Theory of Elasticity

adiabatic angle axes axis bending biharmonic equation boundary conditions centre clamped coefficient components constant corresponding cross-section crystal crystallite curvature deflection derivatives Determine the deformation displacement vector edge elastic wave element equations of equilibrium equations of motion expression external forces fluid force F formula free energy frequency function given gives grad div Hence hydrostatic compression integral internal stresses isotropic isotropic body k₁ length Let us consider longitudinal waves medium modulus non-zero perpendicular plane plate PROBLEM quadratic quantities radius region of contact respect result rotation satisfies shear shell small compared SOLUTION strain tensor stress tensor stretching Substituting suffixes symmetry temperature theory of elasticity thermal conduction thin torsion transverse waves undeformed unit volume values velocity of propagation vibrations wave vector x-axis xy-plane Young's modulus zero диг ду дх дхі дхк