can be seen that the linearity for vibration along the thickness direction is slightly poorer (R² = 0.913), which is likely related to the frequency multiplication phenomenon. For vibration along the width direction, the linearity between amplitude and voltage amplitude is very good (R² = 0.9997).

Figure 5: Relationship Between Vibration Amplitude and Voltage Amplitude Along Thickness and Width Directions for Specimen 3

Aigtek ATA-2081 High-Voltage Amplifier:

Figure: ATA-2081 High-Voltage Amplifier Specifications and Parameters