Abstract: A system for detecting responses of a MEMS resonator device includes first and second signal sources, a signal divider and a frequency mixer. The first signal source provides a first signal and the second signal source provides a second signal that electrostatically drives the MEMS resonator device, causing mechanical vibration. The signal divider divides the first signal into a probe signal and a local oscillator (LO) signal, the probe signal being applied to the MEMS resonator device and reflected by a capacitance of the MEMS resonator device. A reflection coefficient is modulated onto the reflected probe signal at the mechanical resonance frequency by variations in the capacitance induced by the mechanical vibration of the MEMS resonator device. The frequency mixer mixes the reflected probe signal and the LO signal and outputs an intermediate frequency (IF) signal, which represents modulation of the reflection coefficient, providing an image of the mechanical vibration.

Abstract: During a measurement in KFM mode of the surface potential of a material (P), a detection point (1) is arranged above a surface (S) of the material. Two piezoelectric actuators (2, 5) are used to monitor a mean distance of the detection point relative to the surface of the material and a mechanical oscillation of said point. During the measurement, a control voltage is applied between control electrodes (2a, 2b) of the piezoelectric actuator (2) which is dedicated to the mechanical oscillation of the detection point (1), said control voltage not having an alternative component to an angular frequency of electrical energization of said detection point. A result of the KFM measurement is therefore separate from operating parameters such as a projection angle used to perform closed-loop control and a value of the angular frequency of electrical energization. The invention thus provides absolute measurements of surface potentials.

Abstract: A system for detecting responses of a MEMS resonator device includes first and second signal sources, a signal divider and a frequency mixer. The first signal source provides a first signal and the second signal source provides a second signal that electrostatically drives the MEMS resonator device, causing mechanical vibration. The signal divider divides the first signal into a probe signal and a local oscillator (LO) signal, the probe signal being applied to the MEMS resonator device and reflected by a capacitance of the MEMS resonator device. A reflection coefficient is modulated onto the reflected probe signal at the mechanical resonance frequency by variations in the capacitance induced by the mechanical vibration of the MEMS resonator device. The frequency mixer mixes the reflected probe signal and the LO signal and outputs an intermediate frequency (IF) signal, which represents modulation of the reflection coefficient, providing an image of the mechanical vibration.

Abstract: During a measurement in KFM mode of the surface potential of a material (P), a detection point (1) is arranged above a surface (S) of the material. Two piezoelectric actuators (2, 5) are used to monitor a mean distance of the detection point relative to the surface of the material and a mechanical oscillation of said point. During the measurement, a control voltage is applied between control electrodes (2a, 2b) of the piezoelectric actuator (2) which is dedicated to the mechanical oscillation of the detection point (1), said control voltage not having an alternative component to an angular frequency of electrical energisation of said detection point. A result of the KFM measurement is therefore separate from operating parameters such as a projection angle used to perform closed-loop control and a value of the angular frequency of electrical energisation. The invention thus provides absolute measurements of surface potentials.

Abstract: Pipes undergoing torsion stresses at one fixed extremity, the other extremity being flexibly supported, and in particular, exhaust pipes for motor vehicles. The concentration of stresses at the fixed end are eliminated and distributed in the center of the pipe by reinforcing its moment of inertia and its rigidity at the fixed extremity, and by creating a series of localized zones with a reduced moment of inertia in the center area, where the stresses undergone by the pipe at its fixed end are distributed in limited fashion. The invention is especially applicable to the exhaust pipes of internal combustion engines.