A mathematical electro-mechanical model of a representative fragment of a gas-analytical optical fiber piezoelectroluminescent sensor with a special external absorption layer for monitoring extended areas has been developed. Informative light signal is generated as a result of mechanoluminescent effect caused by contact interaction of piezoelectric and electroluminescent cylindrical layers (coatings) of fiber in case of forced electromechanical vibrations of sensor under action of applied harmonic control electric voltage. The algorithm for finding the sorption spectrum (changes in the density of the absorption layer along the length of the sensor) is presented through the solution of the Fredholm integral equation based on the results of measuring the informative light spectrum of the intensity of the light at the output from the fiber of the sensor. Numerical solution of coupled stationary boundary value problem of electroelasticity for representative fragment of sensor is implemented. Natural frequencies and shapes of sensor oscillations were found taking into account geometric shape, relative location and anisotropy of electroelastic properties of its structural elements, including characteristics of absorption layer. Regularities of influence of diagnosed value of absorption layer density on informative values of resonance frequencies of different forms of sensor oscillations were revealed.

An electro-mechanical model has been developed for the functioning of a tactile polymer coating with a built-in fiber optic piezoelectroluminescent (PEL) sensor and many villi (vibrisses) on the surface of the coating along the sensor. Local deformation of the coating and the built-in sensor is carried out in the disturbance zones, witch are local areas of the coating (sensor) near the points of cantilever fastening of the tufts at their contacts with the analyzed object. Mechanoluminescent effect occurs on deformed sections of sensor when electric field of section of its piezoelectric layer affects adjacent section of electroluminescent layer. Modeling and analysis of substantially inhomogeneous deformation and electric fields occurring in piezoelectric and electroluminescent layers of the sensor were carried out and characteristic forms of generated informative light signals for different cases of deformation of bending villi in different planes and torsion as a result of contact of villi ends with the surface of the analyzed object were revealed.

An electro-mechanical mathematical model of the functioning of an optical fiber resonance piezoelectroluminescent (RPEL) sensor with an external nonlinear elastic buffer layer has been developed. The sensor is designed to measure the distribution spectrum along the length of the dynamic and/or static pressure sensor using a resonant diagnostic method based on the results of measuring the amplitude spectrum of the intensity of the resulting light flux at the output from the fiber of the sensor. The numerical values of the frequency characteristics (- these are the proportionality coefficients for the informative relationship "pressure/resonance frequency") of the optical fiber RPEL sensor, which are used in the algorithm for finding the pressure spectrum, for different (first six) modes of vibration, are determined.