the integrated analysis of vibrations of quartz crystal plates ‎through artificial coupling factors

We introduce smaller artificial factors into the elastic constants matrix and manage to make mindlin firstorder plate theoryequations of motions coupled for a uniform and integrated analysis. the energy distributions of the five coupled modes are obtained and all the five vibration modes are identified through the energy calculation. this analytical approach based on artificial couplings of vibration modes suggests that all vibration modes of structural components can be analyzed through the same procedure and computer code if the right elastic constants are modified and the mode identification can be done with the energy method. this is a new technique to study multimode vibrations of structures in a broad frequency range with just one procedure and calculation tool for simplification.