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The duality between the sensor equation and the equivalent piezoelectric loads is emphasized. The danger of using the oversimplified beam theory for predicting the transmission zeros of slender structures with collocated actuator and sensor is pointed out. 1). ) due to the motion. In the Laplace domain, where is the impedance of the coil. ; appears in the relationship between the coil is called the voice coil constant. f. appears as an additional damping in the system. ). 1. Above some critical frequency the proof-mass actuator behaves like an ideal force generator (constant amplitude, no phase difference).
Due to the motion. In the Laplace domain, where is the impedance of the coil. ; appears in the relationship between the coil is called the voice coil constant. f. appears as an additional damping in the system. ). 1. Above some critical frequency the proof-mass actuator behaves like an ideal force generator (constant amplitude, no phase difference). The resonance frequency (and therefore the critical frequency ) can be adapted by changing the mass Because the reaction mass is attached to the structure by a spring, the proof-mass actuator has no authority over the rigid body modes (in contrast to reaction wheels).
The orthogonality conditions are often written as where is the Kronecker delta index is the modal mass of mode Since the mode shapes can be scaled arbitrarily, it is usual to normalize them in such a way that If one defines the matrix of the mode shapes the orthogonality relationships read To demonstrate the orthogonality conditions, we have used the fact that the natural frequencies were distinct. If several modes have the same natural frequency (as often occurs in practice because of symmetry), they form a subspace of dimension equal to the multiplicity of the eigenvalue.