Method and apparatus for increasing spring rate of linear springs

A method of counteracting a forward overturning moment in an airfoil of a ceramic matrix composite (CMC) vane, comprising:

• preparing a constrained linear spring by:
• providing a linear spring element formed of resilient material, the linear spring element having a first end and extending in a first direction to a second end, and including one or more undulations extending in a second direction transverse to the first direction, wherein the linear spring element has a first spring rate when compressed in the second direction with the first and second ends unconstrained;
• and
• constraining the linear spring element with a constraining element dimensioned to contact the first and second ends and a least one undulation of the linear spring element when the linear sprint element is uncompressed, wherein the constrained linear spring element of the linear spring has a second spring rate higher than the first spring rate when compressed in the second direction;
• applying the linear spring to provide a force between a support surface and at least one of a lower forward portion of an inner vane platform adjacent a leading edge of the airfoil and an upper rear portion of an outer vane platform adjacent a trailing edge of the airfoil to counteract the forward overturning moment in the airfoil.