Yes. HIMARI and SORA can be used on a slatted bed frame or a solid platform if the surface is firm, level and stable, and the slats are close enough that the shikibuton cannot sag between them. A slatted base also lets moisture escape from underneath; a solid platform does not, so lift the shikibuton each morning.
Slatted frames
Flat, rigid slats set close together suit a shikibuton well. Widely spaced slats, or flexible curved slats designed for sprung mattresses, can let it dip between them; in that case, lay a thin rigid board or a roll-out slatted base over the frame first.
Solid platforms and storage beds
A solid platform gives even support but less airflow. Use a moisture-absorbing pad, and lift or fold the shikibuton regularly so the surface beneath can dry. Storage beds with closed boxes can trap damp, so air them as well.
On top of an existing mattress
A shikibuton is designed to lie on a firm surface. Laid over a soft sprung or foam mattress, it takes on that mattress’s give and will not feel as intended.
Checking the fit
HIMARI 日葵 is 210 cm long and SORA 宙 200 cm long, in Japanese widths of 100 to 140 cm. Frames are usually built for local mattress sizes, so measure the frame’s inside dimensions and make sure the whole shikibuton is supported, with no edge resting over an open gap.